Add Gaussian Process Regression

[AtharvaPatange]

Overview
This implementation defines a Gaussian Process (GP) regression model in R using the kernlab package. GP is a non-parametric Bayesian regression algorithm that predicts continuous outputs while providing uncertainty estimates. It models a prior over functions via a kernel and updates the posterior distribution using observed data.

Features

Performs regression with uncertainty quantification for predictions.
Supports small datasets effectively and works well with sparse data.
Uses a kernel function (e.g., RBF) to define similarity between data points.
Provides mean and variance (confidence) for each prediction.
Handles non-linear relationships automatically through the kernel.
Demonstrates predictions on synthetic or real regression datasets.
Plotting functionality included for visualizing predictions against observations.

Complexity

Time Complexity: O(n³) due to kernel matrix inversion

Space Complexity: O(n²) for storing the kernel matrix

Demonstration

The included R script trains a GP model on a synthetic sine-wave dataset with noise.
Predictions are made on test inputs, including plotting mean predictions.
Replace x and y with other datasets for custom regression tasks.
For large datasets, consider sparse GP approximations.

[Copilot]

Pull Request Overview

Adds a Gaussian Process (GP) regression example using kernlab, alongside new k-NN, CNN, and Kadane’s algorithm scripts. Key changes:

• Introduces a GP regression script with rbfdot kernel and plotting.
• Adds a from-scratch k-NN implementation with classification/regression and examples.
• Adds Kadane’s algorithm and a simple CNN architecture example.

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 8 comments.

File	Description
machine_learning/guassian_process.r	New GP regression script using kernlab with example and plotting
machine_learning/k-NN.r	New k-NN implementation (classification/regression) with normalization and examples
machine_learning/cnn.r	CNN architecture definition using keras; prints model summary
dynamic_programming/kadane's_algo.r	Kadane’s algorithm with examples and a circular variant

[Copilot]

Pull Request Overview

Copilot reviewed 4 out of 4 changed files in this pull request and generated 6 comments.

[Copilot]

Pull Request Overview

Copilot reviewed 4 out of 4 changed files in this pull request and generated 7 comments.

[siriak]

Please resolve conflicts

[siriak]

This algorithm is already implemented

[Copilot]

Pull Request Overview

Copilot reviewed 4 out of 4 changed files in this pull request and generated 2 comments.

[Copilot]

Filename contains typo: 'guassian_process.r' should be 'gaussian_process.r' (missing 'i' in Gaussian).

[Copilot]

File extension must be lowercase '.r'. The filename 'guassian_process.r' uses lowercase extension, which is correct, but the filename itself contains a spelling error ('guassian' instead of 'gaussian'). Please rename to 'gaussian_process.r'.