Class BayesianRegressionOptions<T>
Configuration options for Bayesian regression algorithms.
public class BayesianRegressionOptions<T> : RegressionOptions<T>Type Parameters
TThe data type used by the regression model.
- Inheritance
-
BayesianRegressionOptions<T>
- Inherited Members
Remarks
Bayesian regression is a statistical approach that applies Bayes' theorem to regression analysis. Unlike traditional regression which produces point estimates, Bayesian regression provides probability distributions for the model parameters, allowing for uncertainty quantification in predictions.
For Beginners: Bayesian regression is like traditional regression (finding relationships between variables) but with an added layer of confidence information. Instead of just saying "we think y = 2x + 3," Bayesian regression says "we think y = 2x + 3, and we're 90% confident that the 2 is between 1.8 and 2.2." This approach is especially useful when you have limited data or want to incorporate prior knowledge about what the relationship might be. It helps you understand not just what the relationship is, but also how certain you can be about that relationship.
Properties
Alpha
Gets or sets the alpha parameter, which controls the precision of the prior distribution.
public double Alpha { get; set; }Property Value
- double
The alpha value, defaulting to 1.0.
Remarks
In Bayesian statistics, alpha is a hyperparameter for the prior distribution that represents your initial belief about the model parameters before seeing any data.
For Beginners: Think of alpha as how strongly you believe in your initial guess before seeing any data. A higher value (greater than 1.0) means you're more confident in your prior beliefs, while a lower value means you're more willing to let the data speak for itself. The default value of 1.0 represents a balanced approach that doesn't strongly favor either prior beliefs or the observed data. If you're unsure, it's best to start with this default value.
Beta
Gets or sets the beta parameter, which controls the precision of the likelihood function.
public double Beta { get; set; }Property Value
- double
The beta value, defaulting to 1.0.
Remarks
Beta represents the precision (inverse of variance) of the noise in the observed data. Higher values indicate lower noise levels and more confidence in the observed data.
For Beginners: Beta represents how much you trust your data measurements. A higher beta value (greater than 1.0) means you believe your data has less noise or random error, so the algorithm will fit more closely to the observed points. A lower value suggests your data might be noisy, so the algorithm will create a smoother fit that doesn't necessarily pass through every data point. The default value of 1.0 provides a balanced approach for most datasets.
Coef0
Gets or sets the independent term (coef0) in Polynomial and Sigmoid kernels.
public double Coef0 { get; set; }Property Value
- double
The coef0 value, defaulting to 0.0.
Remarks
This parameter is only significant for Polynomial and Sigmoid kernels. For the Polynomial kernel, it controls the degree of homogeneity. For the Sigmoid kernel, it defines the vertical shift.
For Beginners: This is an additional parameter that affects how Polynomial and Sigmoid kernels work. For Polynomial kernels, it adds a constant term to the equation (like the "+c" in "y = x² + x + c"). For Sigmoid kernels, it shifts the S-curve up or down. The default value of 0.0 works well in most cases. You can safely ignore this parameter if you're using the Linear or RBF kernel types.
DecompositionType
Gets or sets the matrix decomposition method used for solving linear systems.
public MatrixDecompositionType DecompositionType { get; set; }Property Value
- MatrixDecompositionType
The decomposition type, defaulting to Lu.
Remarks
Matrix decomposition is a numerical method used to solve the linear algebra problems that arise during Bayesian regression. Different decomposition methods offer trade-offs between numerical stability, computational efficiency, and applicability to different types of matrices.
For Beginners: This is a technical setting about how the math is solved behind the scenes. The default LU decomposition works well for most problems. Other options include:
- Cholesky: Faster but requires positive definite matrices
- QR: More stable for ill-conditioned problems
- SVD: Most stable but slowest option
Gamma
Gets or sets the gamma parameter used in RBF, Polynomial, and Sigmoid kernels.
public double Gamma { get; set; }Property Value
- double
The gamma value, defaulting to 1.0.
Remarks
Gamma defines how far the influence of a single training example reaches, with low values meaning 'far' and high values meaning 'close'. It can be seen as the inverse of the radius of influence of samples selected by the model as support vectors.
For Beginners: Gamma controls how much influence each data point has on its surroundings. Think of it like the radius of influence around each point. A high gamma value means each point only influences predictions very close to it (creating a more complex, potentially wiggly model). A low gamma means each point influences a wider area (creating a smoother model). This parameter only matters when using non-linear kernels like RBF, Polynomial, or Sigmoid. The default value of 1.0 is a good starting point, but you might need to adjust it based on your specific data.
KernelType
Gets or sets the type of kernel function to use in the regression model.
public KernelType KernelType { get; set; }Property Value
- KernelType
The kernel type, defaulting to Linear.
Remarks
The kernel function determines how the algorithm measures similarity between data points, which affects how it generalizes from observed data points to make predictions.
For Beginners: The kernel type determines what kind of relationship the model can find between your variables. The default Linear kernel looks for straight-line relationships (like y = mx + b). Other options include:
- RBF (Radial Basis Function): Can find complex, curvy relationships
- Polynomial: Can find relationships with curves like y = x² + 2x + 1
- Sigmoid: Useful for S-shaped relationships
LaplacianGamma
Gets or sets the gamma parameter for the Laplacian kernel.
public double LaplacianGamma { get; set; }Property Value
- double
The Laplacian gamma value, defaulting to 1.0.
Remarks
This parameter is only used when the KernelType is set to Laplacian. It controls the width of the exponential function in the Laplacian kernel.
For Beginners: This is similar to the regular Gamma parameter, but specifically for the Laplacian kernel (if you choose to use it). The Laplacian kernel is less commonly used than RBF but can be better for certain types of data. A higher value creates a more complex model that fits training data more closely, while a lower value creates a smoother model. The default value of 1.0 is a good starting point if you decide to use the Laplacian kernel. This parameter is ignored if you're using any other kernel type.
PolynomialDegree
Gets or sets the degree of the Polynomial kernel.
public int PolynomialDegree { get; set; }Property Value
- int
The polynomial degree, defaulting to 3.
Remarks
This parameter is only used when the KernelType is set to Polynomial. It determines the highest power in the polynomial equation.
For Beginners: If you're using the Polynomial kernel, this sets the highest power in your equation. For example, a value of 3 (the default) allows the model to find relationships up to cubic terms (like y = ax³ + bx² + cx + d). A higher degree can capture more complex relationships but risks overfitting to your training data. A value of 1 would be equivalent to a linear model, while 2 would allow quadratic relationships. This parameter is ignored if you're not using the Polynomial kernel type.