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Spline:
A spline is a continuous function Math image which coincides with a polynomial on every subinterval Math image of the whole interval Math image on which Math image is defined. In other words, splines arefunctions which are piecewise polynomial. The coefficients of the polynomial differs from interval to interval,but the order Math image of the polynomial is the same. Splines are often named after the order Math image of the spline,
e.g. cubic splines correspond to Math image
Uses:
Creation of hard objects, like cars, buildings, and furniture.
Creating objects which may be a combination of angular and curved shapes.
In interpolating problems,
low degree polynomials
Advantages:
The advantage of splines is their inherent smoothness when dealing with sparse data.Stability and consistency analysis of semi-Lagrangian methods for the linear problemcomputations are simple

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Spline based model:
A spline is a continuous function which coincides with a polynomial on every subinterval of the whole interval on which is defined. In other words, splines are functions which are piecewise polynomial. The coefficients of the polynomial differs from interval to interval, but the order of the polynomial is the same.

Uses:
Spline regression models are used when a regression line is broken into a number of line segments separated by special join points known as spline knots. The regression line changes direction at these join points, but does not “jump” at these points.

Advantages:

These models are good for making interpolations.

Adjusting for quantitative confounders which have nonlinear effect.

Valid for identifying causal and nonlinear effects

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What is Spline based model?
A spline is a curve in 3D space defined by at least two control points. The most common splines used in 3D art are bezier curves and NURBS Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available.
USES:
Spline modeling is used primarily for the creation of hard objects, like cars, buildings, and furniture. Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes.

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The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional.
Spline Model:
spline model can be defined as a regression model that consists of a continuous explanatory variable defined over specified segments of the domain of that variable and a dependent variable that is a continuous function of that explanatory variable over all segments, but with different slopes.
Spline or patch modeling: A spline is a curve in 3D space defined by at least two control points. ... Spline modeling is used primarily for the creation of hard objects, like cars, buildings, and furniture. Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes.

# data[].attributes.body
What is Spline based model?
A spline is a curve in 3D space defined by at least two control points.Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available.
Uses :
Spline modeling is used primarily for the creation of hard objects, like cars, buildings, and furniture. Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes.

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What is spline based model?
A piecewise linear spline model can be defined as a regression model that consists of a continuous explanatory variable defined over specified segments of the domain of that variable and a dependent variable that is a continuous function of that explanatory variable over all segments,
USES:
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
Advantages:
1)Simplicity
2)we can apply our intuition concerning regression diagnostics directly to curve estimation.
3)Minimize mean squared error
4)A penalty term proportional to average curvature of the function over space

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what is spline based model:
There has been extensive work done on the development of methodology for diagnostic testing and screening. One primary scientific goal in this area is to determine the discriminatory power of a biomarker for detecting disease.
Where it is used :
Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients.

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what is spline?
Spline is a special function(piecewise polynomial function) in maths whereas spline is a polynomial curve in computer science
Spline regression is a non-linear regression which is used to try and overcome the difficulties of linear and polynomial regression algorithms.
In linear regression, the entire dataset is considered at once. But in spline regression, the dataset is divided into bins. Each bin of the data is then made to fit with separate models.

WHERE IT IS USED?

Regression Spline-Model in Machine Learning for Signal Prediction and Parameterization

ADVANTAGES:
higher accuracy
less computational effort

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SPLINE BASED MODELS

1.What is Spline based model?
Spline means piece-wise polynomial curve. The spline is defined by a piece-wise polynomial function. It is one of the non-parametric regression methods.

2.What are the uses?
Spline models are used in interpolation problems.
Spline interpolation is often preferred to polynomial interpolation because, even when using low-grade polynomials, it yields similar results.

3.Advantages
The benefits of using splines for data analysis are that splines are computationally simple and satisfy the minimum property of curvature.

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Spline based model
A spline is a function that is constructed piece-wise from polynomial functions. The term
comes from the tool used by shipbuilders and drafters to construct smooth shapes having desired properties. Drafters have long made use of a bendable strip fixed in position at a number of
points that relaxes to form a smooth curve passing through those points. The malleability of the spline material combined with the constraint of the control points would cause the strip to take
the shape that minimized the energy required for bending it between the fixed points, this being the smoothest possible shape. We shall rely on a class of splines called B-splines. A B-spline function is the maximally differentiable interpolative basis function. The B-spline is a
generalization of the Bezier curve. B-splines are defined by their order m and number of interior ‘knots’ N (there are two ‘endpoints’ which are themselves knots so the total number of knots will be N +2). The degree of the B-spline polynomial
will be the spline order m minus one (degree = m − 1).

