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1. Registration: 9 – 9:30 am

(College of Business Courtyard)

2. Introduction & Schedule of Events: 9:30 – 9:45 am

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3. Industry Panel: 9:45-11:15 am

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4. Breakout Sessions I: 11:15-12:15 pm

How LLMs Transformed My Data Science Workflow—And How They’ll Change Yours (COB-236)

Chatbots: Your AI-Powered Data Assistant (COB-237A)

Bayesian Sports Analytics: Learning from Data, One Free Throw at a Time (COB- 237B)

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8. Concluding Remarks and prize drawing (2:15pm-2:30pm, COB-140)

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Andrew is an MS Applied Statistics graduate currently working on his PhD at UC Santa Cruz.

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GitHub - dantonnoriega/csulb-data-day-2025: Collection of materials for CSULB Data Day 2025 Breakout Session

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Collection of materials for CSULB Data Day 2025 Breakout Session - dantonnoriega/csulb-data-day-2025

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This project aims to inspire both students and data science enthusiasts to undertake their own projects, with the aspiration that through continued practice, they'll gain a deeper appreciation for the boundless creativity and narrative potential inherent in data and visualizations.

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Music Repo for sentiment analysis configuration. Contribute to dsrichard97/csulbdataday24M development by creating an account on GitHub.

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Juan Apitz, MS - CSULB Institutional Research and Analytics

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Juan Apitz, MS - CSULB Institutional Research and Analytics

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Dive into repositories focused on data visualization libraries and projects. Collaborate and contribute to the growing field.

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Prompt Engineering for Chat GPT free Coursera course

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ChatGPT and other large language models are going to be more important in your life and business than your smartphone, if you use them right. ChatGPT can tutor your child in math, generate a meal plan and recipes, write software applications for your business, help you improve your personal cybersecurity, and that is just in the first hour that you use it. This course will teach you how to be an expert user of these generative AI tools. The course will show amazing examples of how you can tap into these generative AI tools' emergent intelligence and reasoning, how you can use them to be more productive day to day, and give you insight into how they work.

Large language models respond to instructions and questions posed by users in natural language statements, known as "prompts". Although large language models will disrupt many fields, most users lack the skills to write effective prompts. Expert users, who understand how to write good prompts, are orders of magnitude more productive and can unlock significantly more creative uses for these tools. This course introduces students to the patterns and approaches for writing effective prompts for large language models. Anyone can take the course and the only required knowledge is basic computer usage skills, such as using a browser and accessing ChatGPT. Students will start with basic prompts and build towards writing sophisticated prompts to solve problems in any domain. By the end of the course, students will have strong prompt engineering skills and be capable of using large language models for a wide range of tasks in their job, business, personal life, and education, such as writing, summarization, game play, planning, simulation, and programming.

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Offered by Vanderbilt University. ChatGPT and other large language models are going to be more important in your life and business than your ... Enroll for free.

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Cylurian is a repository of mathematical videos. These videos are intended to expand your conceptual understanding of the material. These videos will help you understand the applied nature of Mathematics by learning it step-by-step.

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Jessica Valencia Alvarado, MS - American Institutes for Research

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Jessica Valencia Alvarado, MS - American Institutes for Research

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LinkedIn Profile: https://www.linkedin.com/in/jessica-valencia-alvarado/

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"Data helps us make better decisions and it uncovers stories waiting to be told."

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Introduction

Fútbol has been an integral part of my journey from the first time I stepped onto the field. The thrill of playing as a left winger, the strategy behind every move, and the joy of scoring have deeply influenced my understanding and love for the sport. This passion has seamlessly intertwined with my growing interest in analytics, leading me to explore the untapped potential of data in revealing hidden aspects of the game, such as player dynamics, strategic patterns, and performance metrics.

Liga MX is more than just a league to me; it's a big part of Mexican culture. The Apertura and Clausura tournaments show the excitement and spirit of Mexican soccer, bringing stories of victory and defeat that engage fans every year.

In this study, I'll concentrate on the key players in defense: the center-backs. Their role, often overshadowed by the flamboyance of attackers, is crucial in orchestrating the team's defensive harmony. Leveraging unsupervised machine learning techniques such as Principal Component Analysis (PCA), K-means clustering, and Hierarchical Clustering, I aim to dissect and categorize the playing styles of these pivotal figures. Each technique serves a purpose: PCA to reduce dimensionality and highlight important performance indicators, K-means to group similar player profiles based on these indicators, and Hierarchical Clustering to build a detailed taxonomy of player types based on their on-field behavior.

This study is more than just research; it's an exploration into Liga MX using data analytics. By applying these unsupervised learning methods, we will uncover the nuanced contributions of center-backs, offering new insights and appreciation for their role in the beautiful game. Join me in this analytical journey, where numbers meet the pitch, and discover the unseen stories of Liga MX's defensive performances.

Data

For this research, I utilized a package tool called worldfootballr, which is designed to pull global football (soccer) data from platforms like FBref, Transfermarkt, Understat, and FotMob. This tool helped me gather advanced statistics provided by Opta, which were then formatted into a CSV file capturing player performances throughout the Clausura 2024 regular season. Initially, the dataset comprised 2,428 entries across 47 different columns. In the process of refining this dataset, I removed information irrelevant to our specific analysis. This process also involved using a histogram shown in Figure 1 of each player's total minutes to distinguish those who had accumulated at least 120 minutes of playtime from the start of the season until matchday 9.

After these adjustments, the final dataset presented 57 unique center-back players alongside 15 variable features. Each record within this dataset corresponds to an individual player, encompassing important performance data from the season, such as the number of tackles made, tackles within the defensive third, and instances of lost challenges. Below in Table 1 are the first 6 observations:

Below in Table 2 are the description of each variable used for the analysis:

Variables

Description

Tkl_Tackles

Number of players tackled

TklW_Tackles

Tackles in which the tackler's team won possession of the ball

Def 3rd_Tackles

Tackles in defensive 1/3

Mid 3rd_Tackles

Tackles in middle 1/3

Att 3rd_Tackles

Tackles in attacking 1/3

Tkl_Challenges

Number of dribblers tackled

Att_Challenges

Number of unsuccessful challenges plus number of dribblers tackled

Lost_Challenges

Number of unsucessful attempts to challenge a dribbling player

Blocks_Blocks

Number of times blocking the ball by standing in its path

Sh_Blocks

Number of times blocking a shot by standing in its path

Pass_Blocks

Number of times blocking a pass by standing in its path

Int

Interceptions

Tkl+Int

Number of players tackled plus number of interceptions

Clr

Clearances

Err

Mistakes leading to an opponent's shot

Principal Component Analysis (PCA)

Principal component analysis aims to describe the variance-covariance relationship among a group of variables by using a small number of linear combinations of these variables. The primary goals are to reduce the dimensionality of the data and to provide an interpretation through the rotation process.

Algebraically, principal components are unique linear combinations of the p random variables \(X_1,X_2,\ldots,X_p\). Geometrically, this translates to forming a new set of axes through the rotation of the original coordinate system, where \(X_1,X_2,\ldots,X_p\) are the axes. These newly established axes stand for the most significant variation directions, simplifying and condensing the description of the covariance matrix.

Let the random vector \(X' = [X_1,X_2,\dots,X_p]\) have the covariance matrix \(\Sigma\) with eigenvalues \(\lambda_1 \geq \lambda_2 \geq \ldots \geq \lambda_p = 0\).

Consider the linear combinations \[\begin{align*} Y_1 &= \boldsymbol{a'_1X} = a_{11}X_1 + a_{12}X_2 +\ldots+ a_{1p}X_p \\ Y_2 &= \boldsymbol{a'_2X} = a_{21}X_1 + a_{22}X_2 +\ldots+ a_{2p}X_p \\ &\vdots\\ Y_p &= \boldsymbol{a'_pX} = a_{p1}X_1 + a_{p2}X_2 +\ldots+ a_{pp}X_p \end{align*}\]

Then, we obtain \[\begin{align*} \text{Var}(Y_i) &= \boldsymbol{a'_i\Sigma a_i} \qquad &i = 1,2,...,p \\ \text{Cov}(Y_i,Y_k) &= \boldsymbol{a'_i\Sigma a_k} \qquad &i,k = 1,2,\ldots,p \end{align*}\]

The principal components are distinct linear combinations formed from the original variables, designed to be independent of each other.

