Class KernelRidgeRegressionOptions
Configuration options for Kernel Ridge Regression, which combines ridge regression with the kernel trick to model non-linear relationships in data.
public class KernelRidgeRegressionOptions : NonLinearRegressionOptions- Inheritance
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KernelRidgeRegressionOptions
- Inherited Members
Remarks
Kernel Ridge Regression (KRR) extends standard ridge regression by applying the "kernel trick" to implicitly map input features into a higher-dimensional space where linear relationships can better capture complex patterns in the data. This allows the model to learn non-linear relationships while still maintaining the computational benefits and regularization of ridge regression.
For Beginners: Kernel Ridge Regression is a powerful technique that helps your model capture complex, non-linear patterns in your data.
Imagine you have data points that can't be fit well with a straight line. For example, the relationship between a car's speed and its fuel efficiency might be more of a U-shape (very efficient at moderate speeds, less efficient at very low or very high speeds). Kernel Ridge Regression can help model these curved relationships.
The "kernel trick" is like giving your model special glasses that let it see your data transformed in a way that makes complex patterns easier to find. Instead of trying to fit a straight line to a curve, it transforms the problem so that a straight line in the transformed space corresponds to a curve in the original space.
The "ridge" part helps prevent overfitting by keeping the model from becoming too complex, similar to how guardrails keep a car on the road.
This class inherits from NonLinearRegressionOptions, so all the general non-linear regression settings are also available. The additional settings specific to Kernel Ridge Regression let you fine-tune how the algorithm balances fitting the data versus keeping the model simple.
Properties
DecompositionType
Gets or sets the type of matrix decomposition used to solve the kernel ridge regression equations.
public MatrixDecompositionType DecompositionType { get; set; }Property Value
- MatrixDecompositionType
The matrix decomposition type, defaulting to Cholesky.
Remarks
Different matrix decomposition methods offer different trade-offs between numerical stability, computational efficiency, and applicability to specific types of kernel matrices. Cholesky decomposition is generally faster but requires the kernel matrix to be positive definite, while SVD (Singular Value Decomposition) is more robust but computationally more expensive.
For Beginners: This setting determines the mathematical method used to solve the equations in Kernel Ridge Regression. The default value (Cholesky) works well for most cases and is computationally efficient.
Think of matrix decomposition like solving a complex puzzle. There are different strategies to solve the puzzle, each with its own advantages:
Cholesky decomposition (the default) is like a fast, efficient strategy that works well for most standard puzzles. It's quick but might struggle with certain unusual puzzle types.
SVD (Singular Value Decomposition) is like a more thorough, methodical strategy that can handle even the most challenging puzzles, but takes longer to complete.
QR decomposition falls somewhere in between, offering a balance of robustness and efficiency.
Most beginners should stick with the default Cholesky decomposition. You might consider changing this setting if:
- You encounter numerical stability issues (error messages about matrix decomposition)
- You're working with a very large dataset and need to optimize performance
- You're using a specialized kernel function that creates unusual kernel matrices
In these cases, trying a different decomposition type might help resolve issues or improve performance.
LambdaKRR
Gets or sets the regularization parameter (lambda) for Kernel Ridge Regression.
public double LambdaKRR { get; set; }Property Value
- double
The regularization parameter, defaulting to 1.0.
Remarks
This parameter controls the strength of regularization applied to the model. Higher values result in stronger regularization, which helps prevent overfitting but may cause underfitting if set too high. Lower values allow the model to fit the training data more closely but may lead to overfitting if set too low.
For Beginners: This setting controls how much the model prioritizes simplicity versus fitting the training data perfectly. With the default value of 1.0, the model tries to balance these two goals.
Think of it like adjusting the tension on a spring:
- Higher values (e.g., 10.0) create more tension, pulling the model toward simplicity. This helps prevent overfitting (where the model memorizes the training data but performs poorly on new data), but if set too high, the model might be too simple to capture important patterns (underfitting).
- Lower values (e.g., 0.1) reduce the tension, allowing the model to fit the training data more closely. This can help capture complex patterns, but if set too low, the model might start fitting to noise in the data (overfitting).
Finding the right value often requires experimentation. You might start with the default of 1.0 and then try values that are 10 times larger (10.0) or smaller (0.1) to see how they affect performance. Many practitioners use techniques like cross-validation to find the optimal value for their specific dataset.