This book is very easy to read and understand. Unlike Hastie's Statistical Learning book, it is not geared towards those with an expert level knowledge of statistics, and instead takes time to explain functions and formulas for the person with a decent but not extrordinary understanding of statistical/math concepts. For example, their description of a Gaussian was the clearest I've seen. On the other hand, if you're math/statistics background is considerable, you may find this book somewhat simplistic or tedious. The book has a good coverage of techniques and algorithms, although I was somewhat disappointed that they do not mention Influence Diagrams, considering the amount of coverage of both decision trees and Bayesian techniques.
We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.
Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily account for explanatory variables and share statistical strength across groups of related time series. We derive an efficient approximate inference technique, and illustrate its performance on a number of datasets from supply chain planning.
Massive transaction data sets are recorded in a routine manner in telecommunications, retail commerce, and Web site management. In this paper we address the problem of inferring predictive individual profilesfrom such historical transaction data. We describe a generative mixture model for count data and use an an approximate Bayesian estimation framework that effectively combines anindividual's specific history with more general population patterns. We use a large real-world retail transaction data set to illustrate how these profiles consistently outperform non-mixture and non-Bayesian techniques in predicting customer behavior in out-of-sample data.
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Recent work has shown that using a low-rank factorization of this kernel provides remarkable scalability improvements that open the door to training on large-scale datasets and computing online recommendations, both of which are infeasible with standard DPP models that use a full-rank kernel. In this paper we present a low-rank DPP mixture model that allows us to represent the latent structure present in observed subsets as a mixture of a number of component low-rank DPPs, where each component DPP is responsible for representing a portion of the observed data. The mixture model allows us to effectively address the capacity constraints of the low-rank DPP model. We present an efficient and scalable Markov Chain Monte Carlo (MCMC) learning algorithm for our model that uses Gibbs sampling and stochastic gradient Hamiltonian Monte Carlo (SGHMC). Using an evaluation on several real-world product recommendation datasets, we show that our low-rank DPP mixture model provides substantially better predictive performance than is possible with a single low-rank or full-rank DPP, and significantly better performance than several other competing recommendation methods in many cases.