Bayesian Inference


How to Improve Political Forecasts - Issue 70: Variables

Nautilus

The 2020 Democratic candidates are out of the gate and the pollsters have the call! Bernie Sanders is leading by two lengths with Kamala Harris and Elizabeth Warren right behind, but Cory Booker and Beto O'Rourke are coming on fast! The political horse-race season is upon us and I bet I know what you are thinking: "Stop!" Every election we complain about horse-race coverage and every election we stay glued to it all the same. The problem with this kind of coverage is not that it's unimportant.


A Multi-armed Bandit MCMC, with applications in sampling from doubly intractable posterior

arXiv.org Artificial Intelligence

Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly intractable problem. In this paper, we discussed and compared two existing solutions -- Pseudo-marginal Monte Carlo and Exchange Algorithm. This paper also proposes a novel algorithm: Multi-armed Bandit MCMC (MABMC), which chooses between two (or more) randomized acceptance ratios in each step. MABMC could be applied directly to incorporate Pseudo-marginal Monte Carlo and Exchange algorithm, with higher average acceptance probability.


Markov Networks: Undirected Graphical Models

#artificialintelligence

This article briefs you about Markov Networks which falls under the family of Undirected Graphical Models (UGM). This article is a follow-up to Bayesian Network, which is a type of Directed Graphical Models. Key Motivation behind these networks is to parameterize the Joint Probability Distribution based on Local Independencies between Random Variables. Generally, Bayesian Network requires to pre-define a directionality to assert an influence of random variable. But there might be cases where interaction between nodes ( or random variables) are symmetric in nature, and we would like to have a model which can represent this symmetricity without directional influence.


Rectangular Bounding Process

arXiv.org Artificial Intelligence

Stochastic partition models divide a multi-dimensional space into a number of rectangular regions, such that the data within each region exhibit certain types of homogeneity. Due to the nature of their partition strategy, existing partition models may create many unnecessary divisions in sparse regions when trying to describe data in dense regions. To avoid this problem we introduce a new parsimonious partition model -- the Rectangular Bounding Process (RBP) -- to efficiently partition multi-dimensional spaces, by employing a bounding strategy to enclose data points within rectangular bounding boxes. Unlike existing approaches, the RBP possesses several attractive theoretical properties that make it a powerful nonparametric partition prior on a hypercube. In particular, the RBP is self-consistent and as such can be directly extended from a finite hypercube to infinite (unbounded) space. We apply the RBP to regression trees and relational models as a flexible partition prior. The experimental results validate the merit of the RBP {in rich yet parsimonious expressiveness} compared to the state-of-the-art methods.


An Introduction to Bayesian Reasoning

#artificialintelligence

The coefficients are constrained by the prior and end up smaller in the second example. Although the model is not fit here with Bayesian techniques, it has a Bayesian interpretation. The output here does not quite give a distribution over the coefficient (though other packages can), but does give something related: a 95% confidence interval around the coefficient, in addition to its point estimate. By now you may have a taste for Bayesian techniques and what they can do for you, from a few simple examples. Things get more interesting, however, when we see what priors and posteriors can do for a real-world use case. For part 2, please click here.


Bayes' Theorem: The Holy Grail of Data Science – Towards Data Science

#artificialintelligence

Bayes' theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probabilities. This theorem has enormous importance in the field of data science. For example one of many applications of Bayes' theorem is the Bayesian inference, a particular approach to statistical inference. Bayesian inference is a method in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.


What is Bayes Theorem? - Machine Learning Interview Questions - DataMites

#artificialintelligence

Bayes theorem in basis for many machine learning algorithm, P(c/x) P(x/c)*P(c)/P(x) Popularly used #Naive #Bayes Machine Learning algorithm is used for Text classification. One of the common question is "What is Bayes Theorem?" watch this video to understand this question and how to explain in the interview. If you are looking for Course Details please visit: https://datamites.com/ You can learn business statistics, tableau, deep learning, data mining etc,..


When Bayes, Ockham, and Shannon come together to define machine learning

#artificialintelligence

Thanks to my CS7641 class at Georgia Tech in my MS Analytics program, where I discovered this concept and was inspired to write about it. It is somewhat surprising that among all the high-flying buzzwords of machine learning, we don't hear much about the one phrase which fuses some of the core concepts of statistical learning, information theory, and natural philosophy into a single three-word-combo. Moreover, it is not just an obscure and pedantic phrase meant for machine learning (ML) Ph.Ds and theoreticians. It has a precise and easily accessible meaning for anyone interested to explore, and a practical pay-off for the practitioners of ML and data science. I am talking about Minimum Description Length.



Beyond Confidence Regions: Tight Bayesian Ambiguity Sets for Robust MDPs

arXiv.org Machine Learning

Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition probabilities---which is usually constructed as a multi-dimensional confidence region. Existing methods construct ambiguity sets as confidence regions using concentration inequalities which leads to overly conservative solutions. This paper proposes a new paradigm that can achieve better solutions with the same robustness guarantees without using confidence regions as ambiguity sets. To incorporate prior knowledge, our algorithms optimize the size and position of ambiguity sets using Bayesian inference. Our theoretical analysis shows the safety of the proposed method, and the empirical results demonstrate its practical promise.