🚀 GPredict — Gaussian Process Regression Framework

GPredict is a Python framework for Gaussian Process (GP) regression, designed for predictive modeling and principled uncertainty quantification.

It implements non-parametric Bayesian regression using customizable mean functions and kernel methods, providing posterior predictions with calibrated confidence intervals and predictive sampling.

Author: Kevin Mota da Costa

Portfolio: https://costakevinn.github.io

LinkedIn: https://linkedin.com/in/costakevinnn

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🎯 Project Purpose

GPredict was built to explore regression from a fully probabilistic perspective.

Unlike parametric neural networks, Gaussian Processes:

• Model functions as distributions
• Provide closed-form posterior inference
• Naturally quantify predictive uncertainty
• Adapt complexity to the data

This project reflects a statistical-first engineering approach to regression modeling.

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🧠 Gaussian Process Formulation

The model assumes:

f(x) ~ GaussianProcess( m(x), k(x, x') )

Where:

• m(x) → mean function (constant or linear)
• k(x, x') → covariance kernel (RBF or Matern)
• Observational noise is modeled via a diagonal noise matrix

Posterior prediction yields:

• Predictive mean
• Predictive variance
• Full covariance structure
• Posterior samples

This enables non-parametric regression with uncertainty-aware predictions.

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🏗 System Architecture

The framework is modular:

• Mean functions (constant, linear)
• Kernel functions (RBF, Matern)
• Covariance matrix construction
• Noise modeling (heteroscedastic support)
• Posterior computation
• Predictive sampling
• Visualization & result export

All components are cleanly separated for extensibility and experimentation.

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📊 Example: Sinusoidal Regression

Function: sin(x) Observations: 20 points with heteroscedastic noise

Prior vs Posterior

Prior	Posterior

• Prior: expresses assumptions before observing data
• Posterior: updates mean and uncertainty using Bayesian inference

The posterior captures:

• Global structure
• Local smoothness
• Increased uncertainty away from data points

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🔬 Posterior Inference Mechanics

Given training data, GPredict computes:

• Predictive mean via covariance-weighted interpolation
• Predictive covariance via posterior update
• Predictive trajectories via sampling from multivariate normal

Noise is incorporated explicitly in the covariance matrix, allowing realistic predictive intervals.

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📈 Capabilities Demonstrated

• Non-parametric regression modeling
• Kernel engineering (RBF, Matern)
• Bayesian posterior computation
• Heteroscedastic noise handling
• Predictive sampling
• Visualization of uncertainty bands
• Reproducible probabilistic workflows

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📚 Engineering Decisions

• Modular separation of kernels, means, and inference
• Explicit covariance construction for transparency
• Analytical posterior computation (no black-box frameworks)
• Fixed random seed for reproducibility
• Structured output generation (data, plots, results)

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🛠 Tech Stack

Python

NumPy

Linear algebra (matrix inversion & covariance operations)

Bayesian inference

Kernel methods

Scientific visualization

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▶ Usage

python3 main.py

Outputs:

• data/ → observational datasets
• plots/ → GP prior & posterior visualizations
• results/ → numerical predictive summaries

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📁 Project Structure

GPredict/
├── data/          # Observations
├── plots/         # Prior and posterior plots
├── results/       # Predictive summaries
├── gp.py          # GP fitting and prediction
├── kernels.py     # Kernel definitions
├── means.py       # Mean functions
├── utils.py       # Plotting utilities
├── examples.py    # Example workflows
└── main.py        # Entry point

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🌐 Portfolio

This project is part of my Machine Learning portfolio: 👉 https://costakevinn.github.io

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License

MIT License — see LICENSE for details.