Priors on the Variance in Sparse Bayesian Learning; the demi-Bayesian Lasso

We explore the use of proper priors for variance parameters of certain sparse Bayesian regression models. This leads to a connection between sparse Bayesian learning (SBL) models (Tipping, 2001) and the recently proposed Bayesian Lasso (Park and Casella, 2008). We outline simple modifications of existing algorithms to solve this new variant which essentially uses type-II maximum likelihood to fit the Bayesian Lasso model. We also propose an Elastic-net (Zou and Hastie, 2005) heuristic to help with modeling correlated inputs. Experimental results show the proposals to compare favorably to both the Lasso and traditional and more recent sparse Bayesian algorithms

Sequential Event Prediction

In sequential event prediction, we are given a “sequence database” of past event sequences to learn from, and we aim to predict the next event within a current event sequence. We focus on applications where the set of the past events has predictive power and not the specific order of those past events. Such applications arise in recommender systems, equipment maintenance, medical informatics, and in other domains. Our formalization of sequential event prediction draws on ideas from supervised ranking. We show how specific choices within this approach lead to different sequential event prediction problems and algorithms. In recommender system applications, the observed sequence of events depends on user choices, which may be influenced by the recommendations, which are themselves tailored to the user’s choices. This leads to sequential event prediction algorithms involving a non-convex optimization problem. We apply our approach to an online grocery store recommender system, email recipient recommendation, and a novel application in the health event prediction domain

Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University

Bayesian Hierarchical Rule Modeling for Predicting Medical Conditions

We propose a statistical modeling technique, called the Hierarchical Association Rule Model (HARM), that predicts a patient’s possible future medical conditions given the patient’s current and past history of reported conditions. The core of our technique is a Bayesian hierarchical model for selecting predictive association rules (such as “condition 1 and condition 2 → condition 3”) from a large set of candidate rules. Because this method “borrows strength” using the conditions of many similar patients, it is able to provide predictions specialized to any given patient, even when little information about the patient’s history of conditions is available.National Science Foundation (U.S.) (NSF Grant IIS-10-53407)Google (Firm) (Ph.D. fellowship in statistics

Learning Theory Analysis for Association Rules and Sequential Event Prediction

We present a theoretical analysis for prediction algorithms based on association rules. As part of this analysis, we introduce a problem for which rules are particularly natural, called “sequential event prediction." In sequential event prediction, events in a sequence are revealed one by one, and the goal is to determine which event will next be revealed. The training set is a collection of past sequences of events. An example application is to predict which item will next be placed into a customer's online shopping cart, given his/her past purchases. In the context of this problem, algorithms based on association rules have distinct advantages over classical statistical and machine learning methods: they look at correlations based on subsets of co-occurring past events (items a and b imply item c), they can be applied to the sequential event prediction problem in a natural way, they can potentially handle the “cold start" problem where the training set is small, and they yield interpretable predictions. In this work, we present two algorithms that incorporate association rules. These algorithms can be used both for sequential event prediction and for supervised classification, and they are simple enough that they can possibly be understood by users, customers, patients, managers, etc. We provide generalization guarantees on these algorithms based on algorithmic stability analysis from statistical learning theory. We include a discussion of the strict minimum support threshold often used in association rule mining, and introduce an “adjusted confidence" measure that provides a weaker minimum support condition that has advantages over the strict minimum support. The paper brings together ideas from statistical learning theory, association rule mining and Bayesian analysis