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What is spline based model:

Spline is a special function defined piece-wise by polynomials. The term “spline” is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional. Spline Regression is one of the non-parametric regression technique. In this technique the dataset is divided into bins at intervals or points which we called as knots. Also this bin has its separate fit.

Where it can be used?
splines are regularly used for building explanatory models in clinical research.
Indeed, many new methodological developments in modern biostatistics make use of splines to model smooth functions of interest,
including e.g. non-linear effects of continuous covariates, avoiding distributional assumptions and modelling time-dependent effects in survival analysis,
time series, cumulative effects and frequency distributions. It is not only important in statistical methods development but is also widely used in applied clinical research

Advantages

Simplicity

we can apply our intuition concerning regression diagnostics directly to curve estimation.

Minimize mean squared error

A penalty term proportional to average curvature of the function over space

References
http://bactra.org/weblog/870.html

http://bear.fhcrc.org/monopdf/ch03.pdf

https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-019-0666-3

https://medium.com/analytics-vidhya/spline-regression-in-r-960ca82aa62c

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What is spline based model?
Regression model  consists of a continuous explanatory variable defined over specified segments of the domain of that variable and a dependent variable that is a continuous function of that explanatory variable is called a piecewise linear spline based model.
Where it use?
To overcome the disadvantages of polynomial based model, instead of building one model for the entire dataset, divides the dataset into multiple bins and fits each bin with a separate model. This  technique is known as Spline based Regression technique.
Advantages:
simplicity

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In regression modeling when we include a continuous predictor variable in our model, either as the main exposure of interest or as a confounder, we are making the assumption that the relationship between the predictor variable and the outcome is linear. In other words, a one unit increase in the predictor variable is associated with a fixed difference in the outcome. Thus, we make no distinction between a one unit increase in the predictor variable near the minimum value and a one unit increase in the predictor variable near the maximum value. This assumption of linearity may not always be true, and may lead to an incorrect conclusion about the relationship between the exposure and outcome, or in the case of a confounder that violates the linearity assumption, may lead to residual confounding. Spline regression is one method for testing non-linearity in the predictor variables and for modeling non-linear functions.

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Spline Models:
One of the methods of non-parametric regression and which is used to represent the fit as piecewise polynomial.
Where can it be used:
Used in the design, evaluation, and implementation of a framework for detecting and modeling non-linearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples.
Advantages:
1.Reducing bias
2.Smooth by construction
3.Highly flexible
4.Less computational effort
5.High accuracy

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Spline:
A spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials.
Advantages of Spline:
There are many advantages of splines over keys. with 1 or 2 keys, a more uniform transfer of torque and a lower loading on a given part of the shaft/hub interface result. relative motion can occur as between a key and the shaft. mating element can be indexed to various positions.
In Mechanical domain ,Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are used in several places in bicycles.

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Spline based Models: Spline is a special function defined piece wise by polynomials. These piecewise polynomials are referred to as splines, leading to the name spline regression or spline smoothing for this type of nonparametric regression.Instead of building one model for the entire dataset, divides the dataset into multiple bins and fits each bin with a separate model. Such a technique is known as Regression spline.The points where the division occurs are called Knots

Where is Spline based Models used?

Spline are mainly usedwhen you’d like to fit a bunch of points to a smooth curve, but are unsure of what the underlying structure of the data points. When data is unpredictable, and splines help to make it smooth. Application of splines include Maple Spline function and Interpolation with Splines.

Advantages: Splines often provide better results as compared to polynomial regression. In splines, flexibility can be increased by increasing the number of knots and without increasing the degree of the polynomial. They also produce more stable results as compared to polynomial regression.

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In order to overcome the disadvantages of polynomial regression, we can use an improved regression technique which, instead of building one model for the entire dataset, divides the dataset into multiple bins and fits each bin with a separate model. Such a technique is known as Regression spline.
Regression splines is one of the most important non linear regression techniques. In polynomial regression, we generated new features by using various polynomial functions on the existing features which imposed a global structure on the dataset. To overcome this, we can divide the distribution of the data into separate portions and fit linear or low degree polynomial functions on each of these portions. The points where the division occurs are called Knots. Functions which we can use for modelling each piece/bin are known as Piecewise functions. There are various piecewise functions that we can use to fit these individual bins.

