MATLAB Implementation of Relevance Vector Machine (RVM) with Fast Algorithm

This documentation provides MATLAB source code for Relevance Vector Machine (RVM) implementation, incorporating a fast algorithm with detailed usage instructions. The RVM utilizes a sparse probabilistic model sharing the same functional form as Support Vector Machines, designed for predicting or classifying unknown functions. The implementation features several computational advantages: The MATLAB code implements Bayesian learning through iterative evidence maximization, where the algorithm automatically determines relevant vectors via precision parameters. The core functions handle kernel matrix computation with memory-efficient operations and employ sequential sparse Bayesian learning for model optimization. Key advantages of this RVM implementation include: 1. The algorithm outputs both point estimates and full predictive distributions, allowing comprehensive uncertainty quantification through probabilistic outputs. The code computes posterior distributions using analytical marginal likelihood optimization. 2. Implementation uses significantly fewer relevance vectors compared to support vectors, reducing prediction computational complexity through sparse matrix operations. The fast algorithm employs Cholesky decomposition and rank-1 updates for efficient inverse covariance calculations. 3. The RVM framework requires fewer hyperparameter estimations through automatic relevance determination, simplifying model configuration. The code implements type-II maximum likelihood for automatic parameter tuning. 4. The kernel function implementation has no Mercer theorem restrictions, supporting flexible kernel selections including custom kernel functions. The code structure allows easy integration of linear, RBF, and polynomial kernels through modular function design. These enhancements enable more comprehensive understanding and application of RVM algorithms, yielding improved accuracy in prediction and classification tasks through robust probabilistic modeling and computational efficiency.