The first principal component is the linear combination with maximum variance. That is, it maximizes \(\text{Var}(Y_1) = \boldsymbol{a'_i\Sigma a_i}\). It is clear that \(\text{Var}(Y_1) = \boldsymbol{a'_i\Sigma a_i}\) can be increased by multiplying any \(\boldsymbol{a_1}\) by some constant. To eliminate this indeterminacy, it is convenient to restrict attention to coefficient vectors of unit length. We therefore define
\[\begin{align*} \text{First principal component} =\ &\text{linear combination}\ \boldsymbol{a'_1X}\ \text{that maximizes} \\ &\text{Var}(\boldsymbol{a'_1X})\ \text{subject to a}\ \boldsymbol{a'_1a_1} = 1 \end{align*}\] \[\begin{align*} \text{Second principal component} =\ &\text{linear combination}\ \boldsymbol{a'_2X}\ \text{that maximizes} \\ &\text{Var}(\boldsymbol{a'_2X})\ \text{subject to a}\ \boldsymbol{a'_2a_2} = 1\ \text{and} \\ &\text{Cov}(\boldsymbol{a'_1X,a'_2X}) = 0 \end{align*}\]
At the \(i\)th step, \[\begin{align*} i\text{th principal component} =\ &\text{linear combination}\ \boldsymbol{a'_iX}\ \text{that maximizes} \\ &\text{Var}(\boldsymbol{a'_iX})\ \text{subject to a}\ \boldsymbol{a'_ia_i} = 1\ \text{and} \\ &\text{Cov}(\boldsymbol{a'_iX,a'_kX}) = 0\ \text{for}\ k < i \end{align*}\]

Initially, the data is scaled to normalize the scale of each variable. This ensures that all variables contribute equally to the analysis. This standardization process is crucial and is mathematically represented as,
\[\begin{align*} Z_1 &= \frac{(X_1 - \mu_1)}{\sqrt{\sigma_{11}}} \\ Z_2 &= \frac{(X_2 - \mu_2)}{\sqrt{\sigma_{22}}} \\ &\vdots\\ Z_p &= \frac{(X_p - \mu_p)}{\sqrt{\sigma_{pp}}} \end{align*}\]
In matrix form, \[\begin{align*} \boldsymbol{Z} = (\boldsymbol{V}^{1/2})^{-1}(\boldsymbol{X} - \boldsymbol{\mu}) \end{align*}\]

where the diagonal standard deviation matrix is \(\boldsymbol{V}^{1/2}\).

After standardizing the data, we compute its covariance matrix to examine the relationships among the variables, which is mathematically represented as:
\[\begin{align*} \text{Cov}(\boldsymbol{Z}) = (\boldsymbol{V}^{1/2})^{-1}\boldsymbol{\Sigma}(\boldsymbol{V}^{1/2})^{-1} = \boldsymbol{\rho} \end{align*}\]
In this formula, \(\boldsymbol{\rho}\) denotes the correlation matrix of the original variables \(\boldsymbol{X}\), after transformation into the standardized form \(\boldsymbol{Z}\). This step is crucial for understanding how variables relate to one another in the scaled space. Following this, we determine the eigenvalues and eigenvectors from this correlation matrix, \(\boldsymbol{\rho}\). The eigenvalues quantify the amount of variance each principal component captures, while the eigenvectors specify the directional orientation of these components, providing insight into the underlying structure of the data.

The standardized data is shown below in Table 3:

In our analysis, we specifically focus on the loadings of the first two principal components. These loadings reflect how each original variable contributes to the formation of the principal components. By analyzing the loadings of the first two components, we gain insights into the most significant patterns and variations within the data.

The mathematical approach of the \(i\)th principal component of the standardized variables \(\boldsymbol{Z}' = [Z_1,Z_2,\ldots,Z_p]\) with \(\text{Cov}(\boldsymbol{Z}) = \boldsymbol{\rho}\) is represented as:
\[\begin{align*} \boldsymbol{Y_i}' = \boldsymbol{{e_i{Z}}} = \boldsymbol{e'_{i}}(\boldsymbol{V}^{1/2})^{-1}(\boldsymbol{X}-\boldsymbol{\mu}), \qquad i = 1,2,\ldots,p \end{align*}\]
The loadings for the first and second principal components, denoted as PC1 and PC2 respectively, are presented below in Table 4:

Code

cov_df <- cov(scaled_df) eigen_df <- eigen(cov_df) phi <- eigen_df$vectors[,1 : 2] row.names(phi) <- colnames(clean_df) colnames(phi) <- c("PC 1", "PC 2") phi %>% knitr:: kable(digits = 2)

The total variance for the standardized variables in the population is equal to \(p\), which represents the sum of the diagonal elements of the matrix, also known as the trace of the correlation matrix \(\boldsymbol{\rho}\). Consequently, the fraction of the total variance accounted for by the \(k\)th principal component of \(\boldsymbol{Z}\) is determined as follows:

\[ \begin{pmatrix} \text{Proportion of (standardized)}\\ \text{population variance due}\\ \text{to}\ k\text{th principal component} \end{pmatrix} = \frac{\lambda_k}{p}, \qquad k = 1,2,\ldots,p \] where the \(\lambda_k's\) are the eigenvalues of \(\boldsymbol{\rho}\).

The Proportion of Variance for each Principal Component (PC) is presented below in Table 5:

Code

sum_cov <- sum(diag(cov(scaled_df))) results <- eigen_df$values/sum_cov prop_var <- tibble( principal_components = paste0("PC ", 1 : 15), results = results ) prop_var %>% gt() %>% cols_label( principal_components = md("**Principal Components**"), results = md("**Results**") ) %>% fmt_number( columns = results, decimals = 2 ) %>% opt_table_font( google_font(name = "Roboto") ) %>% tab_options(data_row.padding = px(1))

Principal Components

Results

PC 1

0.43

PC 2

0.13

PC 3

0.10

PC 4

0.08

PC 5

0.07

PC 6

0.07

PC 7

0.05

PC 8

0.03

PC 9

0.02

PC 10

0.02

PC 11

0.01

PC 12

0.00

PC 13

0.00

PC 14

0.00

PC 15

0.00

Now, the proportion of total variance explained by the first and second principal components is calculated as the sum of the first eigenvalue divided by the total variance plus the second eigenvalue divided by the total variance, represented as:
\[\begin{align*} (\frac{\lambda_{1} + \lambda_{2}}{p})100\% = (\frac{6.376 + 1.960}{15})100\% = 55.6\% \end{align*}\]
of the total (standardized) variance, have interesting interpretations.

Code

total_prop_var <- (eigen_df$values[1] + eigen_df$values[2]) / sum_cov print(paste0("Total variance explained by PC1 and PC2: ", round(total_prop_var, 4) * 100, "%"))

[1] "Total variance explained by PC1 and PC2: 55.58%"

The PCA scores for each player, as shown below in Table 6, represent the coordinates of each player in the space defined by the first two principal components (PC1 and PC2). These scores are calculated based on the original data transformed by the respective principal component loadings.

Player

Team

PC1

PC2

Scores For Each Player

Figure 2 indicates the presence of two outliers, specifically players Guido Pizarro from Tigres UANL and Andres Micolta Arroyo from CF Pachuca. We will examine the impact of these outliers on the clustering process in subsequent steps.

