Bayesian Neural Networks (BNNs) represent a fusion of two powerful concepts in machine learning: neural networks and Bayesian inference. While traditional neural networks are deterministic and lack a natural way to account for uncertainty, Bayesian Neural Networks introduce a probabilistic …
Bayesian Neural Networks – A comprehensive review More details
The Metropolis-Hastings algorithm is a Markov Chain Monte Carlo (MCMC) method widely used for generating samples from a probability distribution, especially when direct sampling is challenging or impractical. The primary goal of the Metropolis-Hastings algorithm is to simulate a Markov …
Markov chain and The Metropolis-Hastings algorithm More details
Although it is also called a sampling method, the technique of importance sampling provides a framework for approximating expectations directly but does not itself provide a mechanism for drawing samples from distribution $p(\mathbf{z})$, like inverse transform sampling discussed in the last post. The …
Inverse Transform Sampling is a powerful technique used in probability and statistics to generate random samples from a desired probability distribution. The method relies on the cumulative distribution function (CDF) of the target distribution and its inverse. The key idea …
Note: The content of this post is largely inspired by the book “Gaussian Process for Machine Learning” Click here for the link of the book. For most interesting models for machine learning, the required computations (integrals over parameter space, $p(\mathbf{y} …
Bayesian Model Selection for Gaussian Processes More details
Unlike traditional model selection methods that rely on frequentist statistics, Bayesian Model Selection provides a coherent and probabilistic approach to assess the relative merits of competing models. At its core, Bayesian Model Selection incorporates prior knowledge or beliefs about model …
Apart from classification, Support Vector Machine models can also be applied to regression problem, and is often called Support Vector Regression (SVR). The fundamental idea behind SVR is to find a hyperplane in a high-dimensional space that best captures the …
At its core, Support Vector Machine aims to find the optimal hyperplane that separates data points belonging to different classes with the maximum margin. The term “support vectors” refers to the data points that lie closest to the decision boundary, …
We have look at how to apply the method of Gaussian Processes to the problem of regression, let us now explore the application of Gaussian Processes to classification. As we will discover, many of the integral used in the formulation …
In the first few posts I created on the site, we have discussed about Gaussian Processes and how these models can be used in the problem of regression, as shown in the book “Gaussian Processes for Machine Learning” by Rasmussen. …
