Statistics

2009 Submissions

[2] viXra:2009.0135 [pdf] replaced on 2021-07-11 15:23:07

A Joint Introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman Filtering and Other Kernel Smoothers

Authors: L. Martino, J. Read
Comments: L. Martino, J. Read, "A Joint introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman filtering and other Kernel Smoothers", Information Fusion, Volume 74, Pages 17-38, 2021

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and interpretability via uncertainty analysis. This article introduces and discusses two methods which straddle the areas of probabilistic Bayesian schemes and kernel methods for regression: Gaussian Processes and Relevance Vector Machines. Our focus is on developing a common framework with which to view these methods, via intermediate methods a probabilistic version of the well-known kernel ridge regression, and drawing connections among them, via dual formulations, and discussion of their application in the context of major tasks: regression, smoothing, interpolation, and filtering. Overall, we provide understanding of the mathematical concepts behind these models, and we summarize and discuss in depth different interpretations and highlight the relationship to other methods, such as linear kernel smoothers, Kalman filtering and Fourier approximations. Throughout, we provide numerous figures to promote understanding, and we make numerous recommendations to practitioners. Benefits and drawbacks of the different techniques are highlighted. To our knowledge, this is the most in-depth study of its kind to date focused on these two methods, and will be relevant to theoretical understanding and practitioners throughout the domains of data-science, signal processing, machine learning, and artificial intelligence in general.
Category: Statistics

[1] viXra:2009.0082 [pdf] submitted on 2020-09-12 12:49:17

Importance of Statistical Tools and Methods in Data Science

Authors: Krish Bajaj
Comments: 10 Pages.

This paper aims to highlight the prominent position of statistics as a foundational pillar for descriptive and inferential statistical analysis to deduce underlying patterns in a population by looking at a sample drawn from the population. It focusses on the intuitive aspects of the statistical tools and its relevance and applicability .The paper concludes by highlighting some common misconceptions and misuse of statistics.
Category: Statistics