Principal Component Analysis with prcomp Function

R offers an easy method for data analysis with its builtin prcomp function, used for Principal Component Analysis. If you set scale = TRUE, it standardizes the data automatically. This function provides principal components and their impact on variance. The summary given by the function shows detailed variance information for each component, making it easier to understand and reduce complex data.

Code

pca_df <- prcomp(clean_df, scale = TRUE) summary(pca_df)

Importance of components: PC1 PC2 PC3 PC4 PC5 PC6 PC7 Standard deviation 2.5251 1.4001 1.19456 1.08645 1.04146 1.0188 0.84045 Proportion of Variance 0.4251 0.1307 0.09513 0.07869 0.07231 0.0692 0.04709 Cumulative Proportion 0.4251 0.5558 0.65090 0.72959 0.80190 0.8711 0.91819 PC8 PC9 PC10 PC11 PC12 PC13 Standard deviation 0.69325 0.57368 0.53408 0.36360 0.00566 0.005024 Proportion of Variance 0.03204 0.02194 0.01902 0.00881 0.00000 0.000000 Cumulative Proportion 0.95022 0.97217 0.99118 0.99999 1.00000 1.000000 PC14 PC15 Standard deviation 0.003521 0.002493 Proportion of Variance 0.000000 0.000000 Cumulative Proportion 1.000000 1.000000

The summary indicates that the initial principal components, particularly PC1 and PC2, play significant roles in capturing the dataset's variance, with PC1 alone accounting for 42.51% and PC2 adding another 13.07%. This showcases their importance in representing the dataset's structure. As more components are added, the cumulative variance explained increases, reaching virtually 100% by PC12, which suggests that the components beyond this point have minimal impact on explaining additional variance. That means that when \(\rho\) is near 1, the last \(\rho - 1\) components collectively contribute very little to the total variance and can often be neglected. Therefore, focusing on the first few components is essential for effective dimensionality reduction and dataset interpretation, while the latter components can generally be omitted from further analysis.

The scree plot in Figure 3 above is a useful visual aid to determining an appropriate number of principal components. The first principal component explain 42.51% of the total variance. The first two principal components, collectively, explain 55.58% of the total variance. An elbow occurs at about \(i = 3\). That is, the eigenvalues after \(\lambda_2\) are all relatively small and about the same size. In this case, it appears, without any other evidence, that two sample principal components effectively summarize the total variance of the data.

Contributions of variables to PCs

The key variables, which contribute most significantly, can be emphasized in the correlation plot as follows:

All the variables grouped together Figure 4, such as Tkl+Int, Def_3rd_Tackles, Tkl_Tackles, Att_3rd_Tackles, TklW_Tackles, Tkl_Challenges, Mid_3rd_Tackles, Att_Challenges, and Lost_Challenges are positively correlated with each other. This positive correlation is due to their proximity to each other and their downward direction. Conversely, Sh_Blocks, Blocks_Blocks, and Clr are grouped together and show a positive correlation, as their vectors point upwards. This indicates that these two sets of variables move in opposite directions, meaning they are negatively correlated. Negatively correlated variables are positioned on opposite sides of the plot's origin, in opposed quadrants. The distance between variables and the origin measures how well the variables are represented on the factor map; those further from the origin are better represented.

This bar plot displays the contributions of various variables to PC1 (dim1) on the left and to PC2 (dim2) on the right. The red dashed line across the graph represents the expected average contribution for each dimension.

Biplot

In the biplot, individual player scores are plotted alongside variables, allowing for a comprehensive visual representation of their performances in relation to the different measured factors.

In this biplot analysis plot from Figure 5, it's crucial to understand that a player's position relative to a specific variable indicates their performance in that area. Players on the same side as a variable typically exhibit high values for that trait, while those on the opposite side represent lower values. For instance, several players located in the third quadrant, where most Dim1 contributing variables are present, demonstrate significant defensive actions. Sebastian Olmedo from Club Puebla, notable for his high Dim1 representation, exemplifies a player actively involved in defense. Similarly, players like Arturo Ortiz, who are positioned close to Olmedo, share these defensive characteristics, forming a group identified as traditional old-school defenders.

Conversely, in the second quadrant, opposite the traditional defenders, we find variables negatively correlated with defensive actions, such as Blocks_Blocks, Sh_Blocks, and Clr. Santiago Nunez of Santos Laguna stands out here as a "stopper," excelling in blocking, indicative of a different defensive skill set.

Additionally, outliers like Andres Micolta Arroyo from C.F. Pachuca and Guido Pizarro from Tigres UANL are positioned apart from clusters, suggesting unique styles of play that, while distinct, significantly impact the game by contributing to key variables.

Lastly, there's a distinct group known as Att.3rd_tackles players, including Diego de Buen from Club Puebla and Ventura Alvarado from Mazatlan F.C. These individuals specialize in stopping counter-attacks and play a crucial role during 'el balón parado' situations, as they call it in Spanish, which refers to set pieces or moments when the ball is stationary. Their positioning in the biplot underscores their expertise in initiating defensive maneuvers during these pivotal moments of the game.

Non-Hierarchical Clustering

K-Means Clustering

Following the PCA analysis, we will now proceed with K-means clustering to further explore our dataset. This method will allow us to categorize the data into distinct groups based on similarities identified during the PCA. By applying K-means clustering, we aim to enhance our understanding of the underlying structures and relationships within the data, facilitating more targeted interpretations and insights. This step is crucial in identifying natural groupings among players or variables, leading to more nuanced conclusions and strategic decisions.

A Focus on Euclidean Distance: An essential step in K-means clustering involves discussing the dissimilarity or distance measurement within the data. In our analysis, we opt for the Euclidean distance, which is the standard method for K-means and measures the straight-line distance between points in multidimensional space. This choice is due to its simplicity and effectiveness in quantifying the dissimilarity between data points. By utilizing Euclidean distance, we can ensure that the clusters formed are based on the actual spatial differences among data points, making it a suitable and intuitive approach for our clustering objectives.

The Euclidean distance between two p-dimensional points is given by the formula:

\[ d(x, y) = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + \cdots + (x_p - y_p)^2} = \sqrt{(x - y)'(x - y)} \]

K-Means Clustering: the process is composed of these three steps:

1. Partition the items into \(K\) initial clusters.

2. Proceed through the list of items, assigning an item to the cluster whose centroid (mean) is nearest. (Distance is usually computed using Euclidean distance with either standardized or standardized.) Recalculate the centroid for the cluster receiving the new item and for the cluster losing the item.

3. Repeat Step 2 until no more reassignments take place. In practice, such as in R, this process might begin with a default of 10 iterations to ensure stability and convergence of clusters.

To determine the optimal number of clusters (k) in our analysis, we employed two methods: the Within-Sum-of-Squares (WSS) and the Gap Statistic. The WSS method helps identify the elbow point where the addition of another cluster does not significantly improve the total variance within clusters. Meanwhile, the Gap Statistic compares the log-wss of our dataset against expected values under a null reference distribution of the data, providing a more robust estimation of the optimal k.

Based on the analysis plot from Figure 6 of the Total Within Sum of Square and the Gap Statistic plots, the optimal number of clusters for the data is recommended to be three. The Elbow Method suggests a bend at three or four clusters, while the Gap Statistic clearly peaks and maximizes at three clusters, indicating the most suitable partitioning of the data.

After identifying the optimal number of clusters as three through both the Elbow Method and the Gap Statistic, we proceed with the segmentation of the dataset to uncover distinct groupings and patterns. This allows us to visualize and analyze the inherent structures and relationships within our data.

Light Green Cluster (Circle): "Defensores tradicionales"

Players in this cluster, like Sebastian Olmedo and Arturo Ortiz, exhibit strong defensive capabilities, as evidenced by the cluster's alignment with key defensive actions such as tackles, interceptions, and blocks. This group is indicative of players who excel in defensive duties, demonstrating a high degree of proficiency in preventing opposition attacks. The outliers "Andres Micolta Arroyo" and "Guido Pizarro" may represent players with unique defensive styles or roles that differ from the standard defensive metrics, warranting closer examination.

