Class GaussianProcessRegressionOptions
Configuration options for Gaussian Process Regression, a flexible non-parametric approach to regression that provides uncertainty estimates along with predictions.
public class GaussianProcessRegressionOptions : NonLinearRegressionOptions- Inheritance
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GaussianProcessRegressionOptions
- Inherited Members
Remarks
Gaussian Process Regression (GPR) is a powerful machine learning technique that models the target function as a sample from a Gaussian process. Unlike many other regression methods, GPR not only provides point predictions but also uncertainty estimates, making it valuable for applications where understanding prediction confidence is important.
For Beginners: Think of Gaussian Process Regression as drawing a smooth curve through your data points, but instead of just giving you one "best" curve, it gives you a range of possible curves with information about which ones are more likely. This is like a weather forecast that says "70°F with a 90% chance of being between 65-75°F" rather than just "70°F." This ability to express uncertainty makes GPR especially useful when you need to know not just what your model predicts, but how confident it is in those predictions. GPR works well with small to medium datasets and can capture complex patterns without requiring you to specify the exact form of the relationship beforehand.
Properties
DecompositionType
Gets or sets the type of matrix decomposition to use for numerical stability.
public MatrixDecompositionType DecompositionType { get; set; }Property Value
- MatrixDecompositionType
The matrix decomposition type, defaulting to Cholesky.
Remarks
Gaussian Process Regression involves inverting a covariance matrix, which can be numerically challenging. Different decomposition methods offer trade-offs between speed, stability, and accuracy. Cholesky decomposition is generally fast and stable for well-conditioned matrices, while other methods may be more robust for ill-conditioned matrices.
For Beginners: This setting determines the mathematical technique used to solve the internal equations in the model. With the default value of Cholesky, the model uses a standard method that works well in most cases. Think of it like choosing which route to take to a destination - different methods have different trade-offs in terms of speed and reliability. For most users, the default Cholesky decomposition is the best choice. You might consider changing this only if you encounter numerical errors or if you're working with a very large dataset where computational efficiency becomes critical. Unless you have a background in numerical linear algebra, it's best to leave this at the default setting.
LengthScale
Gets or sets the length scale parameter for the Gaussian Process kernel.
public double LengthScale { get; set; }Property Value
- double
The length scale, defaulting to 1.0.
Remarks
The length scale controls how rapidly the correlation between points decreases with distance. Smaller values make the model more sensitive to small-scale variations, creating more complex and wiggly functions. Larger values make the model focus on broader trends, creating smoother functions.
For Beginners: This setting controls how "wiggly" or "smooth" your model's predictions will be. With the default value of 1.0, the model uses a standard level of smoothness. Think of it like adjusting the flexibility of a rubber band - a smaller length scale (like 0.1) creates a very flexible model that can make sharp turns and follow the data closely, while a larger length scale (like 10.0) creates a stiffer model that makes gentler, more gradual changes. If your data has rapid changes or fine structure, use a smaller length scale. If your data follows broader, smoother trends, use a larger length scale. If OptimizeHyperparameters is true, this value is just used as a starting point for optimization.
NoiseLevel
Gets or sets the assumed noise level in the observations.
public double NoiseLevel { get; set; }Property Value
- double
The noise level, defaulting to 0.00001 (1e-5).
Remarks
This parameter represents the expected amount of random noise or measurement error in the target values. It adds a small value to the diagonal of the covariance matrix to improve numerical stability and account for noise in the observations. Higher values assume more noise in the data and lead to smoother predictions.
For Beginners: This setting tells the model how much random error or "noise" to expect in your data. With the default value of 0.00001, the model assumes your data is very precise with minimal random fluctuations. Think of it like the difference between measuring something with a ruler versus a high-precision laser - the laser measurements have less noise. If your data comes from real-world measurements that might contain errors or random variations, you should increase this value (perhaps to 0.01 or 0.1). Higher values make the model less likely to try fitting to every tiny fluctuation in your data, resulting in smoother predictions. If your model is overfitting (following the training data too closely), increasing this value often helps.
OptimizeHyperparameters
Gets or sets whether to automatically optimize the hyperparameters (length scale and signal variance) based on the training data.
public bool OptimizeHyperparameters { get; set; }Property Value
- bool
Whether to optimize hyperparameters, defaulting to false.
Remarks
When set to true, the model will use maximum likelihood estimation to find optimal values for the length scale and signal variance hyperparameters. This can improve model performance but increases training time. When false, the model uses the manually specified values.
For Beginners: This setting determines whether the model should automatically tune its internal parameters to best fit your data. With the default value of false, you need to manually set the LengthScale and SignalVariance parameters. Setting this to true is like enabling "auto-tune" - the model will try different parameter values and pick the ones that work best for your specific data. This automatic optimization usually improves results but makes training slower. For beginners, it's often best to set this to true unless you have specific knowledge about appropriate parameter values for your problem or need faster training times.
SignalVariance
Gets or sets the signal variance parameter for the Gaussian Process kernel.
public double SignalVariance { get; set; }Property Value
- double
The signal variance, defaulting to 1.0.
Remarks
The signal variance controls the overall magnitude of variations in the function. Larger values allow for larger deviations from the mean function, while smaller values constrain the function to stay closer to the mean. This parameter affects the overall scale of the uncertainty estimates.
For Beginners: This setting controls how much your model's predictions can vary overall. With the default value of 1.0, the model allows for a standard level of variation. Think of it like adjusting the volume on a speaker - a higher signal variance (like 2.0) allows the model to make more dramatic changes in its predictions, while a lower value (like 0.5) keeps predictions more conservative and closer to the average. If your target values have a wide range or large fluctuations, you might increase this value. If your target values stay within a narrow range, you might decrease it. If OptimizeHyperparameters is true, this value is just used as a starting point for optimization.