The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Markov chain designed to overcome bottlenecks that impede the Gibbs sampler. We prove O(\log n) mixing time for attractive binary pairwise GMs (i.e., ferromagnetic Ising models) on stochastic partitioned graphs having n vertices, under some mild conditions, including low temperature regions where the Gibbs sampler provably mixes exponentially slow. Our experiments also confirm that the Swendsen-Wang sampler significantly outperforms the Gibbs sampler when they are used for learning parameters of attractive GMs.

In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we first derive a formula for computing the gradient of the Lagrangian function for percentile risk-constrained MDPs. Then, we devise policy gradient and actor-critic algorithms that (1) estimate such gradient, (2) update the policy in the descent direction, and (3) update the Lagrange multiplier in the ascent direction. For these algorithms we prove convergence to locally optimal policies. Finally, we demonstrate the effectiveness of our algorithms in an optimal stopping problem and an online marketing application.

This does not want to be an exhaustive list of skills for data scientists because the field is moving at a stellar speed (and a tool that is relevant today might not be relevant in six months). It is rather an attempt to provide an extensive list of skills and tools that are useful in developing data science projects, and of course not owning one of those skills do not preclude a data scientist to be identified as such. Note: the above is an adapted excerpt from my book "Big Data Analytics: A Management Perspective" (Springer, 2016).

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available.

This page aims to be a comprehensive collection of publicly available models and algorithms used for credit scoring. The credit scoring model collection focuses on the classic one period credit assessment / classification problem that typically produces a credit score and/or a probabilistic estimate of credit risk on the basis of selected characteristics of a borrower. Credit scoring models have been used globally for decades and in a variety of contexts. The significant overlap of credit scoring methodology with other statistical disciplines means that the entire arsenal of statistical methods has been available and tried with varying degrees of success, usability and adoption. We identify here some key model attributes that can help categorize the variety of models.

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity.

This paper presents an algorithm for the unsupervised learning of latent variable models from unlabeled sets of data. We base our technique on spectral decomposition, providing a technique that proves to be robust both in theory and in practice. We also describe how to use this algorithm to learn the parameters of two well known text mining models: single topic model and Latent Dirichlet Allocation, providing in both cases an efficient technique to retrieve the parameters to feed the algorithm. We compare the results of our algorithm with those of existing algorithms on synthetic data, and we provide examples of applications to real world text corpora for both single topic model and LDA, obtaining meaningful results.

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

The AMIDST Toolbox is a software for scalable probabilistic machine learning with a spe- cial focus on (massive) streaming data. The toolbox supports a flexible modeling language based on probabilistic graphical models with latent variables and temporal dependencies. The specified models can be learnt from large data sets using parallel or distributed implementa- tions of Bayesian learning algorithms for either streaming or batch data. These algorithms are based on a flexible variational message passing scheme, which supports discrete and continu- ous variables from a wide range of probability distributions. AMIDST also leverages existing functionality and algorithms by interfacing to software tools such as Flink, Spark, MOA, Weka, R and HUGIN. AMIDST is an open source toolbox written in Java and available at http://www.amidsttoolbox.com under the Apache Software License version 2.0.

In this tutorial we will begin by laying out a problem and then proceed to show a simple solution to it using a Machine Learning technique called a Naive Bayes Classifier. This tutorial requires a little bit of programming and statistics experience, but no prior Machine Learning experience is required. You work as a software engineer at a company which provides email services to millions of people. Lately, spam has a been a major problem and has caused your customers to leave. Your current spam filter only filters out emails that have been previously marked as spam by your customers.