Red-Orange Cluster (Triangle): "Defendores diferentes"

This cluster features players such as Carlos Salcedo, who are typically positioned further to the right, suggesting a distinct playing style. These individuals may have fewer minutes on the pitch or adopt a defensive approach that doesn't primarily focus on tackles, interceptions, and blocks. An example within this category is Hector Moreno of Monterrey, who exemplifies a style that balances traditional defensive duties with advanced playmaking and ball distribution skills. The outlier "Unai Bilbao" suggests a player who might either excel exceptionally in these areas or possess a unique set of skills differing from the main group.

Purple Cluster (Square): "Defensores Versátiles"

This group, featuring Diego De Buen and Erik Lira, showcases versatility, balancing defensive responsibilities and some with the ability to support midfield and forward play, indicative of a modern, flexible center-back. This adaptability makes them valuable for strategies requiring defensive solidity and midfield support.

Agglomerative Hierarchical Clustering

Agglomerative Hierarchical Clustering is a popular method used in data analysis to group objects into clusters based on their similarities. Starting with each object in its own cluster, it iteratively combines the closest pairs into larger clusters until all objects are in a single group or a stopping criterion is met. This bottom-up approach produces a dendrogram, a tree-like diagram that illustrates the series of merges and the hierarchical structure of the clusters.

Applied the Ward.D2 approach, a specific type of Agglomerative Hierarchical Clustering, our main goal here is to reduce the sum of squared differences, also known as the 'loss of information,' across all clusters. This reduction relies on calculating the squared Euclidean distances among the points in our dataset, a method that aligns with Ward's strategy to decrease the total variance within each cluster continuously. This technique results in clusters that are more evenly distributed and meaningful, facilitating a better interpretation of the dataset's intrinsic structure since it generally forms clusters that are comparable in size.

The resulting dendrogram, illustrated below in Figure 8, visualizes the hierarchical structure and the process of cluster formation. It provides insights into the data's underlying patterns and relationships by showing how individual observations are grouped into clusters based on their similarities and how these clusters are combined into larger clusters as we move up the hierarchy.

Observations:

1. The light green cluster at the bottom includes players such as Sebastian Olmedo and Arturo Ortiz, indicating a group likely characterized by traditional defensive skills.

2. The purple cluster at the top, with players like Jesús Orozco and Igor Lichnovsky, suggesting these may be more versatile defenders who contribute both defensively and in initiating play, possibly indicating a balance between defensive robustness and ability to support midfield or offensive actions.

3. The red-orange cluster in the middle features players like Hector Moreno and Diego Reyes, could represent those who are perhaps less involved in direct defensive actions maybe because they spend less time on the pitch, but might play roles in ball distribution or possess other unique attributes distinguishing them from the purely defensive or hybrid players.

Conclusion

It is clear that different players fulfill their essential roles as center-back defenders. The art of defending, often overshadowed by the allure of goals and assists, remains the cornerstone of every successful football team. No team can dominate their league or excel in individual competitions without a strong defensive line. Employing machine learning classification methods, including PCA, non-hierarchical k-means, and hierarchical clustering, holds profound significance in sports analytics, particularly in identifying similarities among players based on their defensive traits. This approach can significantly aid teams in making informed decisions, especially during the transfer window, by identifying the ideal replacements that fit a specific defensive role, thereby enhancing team performance.

However, it is crucial to acknowledge significant limitations. For instance, there are skilled center-backs returning from injuries who have played minimally this season, which may influence their current performance levels as they regain their form. Additionally, some teams may experience a poor start to the season but later find themselves on a winning streak. The distinction between home and away games can also significantly impact player performance, with the venue potentially playing a crucial role in each match's outcome. Furthermore, matches against top-tier teams in the tournament can demand more from a player defensively, contrasting with games against weaker teams where the defensive workload might be substantially less.

Future enhancements for this project should consider several factors. Initially, the data was collected from the beginning of the tournament, from matchday 1 to matchday 9, which only represents the mid-point of the season. Since each season (Apertura and Clausura) comprises 17 matchdays, a more precise model could be developed with information spanning the entire season. Additionally, incorporating data on full-backs, who also play defensive roles, could alter the classification narrative of players significantly. Lastly, enriching the dataset with additional metrics such as possession and aerial duels could further refine the differentiation of player types in defensive positioning.

Acknowledgments

I would like to express my sincere gratitude to the faculty members who guided me through my graduate studies in Applied Statistics at the Department of Mathematics and Statistics, California State University - Long Beach. Special acknowledgments to Dr. Sung Kim, Dr. Kagba Suaray, Dr. Olga Korosteleva, Dr. Rebecca Le, and Dr. Hojin Moon for their invaluable mentorship and support during my academic journey.

References

Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis. Prentice Hall.

Nadir, N. (2021, September 21). Assessing NBA Player Similarity with Machine Learning. Medium, Towards Data Science. https://towardsdatascience.com/which-nba-players-are-most-similar-machine-learning-provides-the-answers-r-project-b903f9b2fe1f.

OUKHOUYA, H. (2023, April 2). NBA Player Performance Analysis: PCA, Hierarchical Clustering, and K-Means Clustering. RPubs. https://rpubs.com/HassanOUKHOUYA/NBA_Player_Performance_Analysis_PCA_Hierarchical_Clustering_and_K_Means_Clustering.

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Machine Learning Classification of Center-Back Player Types in Liga MX

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Explore the similarities among center-back players in Liga MX using various machine learning and clustering methods including PCA, K-means (non-hierarchical), and Agglomerative Hierarchical Clustering

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About the Funder: HSI Equity Innovation Hub

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About the Funder: HSI Equity Innovation Hub

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https://linktr.ee/HSIEquityInnovationHub

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LinkedIn Profile: https://www.linkedin.com/in/dantonnoriega/overlay/background-image/

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"I think the future will be dependent on speed to information as we see preliminaries with NVIDIA and so it is ever more important to race at the speed of light to consume information in order to stay ahead of the curve."

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M.S. Applied Statistics @ CSULB | Strong background in Statistical Analysis. - dsrichard97

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Richard DiazDeleon: Guide to Land an Internship

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Richard DiazDeleon: Guide to Land an Internship

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In 2019, I was wrapping up my undergraduate studies in Applied Math at California State University Fullerton amidst the onset of the pandemic, a period marked by widespread closures and escalating anxieties. Like many on the cusp of graduation, the impending transition into the professional realm loomed large and daunting. The collegiate environment, for all its merits, often falls short in bridging the gap between academic pursuits and the pragmatic steps toward landing a desired position in a chosen field or industry.

Now, as I near the completion of my graduate degree in Applied Statistics at California State University Long Beach, the journey has been enriched with hands-on experience garnered through a data science internship alongside my academic endeavors. A prevailing myth suggests a dichotomy where data and mathematics are relegated to abstract realms, estranged from real-world applicability. However, this notion dismisses the profound impact that a solid grasp of data and mathematical principles can wield in solving tangible business challenges. The blend of business acumen and mathematical prowess can be a potent formula in navigating the intricate landscape of modern industries.

As I delineate this three-step process, my aspiration is to present a fresh framework that might alleviate a pervasive dilemma: the quest for meaningful employment post-graduation. Through this lens, I hope to dispel some of the uncertainties that beleaguer many graduates, and foster a clearer pathway toward integrating effectively into the industry of choice.

Networking: Reflect on your existing professional and academic connections. Who in your network could provide insights or opportunities in your desired field?

Knowledge Inventory: Assess your current skill set and knowledge base. What are your strengths and how do they align with your career aspirations?

Learning Opportunities: Identify areas for growth and consider additional training or education that could bolster your marketability.

2. Unique Value Proposition

Distinctive Qualities: Reflect on your unique attributes and experiences that set you apart from others. How do your distinctive qualities align with the needs of your desired industry?