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Spline Based Model:
A spline is a curve in 3D space defined by at least two control points. The most common splines used in 3D art are

Bezier curves

NURBS

NURMS(the software Maya has a strong NURBS modeling foundation.) Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available. A cage of splines is created to form a "skeleton" of the object you want to create. The software can then create a patch of polygons to extend between two splines, forming a 3D skin around the shape. Spline modeling is not used very often these days for character creation, due to how long it takes to create good models. The models that are produced usually aren't useful for animation without a lot of modification.

Uses / Applications of Spline based model:

Used for creation of hard objects, like cars, buildings, and furniture

Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes.

Creating a 3D scene that requires curved shapes, spline modeling should be the first choice

Advantages of Spline Based Model:

The advantage of splines is their inherent smoothness when dealing with sparse data.

These models are very good for making interpolations and for adjusting for quantitative confounders which have nonlinear effect.

They are also valid for identifying causal, nonlinear effects but you might find the causal inference difficult to communicate other than graphically.

References:

http://www.animationarena.com/introduction-to-3d-modeling.html

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What is spline based models ?
It is a regression technique in which divides the dataset into multiple
bins and fits each bin with a separate model instead of building one model for
entire data set. It uses a combination of linear/polynomial functions to fit the data.

What are its uses ?
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

What are its advantages ?
Splines are computationally simple.
Inherent smoothness when dealing with sparse data.

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Spline Model :
Spline regression models are used when a regression line is broken into a number of line segments separated by special join points known as spline knots.It uses a combination of linear/polynomial functions to fit the data.

Uses :
These spline functions are typically used to

interpolate data exactly at a set of points;

approximate data at many points, or over an interval.

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18IT073
SPLINE BASED MODELS:
A spline is a curve in 3D space defined by at least two control points. The most common splines used in 3D art are bezier curves and NURBS (the software Maya has a strong NURBS modeling foundation.) Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available. A cage of splines is created to form a "skeleton" of the object you want to create. The software can then create a patch of polygons to extend between two splines, forming a 3D skin around the shape. Spline modeling is not used very often these days for character creation, due to how long it takes to create good models. The models that are produced usually aren't useful for animation without a lot of modification.

These models are very good for making interpolations and for adjusting for quantitative confounders which have nonlinear effect.

They are also valid for identifying causal, nonlinear effects but you might find the causal inference difficult to communicate other than graphically.

# data[].attributes.body
SPLINE BASED MODELS:
A spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials.
WHERE IT IS USED:
Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients.
EXAMPLE: In Mechanical domain ,Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are used in several places in bicycles.
ADVANTAGES OF SPLINE BASED MODELS:
These models are very good for making INTERPOLATIONS and for adjusting quantitative cofounders which have nonlinear effect.
They are also valid for identifying causal,nonlinear effects but you might find the causal inference difficult to communicate other than graphically.
Generally spline models have solid mathematical basis.

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Spline based model - A piecewise linear spline model can be defined as a regression model that consists of a continuous explanatory variable defined over specified segments of the domain of that variable and a dependent variable that is a continuous function of that explanatory variable over all segments.
Uses - Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. eg:bicycle.
Advantages - The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property.

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Spline is also called as patch modeling. A spline is a curve in 3D space defined by at least two control points.
Uses of spline based model:
Spline modelsmake it possible to examine the response as a non-linear function of the predictors.  Splines are used in several places in bicycles.
Advantage of spline model:
Spline models are very good for making interpolations and for adjusting for quantitative confounders which have nonlinear effect.

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Spline based model:

Divides the dataset into multiple bins and fit each bin with separate model instead of building one model for entire data set.
It uses combination of linear/polynomial functions to fit data.Also known as Regression Spline.

Adavantages:
Splines are Computationally simple .
Staisfy the minium curvative property.
Inherent smoothness when dealing with sparse data.

Used In:
Used in applications requiring data interpolation and/or smoothing.
The spline command in AutoCAD is used to create a smooth curve.
Predictiveness curves and surfaces

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What is Spline Regression?

Spline regression is a non-linear regression which is used to try and overcome the difficulties of linear and polynomial regression algorithms. In linear regression, the entire dataset is considered at once. But in spline regression, the dataset is divided into bins. Each bin of the data is then made to fit with separate models. The points where the data is divided are called knots. Since there are separate functions that fit the bins, each function is called piecewise step functions.

# data[].attributes.body
Spline based model:
A spline is a curve in 3D space defined by at least two control points. The most common splines used in 3D art are bezier curves and NURBS (the software Maya has a strong NURBS modeling foundation.) Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available.

Uses:
In mathematics, a spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

Advantages:
The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property.

