This article was posted by Sunil Ray. Sunil is a Business Analytics and BI professional. Here's a situation you've got into: You are working on a classification problem and you have generated your set of hypothesis, created features and discussed the importance of variables. Within an hour, stakeholders want to see the first cut of the model. You have hunderds of thousands of data points and quite a few variables in your training data set.

Social dilemmas have been regarded as the essence of evolution game theory, in which the prisoner's dilemma game is the most famous metaphor for the problem of cooperation. Recent findings revealed people's behavior violated the Sure Thing Principle in such games. Classic probability methodologies have difficulty explaining the underlying mechanisms of people's behavior. In this paper, a novel quantum-like Bayesian Network was proposed to accommodate the paradoxical phenomenon. The special network can take interference into consideration, which is likely to be an efficient way to describe the underlying mechanism. With the assistance of belief entropy, named as Deng entropy, the paper proposes Belief Distance to render the model practical. Tested with empirical data, the proposed model is proved to be predictable and effective.

Department of Informatics, King's College London; osvaldo.simeone@kcl.ac.uk ABSTRACT This monograph aims at providing an introduction to key concepts, algorithms, and theoretical frameworks in machine learning, including supervised and unsupervised learning, statistical learning theory, probabilistic graphical models and approximate inference. The intended readership consists of electrical engineers with a background in probability and linear algebra. The treatment builds on first principles, and organizes the main ideas according to clearly defined categories, such as discriminative and generative models, frequentist and Bayesian approaches, exact and approximate inference, directed and undirected models, and convex and non-convex optimization. The mathematical framework uses information-theoretic measures as a unifying tool. The text offers simple and reproducible numerical examples providing insights into key motivations and conclusions. Rather than providing exhaustive details on the existing myriad solutions in each specific category, for which the reader is referred to textbooks and papers, this monograph is meant as an entry point for an engineer into the literature on machine learning.

This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions. Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates. Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a data set is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Monte Carlo sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster. This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks. Keywords: Distributed Learning, Large Scale Learning, Deep Learning, Bayesian Learn- ing, Variational Inference, Expectation Propagation, Stochastic Approximation, Natural Gradient, Markov chain Monte Carlo, Parameter Server, Posterior Server.

Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and Sun, and information measure introduced by Lindley. A combination of theoretical, empirical, and computational support provides evidence that these information-theoretic metrics may be useful diagnostic tools when performing a Bayesian analysis.

If you search around the internet looking for applying Naive Bayes classification on text, you'll find a ton of articles that talk about the intuition behind the algorithm, maybe some slides from a lecture about the math and some notation behind it, and a bunch of articles I'm not going to link here that pretty much just paste some code and call it an explanation. So I'm going to try to do a little more here, by hopefully writing and explaining enough, is let you yourself write a working Naive Bayes classifier. There are three sections here. First is setup, and what format I'm expecting your text to be in for the classification. Second, I'll talk about how to run naive Bayes on your own, using slow Python data structures.

Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate. In this paper, we prove that under a limited computational budget/time, a larger minibatch size leads to a faster decrease of the mean squared error bound (thus the fastest one corresponds to using full gradients), which motivates the necessity of variance reduction in SG-MCMC. Consequently, by borrowing ideas from stochastic optimization, we propose a practical variance-reduction technique for SG-MCMC, that is efficient in both computation and storage. We develop theory to prove that our algorithm induces a faster convergence rate than standard SG-MCMC. A number of large-scale experiments, ranging from Bayesian learning of logistic regression to deep neural networks, validate the theory and demonstrate the superiority of the proposed variance-reduction SG-MCMC framework.

In essence, people who interact with advanced technology want to be able to trust it appropriately, and then act on that trust. In interpersonal relationships, and otherwise, humans act largely based on trust. For example, a supervisor asks a subordinate to accomplish a task based on several factors that indicate they can trust them to accomplish that task. When consumers make purchases, they do so with trust that the product will perform as promised. Likewise, when using something like an autonomous vehicle, the user must be able to trust it appropriately in order to use it properly. With the rapid advancement of the capabilities of intelligent computing technology to do tasks that were previously assumed to be too complicated for computers, there has been much recent discussion regarding how humans can trust this technology - although the connection to trust is not always made explicit, per se.

In this article, we look at two machine learning (ML) techniques, Naive Bayes classifier and neural networks, and demystify how they work. With all the hype surrounding self-driving cars and video-game-playing AI robots, it's worth taking a step back and reminding ourselves how machine learning programs actually "learn". In this article, we look at two machine learning (ML) techniques–spam filters and neural networks–and demystify how they work. And if you're not sure what machine learning even is, read about the difference between artificial intelligence, machine learning, and deep learning. One common machine learning algorithm is the Naive Bayes classifier, which is used for filtering spam emails.

Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different statistical learning models. We will propose a new two-stage scaling method. First, we use some training data to fit linear regression model and then scale the whole data based on the coefficients of regression. Simulations are conducted to illustrate the advantages of our new scaling method. Some real data analysis will also be given.