Long-term Impact: Consider actions that, though may require a modest initial effort, promise a significant positive impact over time. How can you strategize to ensure your actions today serve your long-term professional objectives?

3. Industry Awareness

Industry Challenges: Research and understand prevalent issues within your desired industry. How might your skill set contribute to addressing these challenges?

Market Dynamics: Evaluate how current market conditions are affecting key players in your industry, and how these conditions might influence the availability and nature of opportunities in your targeted position.

Future Projections: Analyze the industry's trajectory. Is it on a growth curve or facing resistance? Understanding the macro trends can help in making informed decisions and in tailoring your approach to align with the industry's evolving demands.

LinkedIn Photo: https://www.linkedin.com/pulse/bell-curve-prateek-ravi/

I think building a skill is rather easier but knowing when to apply that skill within the business domain is something that has to be learned through coworkers or working within industry. Different industries move different within there time-domain and you must be up to date to that knowledge or if not better. I think graduates or undergraduates must not only be life-long learners but be keen to rapid changes within that current domain. To be more sucessful at aquiring a relevant position. It not good anymore to just know "enough" but rather move at the speed that AI and machine learning is driving us. Be at the frontier of knowledge, industry, and pivoting oneself to try to solve current problems that probably manager, leaders, and coworkers face.

1. What are your current skills? Deep Work by Cal Newport

2. How have you deviated from the norm? Can't Hurt Me by David Goggins

3. Have you done your homework within the industry? Elon Musk Youtube Interview

Books and Video Guidance for the [3 steps]

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How to Land a Data Science & Data Analyst Internship [3 Step Guide]

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In 2019, I was wrapping up my undergraduate studies in Applied Math at California State University Fullerton amidst the onset of the pandemic, a period marked by widespread closures and escalating...

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https://www.linkedin.com/in/antonio-martinez-194138251/

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https://sites.csulb.edu/quest/2023/supporting-stem-and-graduate-studies/

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COMMENTARY: Data Science helps students of color opt in for more math

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UC's decision to rescind high school courses in that area as satisfying a requirement for college admission is a mistake.

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Instructional Technology Instructional Leadership School Site Leadership Career-Technical Education Magnet Coordination Advancement & Enrichment Prog

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Technology Integration Social Media Policy Teacher Leadership WASC Accreditation Teaching & Learning Distributed Leadership Grantswriting New Teacher Mentoring Education Administration

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Dr. Dev has been impacting education for nearly 20 years. She is engaged in a deep and long-term exploration of the application of the tenets, tools, and methods towards performance improvement...

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Read what Dr. Rodgers has published in STEM+C

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Read what Dr. Rodgers has published in STEM+C

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Technology Leadership for Pandemic STEMgagement in Computer Science: A PK12 Case Study

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In this post-pandemic hybrid world of PK12 education, the onus is still on education leaders to close achievement gaps through equitable means. There are current socioeconomic, racial, gender, and geographical disparities that limit students’ full access to computer science education (CS). This case study reports how one urban PK12 school district in the United States is addressing the “leaky pipeline” with sustainable solutions for CS education with minoritized students. Using an online engagement framework, an ethnographic lens was used with document review, to conduct a content analysis of projects, programs, and services set up through the central office for nearly 20,000 students at the primary, middle grades, and secondary levels in computer sciences. Findings acknowledge leadership’s planning for student engagement in STEM+C (science, technology, engineering, math and computer science) for virtual instruction. This study will contribute to the burgeoning knowledge of leadership for CS activities in PK12, and serve as a beacon for learning organizations bolstering CS activities in the future.

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Decolonizing STEM+C: Informal community organizations impacting the computer science pipeline with Black female talent

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Read what Dr. Rodgers has published in STEM+C

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Read what Dr. Rodgers has published in STEM+C

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This documentary investigates the bias in algorithms after M.I.T. Media Lab researcher Joy Buolamwini uncovered flaws in facial recognition technology. Watch trailers & learn more.

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Unmasking AI: My Mission to Protect What Is Human in a World of Machines

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Unmasking AI: My Mission to Protect What Is Human in a World of Machines [Buolamwini, Joy] on Amazon.com. *FREE* shipping on qualifying offers. Unmasking AI: My Mission to Protect What Is Human in a World of Machines

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Algorithms of Oppression: How Search Engines Reinforce Racism

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Algorithms of Oppression: How Search Engines Reinforce Racism [Noble, Safiya Umoja] on Amazon.com. *FREE* shipping on qualifying offers. Algorithms of Oppression: How Search Engines Reinforce Racism

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A New York Times Book Review Notable Book of 2016A Best Book of 2016's Required Reading Picks of 2016's Favorite Books of 2016Best Book of 2016A Chicago Public Library Best Book of 2016A Nature.com Best Book of 2016Editor's Choice's Bestseller is the Big Data story Silicon Valley proponents won't tell.... [It] pithily exposes flaws in how information is used to assess everything from creditworthiness to policing tactics.... a thought-provoking read for anyone inclined to believe that data doesn't lie.""Insightful and disturbing."-New York Review of Books"A fascinating and deeply disturbing book." 's Best Books of 2016"If you've ever suspected there was something baleful about our deep trust in data, but lacked the mathematical skills to figure out exactly what it was, this is the book for you." is full of hard truths and grim statistics, it is also accessible and even entertaining. O'Neil's writing is direct and easy to read-I devoured it in an afternoon." opens the curtain on algorithms that exploit people and distort the truth while posing as neutral mathematical tools. This book is wise, fierce, and desperately necessary.""An avowed math nerd, O'Neil has written an engaging description of the effect of crunched data on our lives.""By tracking how algorithms shape people's lives at every stage, O'Neil makes a compelling case that our bot overlords are using data to discriminate unfairly and foreclose democratic choices. If you work with data, or just produce reams of it online, this is a must-read.""[O'Neil's] propulsive study reveals many models that are currently 'micromanaging' the US economy as opaque and riddled with bias.". It is eye-opening, disturbing, and deeply important."Times Higher Education"Not math heavy, but written in an exceedingly accessible, almost literary style; [O'Neil's] fascinating case studies of WMDs fit neatly into the genre of dystopian literature. There's a little Philip K. Dick, a little Orwell, a little Kafka in her portrait of powerful bureaucracies ceding control of the most intimate decisions of our lives to hyper-empowered computer models riddled with all of our unresolved, atavistic human biases." shines invaluable light on the invisible algorithms and complex mathematical models used by government and big business to undermine equality and increase private power. Combating secrecy with clarity and confusion with understanding, this book can help us change course before it's too late." is a fantastic, plainspoken call to arms. It acknowledges that models aren't going away: As a tool for identifying people in difficulty, they are amazing. But as a tool for punishing and disenfranchising, they're a nightmare." and co-editor of Boing Boing by Cathy O'Neil to deconstruct the latest growing tyranny of an arrogant establishment.". It'll be salutary."
Boston Globe Wired One of
One of Fortune A
Kirkus Reviews An
On Point Best Book of 2016 Maclean

New York Times Book Review
Weapons of Math Destruction "This is a manual for the 21st-century citizen, and it succeeds where other big data accounts have failed - it is accessible, refreshingly critical and feels relevant and urgent."
New York Times "
A Weapons of Math Destruction is an urgent critique of... the rampant misuse of math in nearly every aspect of our lives."
Winner of the 2016 SLA-NY PrivCo Spotlight Award - Yuval Noah Harari , author of Sapiens ;
- The Guardian "A nuanced reminder that big data is only as good as the people wielding it." "O'Neil is an ideal person to write this book. She is an academic mathematician turned Wall Street quant turned data scientist who has been involved in Occupy Wall Street and recently started an algorithmic auditing company. She is one of the strongest voices speaking out for limiting the ways we allow algorithms to influence our lives... While Weapons of Math Destruction
"Readable and engaging... succinct and cogent...

