Table of Contents

Interface IGaussianProcess<T>

Namespace
AiDotNet.Interfaces
Assembly
AiDotNet.dll

Defines an interface for Gaussian Process regression, a powerful probabilistic machine learning technique.

public interface IGaussianProcess<T>

Type Parameters

T

The numeric type used for calculations (e.g., double, float).

Remarks

For Beginners: A Gaussian Process is a flexible machine learning approach that not only makes predictions but also tells you how confident it is about each prediction.

Imagine you're trying to predict house prices in different neighborhoods:

  • Traditional models might just say "this house costs $300,000"
  • A Gaussian Process would say "this house costs about $300,000, and I'm very confident the price is between $290,000 and $310,000"

This is especially useful when:

  • You have limited data
  • You need to know how certain the model is about its predictions
  • You want to make decisions that account for uncertainty

Unlike many other machine learning methods, Gaussian Processes:

  • Don't assume a specific form for the relationship between inputs and outputs
  • Automatically adapt to the complexity of your data
  • Provide uncertainty estimates for each prediction

The "Gaussian" part refers to the normal distribution (bell curve) used to represent uncertainty. The "Process" part means it works with functions rather than simple values.

Methods

Fit(Matrix<T>, Vector<T>)

Trains the Gaussian Process model on the provided data.

void Fit(Matrix<T> X, Vector<T> y)

Parameters

X Matrix<T>

The input features matrix, where each row represents an observation and each column represents a feature.

y Vector<T>

The target values vector corresponding to each observation in X.

Remarks

For Beginners: This method teaches the model using your training data.

The parameters:

  • X: Your input data organized as a matrix (a table of numbers)
    • Each row represents one example (like one house)
    • Each column represents one feature (like size, location, age of the house)
  • y: Your output data as a vector (a list of numbers)
    • Each value is what you want to predict (like the price of each house)

During fitting, the Gaussian Process:

  1. Analyzes patterns in your data
  2. Learns how different features relate to the target values
  3. Builds an internal model of the relationships
  4. Prepares to make predictions with uncertainty estimates

Unlike many other models, Gaussian Processes don't just find coefficients or weights. Instead, they remember the training data and use it directly when making predictions.

Predict(Vector<T>)

Predicts the mean value and variance (uncertainty) for a new input point.

(T mean, T variance) Predict(Vector<T> x)

Parameters

x Vector<T>

The input feature vector for which to make a prediction.

Returns

(T Accuracy, T Loss)

A tuple containing the predicted mean value and the variance (uncertainty) of the prediction.

Remarks

For Beginners: This method makes a prediction and tells you how confident it is about that prediction.

The parameter:

  • x: The features of the new example you want to predict (like the size, location, and age of a house)

The method returns two values:

  1. mean: The predicted value (like the estimated house price)
  2. variance: How uncertain the model is about this prediction
    • A small variance means the model is confident (narrow range of likely values)
    • A large variance means the model is uncertain (wide range of possible values)

This uncertainty information is what makes Gaussian Processes special. It helps you:

  • Know when to trust or question the model's predictions
  • Identify areas where you need more training data
  • Make better decisions when the prediction is uncertain

For example, if predicting house prices:

  • "This house costs $300,000 ± $5,000" (low variance, high confidence)
  • "This house costs $300,000 ± $50,000" (high variance, low confidence)

UpdateKernel(IKernelFunction<T>)

Updates the kernel function used by the Gaussian Process.

void UpdateKernel(IKernelFunction<T> kernel)

Parameters

kernel IKernelFunction<T>

The new kernel function to use.

Remarks

For Beginners: This method changes how the model measures similarity between data points.

The parameter:

  • kernel: A function that determines how similar two data points are

The kernel function is at the heart of a Gaussian Process. It defines:

  • How influence spreads between data points
  • What patterns the model can recognize (linear, periodic, etc.)
  • How smooth the resulting predictions will be

Think of the kernel as defining the "personality" of your model:

  • Some kernels make the model see smooth, gradual changes
  • Others allow the model to capture more abrupt changes
  • Some can detect periodic patterns (like seasonal effects)

Changing the kernel can dramatically change how your model behaves, even with the same training data. This method allows you to update the kernel without retraining the entire model from scratch.

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