Class SplineRegressionOptions

Namespace

AiDotNet.Models.Options

Assembly

AiDotNet.dll

Configuration options for spline regression models, which fit piecewise polynomial functions to data for flexible nonlinear modeling.

public class SplineRegressionOptions : NonLinearRegressionOptions

Inheritance

object

ModelOptions

NonLinearRegressionOptions

SplineRegressionOptions

Inherited Members

NonLinearRegressionOptions.MaxIterations

NonLinearRegressionOptions.Tolerance

NonLinearRegressionOptions.KernelType

NonLinearRegressionOptions.Gamma

NonLinearRegressionOptions.Coef0

NonLinearRegressionOptions.PolynomialDegree

ModelOptions.Seed

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

Spline regression is a flexible nonlinear regression technique that fits piecewise polynomial functions (splines) to data. Unlike simple polynomial regression, which uses a single polynomial for the entire data range, spline regression divides the data into segments and fits separate polynomials to each segment, with constraints ensuring smoothness at the connection points (knots). This approach provides greater flexibility in modeling complex nonlinear relationships while avoiding the oscillatory behavior often seen with high-degree polynomials. This class provides configuration options for spline regression, including the number of knots (which determines the number of segments), the degree of the polynomial functions, and the matrix decomposition method used for solving the regression equations.

For Beginners: Spline regression helps model complex relationships in your data using connected smooth curves.

When simple linear regression isn't flexible enough:

• Linear regression forces a straight line through your data
• Polynomial regression uses a single curved line, but can behave poorly
• Spline regression uses multiple connected curves for more flexibility

Think of spline regression like drawing with multiple connected curve segments:

• Each segment is a polynomial curve (like a parabola)
• The segments connect smoothly at points called "knots"
• This creates a flexible curve that can adapt to different patterns in different regions

Benefits of spline regression:

• More flexible than simple lines or polynomials
• Avoids the wild oscillations that can happen with high-degree polynomials
• Can capture complex relationships while still being relatively simple to interpret

This class lets you configure exactly how the spline regression model will be constructed.

Properties

DecompositionType

Gets or sets the matrix decomposition method used to solve the regression equations.

public MatrixDecompositionType DecompositionType { get; set; }

Property Value

MatrixDecompositionType

A value from the MatrixDecompositionType enumeration, defaulting to MatrixDecompositionType.Cholesky.

Remarks

This property specifies the matrix decomposition method used to solve the system of linear equations that arises when fitting the spline regression model. Different decomposition methods have different characteristics in terms of numerical stability, computational efficiency, and applicability to specific types of matrices. The Cholesky decomposition (the default) is efficient and numerically stable for the positive definite matrices that typically arise in regression problems. Other options might include QR decomposition (more stable for ill-conditioned matrices but less efficient), SVD (Singular Value Decomposition, most stable but least efficient), or LU decomposition (efficient but less stable). The choice of decomposition method can affect the accuracy and efficiency of the regression, particularly for large datasets or ill-conditioned problems.

For Beginners: This setting selects the mathematical method used to solve the regression equations.

Fitting a spline regression involves solving a system of equations:

• Different mathematical methods (decompositions) can solve these equations
• Each method has trade-offs in terms of speed, accuracy, and numerical stability

The default Cholesky decomposition:

• Is very efficient for regression problems
• Works well when the data is well-behaved
• Is the standard choice for most regression applications

Other common decomposition types include:

• QR: More stable for problematic data, but slower
• SVD: Most stable for difficult cases, but significantly slower
• LU: Fast but less stable for regression problems

When to adjust this value:

• Keep the default (Cholesky) for most applications
• Consider QR or SVD if you encounter numerical stability issues (like errors about singular or ill-conditioned matrices)

This is an advanced setting that most users won't need to change unless they encounter specific numerical problems with the default method.

Degree

Gets or sets the degree of the polynomial functions used in each segment of the spline.

public int Degree { get; set; }

Property Value

int

A positive integer, defaulting to 3 (cubic splines).

Remarks

This property specifies the degree of the polynomial functions used in each segment of the spline. The degree determines the maximum power of the independent variable in the polynomial. A degree of 1 creates linear segments, a degree of 2 creates quadratic segments, and a degree of 3 (the default) creates cubic segments. Higher-degree polynomials can capture more complex patterns within each segment but increase the risk of overfitting and numerical instability. Cubic splines (degree 3) are the most commonly used in practice because they provide a good balance between flexibility and stability, and they ensure continuity of the first and second derivatives at the knots, resulting in visually smooth curves. For most applications, cubic splines are sufficient, and increasing the number of knots is generally preferred over increasing the polynomial degree when more flexibility is needed.

For Beginners: This setting controls how curved each segment of the spline can be.

The degree determines:

• The complexity of each individual segment between knots
• How many times the curve can change direction within a segment

The default value of 3 means:

• Cubic splines (3rd-degree polynomials) are used
• Each segment can have up to two changes in direction (like an S-curve)
• The connections between segments will be smooth, with matching slopes and curvatures

Common degree values:

• 1: Linear splines (straight line segments, only smooth at knots)
• 2: Quadratic splines (parabolic segments, smooth with matching slopes at knots)
• 3: Cubic splines (the most common, smooth with matching slopes and curvatures)

When to adjust this value:

• Decrease to 1 or 2 for simpler, more interpretable models
• Keep at 3 (default) for most applications
• Rarely increase above 3, as adding more knots is usually better than increasing degree

For example, cubic splines (degree=3) are commonly used in computer graphics for smooth curve drawing and in data analysis for flexible trend fitting.

NumberOfKnots

Gets or sets the number of knots (internal breakpoints) in the spline function.

public int NumberOfKnots { get; set; }

Property Value

int

A positive integer, defaulting to 3.

Remarks

This property specifies the number of knots or breakpoints used in the spline function. Knots are the points where the different polynomial segments connect. The total number of segments in the spline will be one more than the number of knots. More knots allow the spline to capture more complex patterns in the data but increase the risk of overfitting and the computational complexity. The default value of 3 provides a moderate level of flexibility suitable for many applications. For simpler relationships, fewer knots might be appropriate, while for more complex relationships, more knots might be needed. The optimal number of knots can be determined through cross-validation or by comparing model fit statistics like AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion).

For Beginners: This setting controls how many segments the spline curve will have.

The number of knots determines:

• How many places the curve can change its behavior
• How flexible the overall fit will be

The default value of 3 means:

• The data range will be divided into 4 segments (number of knots + 1)
• Each segment will have its own polynomial curve
• The curves will connect smoothly at the knot points

Think of it like this:

• More knots (e.g., 5 or 10): More flexible curve that can capture complex patterns
• Fewer knots (e.g., 1 or 2): Simpler curve that's less likely to overfit

When to adjust this value:

• Increase it when your data shows complex patterns that change multiple times
• Decrease it when you want a simpler model or have limited data

For example, if modeling temperature throughout a day, 3 knots might allow the curve to capture morning warming, midday plateau, and evening cooling patterns.