Weapons of Math Destruction is The Jungle of our age... [It] should be required reading for all data scientists and for any organizational decision-maker convinced that a mathematical model can replace human judgment." Mark Van Hollebeke, Data and Society: Points
"Indispensable... Despite the technical complexity of its subject, Weapons of Math Destruction lucidly guides readers through these complex modeling systems... O'Neil's book is an excellent primer on the ethical and moral risks of Big Data and an algorithmically dependent world... For those curious about how Big Data can help them and their businesses, or how it has been reshaping the world around them, Weapons of Math Destruction is an essential starting place." - National Post Weapons of Math Destruction Jordan Ellenberg , University of Wisconsin-Madison, author of "O'Neil has become [a whistle-blower] for the world of Big Data... [in] her important new book... Her work makes particularly disturbing points about how being on the wrong side of an algorithmic decision can snowball in incredibly destructive ways."

"Illuminating... [O'Neil] makes a convincing case that this reliance on algorithms has gone too far." "O'Neil's work is so important... [her] book is a vital crash-course in the specialized kind of statistical knowledge we all need to interrogate the systems around us and demand better." "Cathy O'Neil, a number theorist turned data scientist, delivers a simple but important message: Statistical models are everywhere, and they exert increasing power over many aspects of our daily lives...
Weapons of Math Destruction provides a handy map to a few of the many areas of our lives over which invisible algorithms have gained some control. As the empire of big data continues to expand, Cathy O'Neil's reminder of the need for vigilance is welcome and necessary." -American Prospect -
- Hicklebee's, San Francisco Chronicle -ArsTechnica "Lucid, alarming, and valuable... [O'Neil's] writing is crisp and precise as she aims her arguments to a lay audience. This makes for a remarkably page-turning read for a book about algorithms. Weapons of Math Destruction should be required reading for anybody whose life will be affected by Big Data, which is to say: required reading for everyone. It's a wake-up call - a journalistic heir to The Jungle and Silent Spring . Like those books, it should change the course of American society." -Aspen Times "You don't need to be a nerd to appreciate the significance of [O'Neil's] message... Weapons is a must-read for anyone who is working to combat economic and racial discrimination." -Goop "Cathy O'Neil's book... is important and covers issues everyone should care about. Bonus points: it's accessible, compelling, and - something I wasn't expecting - really fun to read." "Often we don't even know where to look for those important algorithms, because by definition the most dangerous ones are also the most secretive. That's why the catalogue of case studies in O'Neil's book are so important; she's telling us where to look." -In These Times "In this simultaneously illuminating and disturbing account, [O'Neil] describes the many ways in which widely used mathematic models-based on 'prejudice, misunderstanding, and bias'-tend to punish the poor and reward the rich... She convincingly argues for both more responsible modeling and federal regulation. An unusually lucid and readable look at the daunting algorithms that govern so many aspects of our lives." - Kirkus Reviews

"Cathy O'Neil has seen Big Data from the inside, and the picture isn't pretty. (starred)
- Weapons of Math Destruction . Though terrifying, it's a surprisingly fun read: O'Neil's vision of a world run by algorithms is laced with dark humor and exasperation-like a modern-day Dr. Strangelove or Catch-22 Steven Strogatz , Cornell University, author of The Joy of x Publishers Weekly Paris Review Weapons of Math Destruction Astra Taylor
, author of The People's Platform: Taking Back Power and Culture in the Digital Age Weapons of Math Destruction Cory Doctorow , author of Little Brother
Weapons of Math Destruction Ralph Nader , author of Unsafe at Any Speed danah boyd , founder of Data & Society and author of It's Complicated "From getting a job to finding a spouse, predictive algorithms are silently shaping and controlling our destinies. Cathy O'Neil takes us on a journey of outrage and wonder, with prose that makes you feel like it's just a conversation. But it's an important one. We need to reckon with technology." - Linda Tirado , author of Hand to Mouth: Living in Bootstrap America Weapons of Math Destruction Felix Salmon , Fusion

-The Guardian
"O'Neil is passionate about exposing the harmful effects of Big Data-driven mathematical models (what she calls WMDs), and she's uniquely qualified for the task... [She] makes a convincing case that many mathematical models today are engineered to benefit the powerful at the expense of the powerless... [and] has written an entertaining and timely book that gives readers the tools to cut through the ideological fog obscuring the dangers of the Big Data revolution."

"Even as a professional mathematician, I had no idea how insidious Big Data could be until I read
-

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"Through harrowing real-world examples and lively story-telling,
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"Many algorithms are slaves to the inequalities of power and prejudice. If you don't want these algorithms to become your masters, read
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"Next time you hear someone gushing uncritically about the wonders of Big Data, show them
-

1

BOMB PARTS
What Is a Model?

It was a hot August afternoon in 1946. Lou Boudreau, the player-manager of the Cleveland Indians, was having a miserable day. In the first game of a doubleheader, Ted Williams had almost single-handedly annihilated his team. Williams, perhaps the game's greatest hitter at the time, had smashed three home runs and driven home eight. The Indians ended up losing 11 to 10.

Boudreau had to take action. So when Williams came up for the first time in the second game, players on the Indians' side started moving around. Boudreau, the shortstop, jogged over to where the second baseman would usually stand, and the second baseman backed into short right field. The third baseman moved to his left, into the shortstop's hole. It was clear that Boudreau, perhaps out of desperation, was shifting the entire orientation of his defense in an attempt to turn Ted Williams's hits into outs.

In other words, he was thinking like a data scientist. He had analyzed crude data, most of it observational: Ted Williams usually hit the ball to right field. Then he adjusted. And it worked. Fielders caught more of Williams's blistering line drives than before (though they could do nothing about the home runs sailing over their heads).

If you go to a major league baseball game today, you'll see that defenses now treat nearly every player like Ted Williams. While Boudreau merely observed where Williams usually hit the ball, managers now know precisely where every player has hit every ball over the last week, over the last month, throughout his career, against left-handers, when he has two strikes, and so on. Using this historical data, they analyze their current situation and calculate the positioning that is associated with the highest probability of success. And that sometimes involves moving players far across the field.

Shifting defenses is only one piece of a much larger question: What steps can baseball teams take to maximize the probability that they'll win? In their hunt for answers, baseball statisticians have scrutinized every variable they can quantify and attached it to a value. How much more is a double worth than a single? When, if ever, is it worth it to bunt a runner from first to second base?

The answers to all of these questions are blended and combined into mathematical models of their sport. These are parallel universes of the baseball world, each a complex tapestry of probabilities. They include every measurable relationship among every one of the sport's components, from walks to home runs to the players themselves. The purpose of the model is to run different scenarios at every juncture, looking for the optimal combinations. If the Yankees bring in a right-handed pitcher to face Angels slugger Mike Trout, as compared to leaving in the current pitcher, how much more likely are they to get him out? And how will that affect their overall odds of winning?

Baseball is an ideal home for predictive mathematical modeling. As Michael Lewis wrote in his 2003 bestseller, Moneyball, the sport has attracted data nerds throughout its history. In decades past, fans would pore over the stats on the back of baseball cards, analyzing Carl Yastrzemski's home run patterns or comparing Roger Clemens's and Dwight Gooden's strikeout totals. But starting in the 1980s, serious statisticians started to investigate what these figures, along with an avalanche of new ones, really meant: how they translated into wins, and how executives could maximize success with a minimum of dollars.

"Moneyball" is now shorthand for any statistical approach in domains long ruled by the gut. But baseball represents a healthy case study-and it serves as a useful contrast to the toxic models, or WMDs, that are popping up in so many areas of our lives. Baseball models are fair, in part, because they're transparent. Everyone has access to the stats and can understand more or less how they're interpreted. Yes, one team's model might give more value to home run hitters, while another might discount them a bit, because sluggers tend to strike out a lot. But in either case, the numbers of home runs and strikeouts are there for everyone to see.