# data[].attributes.body
Spline based model:
Its a regression model consissting of continuous explanatory variable defined over specified segments of domain for with the predictiveness curves and surfaces
Uses of spline based mdoel:
The spline based model is used to create a smooth curve, which passes through a set of predefined points. It creates a non-uniform curve passing through the points. Thus, spline can be created by defining fit points or Control Vertices (CV) points.
Adavantages
The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property

# data[].attributes.body
What is Spline Based Model?
The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional.Spline s a special function defined piecewise  by polynomials.

Where it is used?
Graphic applications to built curves and structures
Used in CAD applications

Used to model relationships between continuous variables and outcomes.

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What is Spline ?
Technically, it means function defined piecewise  by polynomials.In simpler terms,splines add curves to make irregular curves.They create smooth curves out of irregular data points

Where  it is used ?
It is used in building a model for the entire dataset,  that divides the dataset into multiple bins and fits each bin with a separate mode, to get fit the data .

Advantages:
It makes the Model always become too flexible, which does not work well with unseen data. I then came across another non-linear approach known as Regression Splines. It uses a combination of linear/polynomial functions to fit the data.

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Spline based model

It is a regression technique in which divides the dataset into multiple
bins and fits each bin with a separate model instead of building one model for
entire data set. It uses a combination of linear/polynomial functions to fit the data.

Advantages

Splines are computationally simple.
Inherent smoothness when dealing with sparse data.

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SPLINE BASED MODEL
Regression technique
Special function defined piecewise by polynomials
It  is a non-linear regression which is used to try and overcome the difficulties of linear and polynomial regression algorithms.

USAGE:
In linear regression, the entire dataset is considered at once. But in spline regression, the dataset is divided into bins. Each bin of the data is then made to fit with separate models. The points where the data is divided are called knots. Since there are separate functions that fit the bins, each function is called piecewise step functions.

ADVANTAGES

Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.

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Spline-based modeling
Spline is basically a function defined piecewise polynomials. Regression splines is one of the most important non linear regression techniques. Mathematically,  a piecewise polynomial of degree m with m-1 continuous derivatives is called a Spline.
Uses:
Spline modeling is used primarily for the creation of hard objects, like cars, buildings, and furniture. Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes.
Advantages:
These Models are very good for making interpolations and for adjusting quantitative cofounders which have non-linear effect. They are also valid for identifying casual, nonlinear effects.

# data[].attributes.body
What is Spline based model?
A spline is a curve in 3D space defined by at least two control points.Using splines to create a model is perhaps the oldest, most traditional form of 3D modeling available.
Uses :
Spline modeling is used primarily for the creation of hard objects, like cars, buildings, and furniture. Splines are extremely useful when creating these objects, which may be a combination of angular and curved shapes
Advantages:
The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property.

# data[].attributes.body
Spline based model
spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.
Uses:
Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are used in several places in bicycles.

Advantage is higher accuracy with the less computational effort. It is a computationally efficient method and the produced algorithm can easily be implemented on a computer.

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What is spline based model?
Instead of building one model for the entire dataset, the spline model divides the dataset into multiple bins and fits each bin with a separate model.It is also known as Regression spline. This model overcomes the limitations of polynomial regression. Advantages
Allows to fit flexible models and don’t make the crude assumptions of simple linear models, but at the same time don’t overfit the data too badly.
Very good for making interpolations and for adjusting for quantitative confounders which have nonlinear effect.
They are also valid for identifying causal, nonlinear effects
Where to use?
1.For interpretable coefficients
2.When there is a specific idea of autocorrelation structure
3.to compare nonlinear trends for different samples of different size
4.Forecasting/extrapolation.

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Spline based model

Nonparametric regression techniques, which estimate functions directly from noisy data rather than relying on specific parametric models, now play a central role in statistical analysis.

Roughness in the fitted function is defined in terms of the integrated square of this operator applied to the fitted function.

A fastO(n) algorithm is outlined for this smart smoothing process. Illustrations are provided of where this technique proves useful.

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Spline Based Model :
Aa spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees.

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What is spline based model:
A piecewise linear spline model can be defined as a regression model that consists of a continuous explanatory variable defined over specified segments of the domain of that variable and a dependent variable that is a continuous function of that explanatory variable over all segments, but with different slopes.

Where it is used?
Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are used in several places in bicycles.

Advantages of spline based model:

The advantages of using splines for analyzing data are that splines are computationally simple and they satisfy the minimum curvature property.

uA review of algorithms involving splines as well as a comprehensive theory can be found elsewhere.