Baseball also has statistical rigor. Its gurus have an immense data set at hand, almost all of it directly related to the performance of players in the game. Moreover, their data is highly relevant to the outcomes they are trying to predict. This may sound obvious, but as we'll see throughout this book, the folks building WMDs routinely lack data for the behaviors they're most interested in. So they substitute stand-in data, or proxies. They draw statistical correlations between a person's zip code or language patterns and her potential to pay back a loan or handle a job. These correlations are discriminatory, and some of them are illegal. Baseball models, for the most part, don't use proxies because they use pertinent inputs like balls, strikes, and hits.

Most crucially, that data is constantly pouring in, with new statistics from an average of twelve or thirteen games arriving daily from April to October. Statisticians can compare the results of these games to the predictions of their models, and they can see where they were wrong. Maybe they predicted that a left-handed reliever would give up lots of hits to right-handed batters-and yet he mowed them down. If so, the stats team has to tweak their model and also carry out research on why they got it wrong. Did the pitcher's new screwball affect his statistics? Does he pitch better at night? Whatever they learn, they can feed back into the model, refining it. That's how trustworthy models operate. They maintain a constant back-and-forth with whatever in the world they're trying to understand or predict. Conditions change, and so must the model.

Now, you may look at the baseball model, with its thousands of changing variables, and wonder how we could even be comparing it to the model used to evaluate teachers in Washington, D.C., schools. In one of them, an entire sport is modeled in fastidious detail and updated continuously. The other, while cloaked in mystery, appears to lean heavily on a handful of test results from one year to the next. Is that really a model?

The answer is yes. A model, after all, is nothing more than an abstract representation of some process, be it a baseball game, an oil company's supply chain, a foreign government's actions, or a movie theater's attendance. Whether it's running in a computer program or in our head, the model takes what we know and uses it to predict responses in various situations. All of us carry thousands of models in our heads. They tell us what to expect, and they guide our decisions.

Here's an informal model I use every day. As a mother of three, I cook the meals at home-my husband, bless his heart, cannot remember to put salt in pasta water. Each night when I begin to cook a family meal, I internally and intuitively model everyone's appetite. I know that one of my sons loves chicken (but hates hamburgers), while another will eat only the pasta (with extra grated parmesan cheese). But I also have to take into account that people's appetites vary from day to day, so a change can catch my model by surprise. There's some unavoidable uncertainty involved.

The input to my internal cooking model is the information I have about my family, the ingredients I have on hand or I know are available, and my own energy, time, and ambition. The output is how and what I decide to cook. I evaluate the success of a meal by how satisfied my family seems at the end of it, how much they've eaten, and how healthy the food was. Seeing how well it is received and how much of it is enjoyed allows me to update my model for the next time I cook. The updates and adjustments make it what statisticians call a "dynamic model."

Over the years I've gotten pretty good at making meals for my family, I'm proud to say. But what if my husband and I go away for a week, and I want to explain my system to my mom so she can fill in for me? Or what if my friend who has kids wants to know my methods? That's when I'd start to formalize my model, making it much more systematic and, in some sense, mathematical. And if I were feeling ambitious, I might put it into a computer program.

Ideally, the program would include all of the available food options, their nutritional value and cost, and a complete database of my family's tastes: each individual's preferences and aversions. It would be hard, though, to sit down and summon all that informationoff the top of my head. I've got loads of memories of people grabbing seconds of asparagus or avoiding the string beans. But they're all mixed up and hard to formalize in a comprehensive list.

The better solution would be to train the model over time, entering data every day on what I'd bought and cooked and noting the responses of each family member. I would also include parameters, or constraints. I might limit the fruits and vegetables to what's in season and dole out a certain amount of Pop-Tarts, but only enough to forestall an open rebellion. I also would add a number of rules. This one likes meat, this one likes bread and pasta, this one drinks lots of milk and insists on spreading Nutella on everything in sight.

If I made this work a major priority, over many months I might come up with a very good model. I would have turned the food management I keep in my head, my informal internal model, into a formal external one. In creating my model, I'd be extending my power and influence in the world. I'd be building an automated me that others can implement, even when I'm not around.

There would always be mistakes, however, because models are, by their very nature, simplifications. No model can include all of the real world's complexity or the nuance of human communication. Inevitably, some important information gets left out. I might have neglected to inform my model that junk-food rules are relaxed on birthdays, or that raw carrots are more popular than the cooked variety.

To create a model, then, we make choices about what's important enough to include, simplifying the world into a toy version that can be easily understood and from which we can infer important facts and actions. We expect it to handle only one job and accept that it will occasionally act like a clueless machine, one with enormous blind spots.

Sometimes these blind spots don't matter. When we ask Google Maps for directions, it models the world as a series of roads, tunnels, and bridges. It ignores the buildings, because they aren't relevant to the task. When avionics software guides an airplane, it models the wind, the speed of the plane, and the landing strip below, but not the streets, tunnels, buildings, and people.

A model's blind spots reflect the judgments and priorities of its creators. While the choices in Google Maps and avionics software appear cut and dried, others are far more problematic. The value-added model in Washington, D.C., schools, to return to that example, evaluates teachers largely on the basis of students' test scores, while ignoring how much the teachers engage the students, work on specific skills, deal with classroom management, or help students with personal and family problems. It's overly simple, sacrificing accuracy and insight for efficiency. Yet from the administrators' perspective it provides an effective tool to ferret out hundreds of apparently underperforming teachers, even at the risk of misreading some of them.

Here we see that models, despite their reputation for impartiality, reflect goals and ideology. When I removed the possibility of eating Pop-Tarts at every meal, I was imposing my ideology on the meals model. It's something we do without a second thought. Our own values and desires influence our choices, from the data we choose to collect to the questions we ask. Models are opinions embedded in mathematics.

Whether or not a model works is also a matter of opinion. After all, a key component of every model, whether formal or informal, is its definition of success. This is an important point that we'll return to as we explore the dark world of WMDs. In each case, we must ask not only who designed the model but also what that person or company is trying to accomplish. If the North Korean government built a model for my family's meals, for example, it might be optimized to keep us above the threshold of starvation at the lowest cost, based on the food stock available. Preferences would count for little or nothing. By contrast, if my kids were creating the model, success might feature ice cream at every meal. My own model attempts to blend a bit of the North Koreans' resource management with the happiness of my kids, along with my own priorities of health, convenience, diversity of experience, and sustainability. As a result, it's much more complex. But it still reflects my own personal reality. And a model built for today will work a bit worse tomorrow. It will grow stale if it's not constantly updated. Prices change, as do people's preferences. A model built for a six-year-old won't work for a teenager.

This is true of internal models as well. You can often see troubles when grandparents visit a grandchild they haven't seen for a while. On their previous visit, they gathered data on what the child knows, what makes her laugh, and what TV show she likes and (unconsciously) created a model for relating to this particular four-year-old. Upon meeting her a year later, they can suffer a few awkward hours because their models are out of date. Thomas the Tank Engine, it turns out, is no longer cool. It takes some time to gather new data about the child and adjust their models.

This is not to say that good models cannot be primitive. Some very effective ones hinge on a single variable. The most common model for detecting fires in a home or office weighs only one strongly correlated variable, the presence of smoke. That's usually enough. But modelers run into problems-or subject us to problems-when they focus models as simple as a smoke alarm on their fellow humans.

Racism, at the individual level, can be seen as a predictive model whirring away in billions of human minds around the world. It is built from faulty, incomplete, or generalized data. Whether it comes from experience or hearsay, the data indicates that certain types of people have behaved badly. That generates a binary prediction that all people of that race will behave that same way.

Needless to say, racists don't spend a lot of time hunting down reliable data to train their twisted models. And once their model morphs into a belief, it becomes hardwired. It generates poisonous assumptions, yet rarely tests them, settling instead for data that seems to confirm and fortify them. Consequently, racism is the most slovenly of predictive models. It is powered by haphazard data gathering and spurious correlations, reinforced by institutional inequities, and polluted by confirmation bias. In this way, oddly enough, racism operates like many of the WMDs I'll be describing in this book.

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Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy

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Buy Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy on Amazon.com ✓ FREE SHIPPING on qualified orders

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An exploration of how design might be led by marginalized communities, dismantle structural inequality, and advance collective liberation and ecological survival.

What is the relationship between design, power, and social justice? "Design justice" is an approach to design that is led by marginalized communities and that aims expilcitly to challenge, rather than reproduce, structural inequalities. It has emerged from a growing community of designers in various fields who work closely with social movements and community-based organizations around the world.

This book explores the theory and practice of design justice, demonstrates how universalist design principles and practices erase certain groups of people-specifically, those who are intersectionally disadvantaged or multiply burdened under the matrix of domination (white supremacist heteropatriarchy, ableism, capitalism, and settler colonialism)-and invites readers to "build a better world, a world where many worlds fit; linked worlds of collective liberation and ecological sustainability." Along the way, the book documents a multitude of real-world community-led design practices, each grounded in a particular social movement. Design Justice goes beyond recent calls for design for good, user-centered design, and employment diversity in the technology and design professions; it connects design to larger struggles for collective liberation and ecological survival.

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Design Justice: Community-Led Practices to Build the Worlds We Need (Information Policy)

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Design Justice: Community-Led Practices to Build the Worlds We Need (Information Policy) [Costanza-Chock, Sasha] on Amazon.com. *FREE* shipping on qualifying offers. Design Justice: Community-Led Practices to Build the Worlds We Need (Information Policy)

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Race After Technology: Abolitionist Tools for the New Jim Code

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Race After Technology: Abolitionist Tools for the New Jim Code [Benjamin, Ruha] on Amazon.com. *FREE* shipping on qualifying offers. Race After Technology: Abolitionist Tools for the New Jim Code

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@D_Educator

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About the Funder: Southern California Consortium for Data Science (SCCDS)

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About the Funder: Southern California Consortium for Data Science (SCCDS)

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https://sites.google.com/view/socaldatasci/home

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Quantitative Analysis of Instructional Practices

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Quantitative Analysis of Instructional Practices

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Critical, Intersectional, Quantitative Analyses of Instructional Practices and Changes in Undergraduate Students’ Math Affect - International Journal of Research in Undergraduate Mathematics Education

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As interest in the implementation of active learning practices grows, so too does the body of literature illustrating negative experiences of these practices among some populations of students. These trends necessitate a critical inquiry into how students with identities that are traditionally marginalized in mathematical spaces differentially experience active learning practices. We leverage critical quantitative theories to analyze how shifts in precalculus and calculus students’ math affect are mediated by intersectional race-gender identities and the active learning instructional practices of math engagement, peer collaboration, instructor inquiry, and participation. Drawing on a dataset of over 30,000 U.S. student survey responses, we found that experiencing high levels of all four practices increased math affect for all student identity groups in our dataset. Considering each individual practice revealed variation of students’ affective changes based on race-gender identities, such that not every individual practice benefited every student identity group. These findings emphasize the value in promoting the collective high use of multiple active learning practices, coupled with more in-depth understandings and attention to how these individual practices can differentially impact students.

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Using Python to Reason About Logic and Set Theory: Three Instrumented Action Schemes - Digital Experiences in Mathematics Education

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Many areas of mathematics naturally lend themselves to machine-based computing environments, which suggests that computational environments may serve as useful mediating tools for the teaching and learning of mathematical content. While some mathematics classes are leveraging the use of computational tools, the implementation of computer programming to teach and learn mathematics is not widespread. In this study, I highlight the mathematical activity of four undergraduate students who used Python to solve mathematical tasks in the context of set theory and logic. To understand how the students leveraged the computer programming environment, I use the analytical framework known as the instrumental approach, which can be utilized to investigate the confluence of an artifact (often a piece of technology) and the human mind to solve a mathematical problem. Results indicate that the students were able to use Python and its computational capabilities such as For Loops, If Statements, and Functions as artifacts to reason about propositional statements, set intersection, and subsets. Specifically, three instrumented action schemes emerged from their work on three different tasks. These schemes describe the use of Python in creative ways to solve mathematical tasks, which suggests various implications for teaching and research.

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Richard McElreath
Director
Department of Human Behavior, Ecology, and Culture [link]
Max Planck Institute for Evolutionary Anthropology [link]

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GitHub - dantonnoriega/csulb-data-day-2024: Collection of materials for CSULB Data Day 2024 Breakout Session

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Collection of materials for CSULB Data Day 2024 Breakout Session - dantonnoriega/csulb-data-day-2024

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Time to event analysis of mathematics intervention programs - ProQuest

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Explore millions of resources from scholarly journals, books, newspapers, videos and more, on the ProQuest Platform.

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Applied Statistics Graduate Program

Established in 2003, the Master of Science in Applied Statistics program at California State University, Long Beach (CSULB) is an academic degree program which trains students to draw valid inferences from data. Using conceptual foundations and statistical software packages (SAS, R, and Python), graduates are expected to analyze real world data appropriately and communicate their findings effectively. The tools you learn here will open the door for careers in data science and analytics, or prepare you for a Ph.D.

Typically, the requirements can be satisfied in about 4 semesters. As one of the largest statistics programs at masters granting institutions in the United States, we are building a nationwide network of alumni in industry and academia.

Ready to join our program? Check out How to Apply.

Prospective Student FAQ

The following are questions that are frequently asked by prospective students interested in the Applied Statistics graduate program at CSULB.

Have a question that isn't answered here? Please contact the graduate advisor!

For Fall admission, you must submit your application via Cal State Apply by June 1 ( or April 1 for international students).

For Spring admission, you must submit your application via Cal State Apply by November 1 ( or October 1 for international students).

In addition to the Cal State Apply application, please email the prerequisite worksheet (found on How to Apply) to the Applied Statistics Graduate Advisor.

The prerequisites for the program are as follows:

1. A bachelor's degree in any field from an accredited college or university with a minimum 2.5 GPA. If your bachelors is still in progress, a minimum 2.7 GPA is required.

2. A grade of "B" or better in MATH 247 (Linear Algebra), MATH 380 (upper division Probability), and STAT 381 (upper division Mathematical Statistics) or their equivalents. Each of these classes must be Calculus based. Please see the "Prerequisite Worksheet" (found on How to Apply), which will be part of your application.

If you have not quite met either requirement, please contact the Applied Statistics graduate advisor to develop a strategy to overcome your deficiencies and get on track for admission. Many students satisfy the class prerequisites by taking MATH 380 and STAT 381 at CSULB through Open University.

Although these are required for many graduate programs, they are not required for admission at CSULB. However, if you are a borderline case based on the above qualifications, letters of recommendation can help you make your case.

You will be required to pass 30 semester units (10 classes) and complete a thesis, project, or comprehensive examination to be granted a degree.

Of these 30 units, a maximum of 9 may be credit from another institution, provided all of the following are true:

the units are equivalent to courses offered at CSULB.

the units were not used to count towards another degree.

the units were set aside for graduate school credit before you graduated.

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Established in 2003, the Master of Science in Applied Statistics program at California State University, Long Beach (CSULB) is an academic degree program which trains students to draw valid inferences from data. Using conceptual foundations and statistical software packages (SAS, R, and Python), graduates are expected to analyze real world data appropriately and communicate their findings effectively.

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Learn about the Applied Statistics MS program with a customized Chatbot!

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Machine Learning in Higher Education Certificate

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Machine Learning in Higher Education Certificate

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New certificate program launching summer 2025!

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New major starting Fall 2025

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Bachelor of Science: Applied Data Science

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Our program builds upon a strong foundation of programming and data analysis to prepare data scientists who will be able to apply their skills to real-world applications. Graduates are prepared to join the data analysis workforce or pursue more advanced degrees.

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Data Science applied to business marketing