We discover a screening rule for l1-regularized Ising model estimation. The simple closed-form screening rule is a necessary and sufficient condition for exactly recovering the blockwise structure of a solution under any given regularization parameters. With enough sparsity, the screening rule can be combined with various optimization procedures to deliver solutions efficiently in practice. The screening rule is especially suitable for large-scale exploratory data analysis, where the number of variables in the dataset can be thousands while we are only interested in the relationship among a handful of variables within moderate-size clusters for interpretability. Experimental results on various datasets demonstrate the efficiency and insights gained from the introduction of the screening rule.

The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression problem. In this way, many insights and optimization procedures for sparse logistic regression can be applied to the learning of discrete Markov networks. Specifically, we use the coordinate descent algorithm for generalized linear models with convex penalties, combined with strong screening rules, to solve the pseudo-likelihood problem with $L_1$ regularization. Therefore a substantial speedup without losing any accuracy can be achieved. Furthermore, this method is more stable than the node-wise logistic regression approach on unbalanced high-dimensional data when penalized by small regularization parameters. Thorough numerical experiments on simulated data and real world data demonstrate the advantages of the proposed method.

In large-scale applications of undirected graphical models, such as social networks and biological networks, similar patterns occur frequently and give rise to similar parameters.In this situation, it is beneficial to group the parameters for more efficient learning. We show that even when the grouping is unknown, we can infer theseparameter groups during learning via a Bayesian approach. We impose a Dirichlet process prior on the parameters. Posterior inference usually involves calculating intractableterms, and we propose two approximation algorithms, namely a Metropolis-Hastings algorithm with auxiliary variables and a Gibbs sampling algorithm with"stripped" Beta approximation (Gibbs SBA). Simulations show that both algorithms outperform conventional maximum likelihood estimation (MLE). Gibbs SBA's performance is close to Gibbs sampling with exact likelihood calculation. Modelslearned with Gibbs SBA also generalize better than the models learned by MLE on real-world Senate voting data.

Adverse drug events are a leading cause of danger and cost in health care. We could reduce both the danger and the cost if we had accurate models to predict, at prescription time for each drug, which patients are most at risk for known adverse reactions to that drug, such as myocardial infarction (MI, or "heart attack") if given a Cox2 inhibitor, angioedema if given an ACE inhibitor, or bleeding if given an anticoagulant such as Warfarin. We address this task for the specific case of Cox2 inhibitors, a type of non-steroidal anti-inflammatory drug (NSAID) or pain reliever that is easier on the gastrointestinal system than most NSAIDS. Because of the MI adverse drug reaction, some but not all very effective Cox2 inhibitors were removed from the market. Specifically, we use machine learning to predict which patients on a Cox2 inhibitor would suffer an MI. An important issue for machine learning is that we do not know which of these patients might have suffered an MI even without the drug. To begin to make some headway on this important problem, we compare our predictive model for MI for patients on Cox2 inhibitors against a more general model for predicting MI among a broader population not on Cox2 inhibitors.

Electronic health records (EHRs) are an emerging relational domain with large potential to improve clinical outcomes. We apply two statistical relational learning (SRL) algorithms to the task of predicting primary myocardial infarction. We show that one SRL algorithm, relational functional gradient boosting, outperforms propositional learners particularly in the medically-relevant high recall region. We observe that both SRL algorithms predict outcomes better than their propositional analogs and suggest how our methods can augment current epidemiological practices.

Electronic health records (EHRs) are an emerging relational domain with large potential to improve clinical outcomes. We apply two statistical relational learning (SRL) algorithms to the task of predicting primary myocardial infarction. We show that one SRL algorithm, relational functional gradient boosting, outperforms propositional learners particularly in the medically-relevant high recall region. We observe that both SRL algorithms predict outcomes better than their propositional analogs and suggest how our methods can augment current epidemiological practices.

Learning temporal dependencies between variables over continuous time is an important and challenging task. Continuous-time Bayesian networks effectively model such processes but are limited by the number of conditional intensity matrices, which grows exponentially in the number of parents per variable. We develop a partition-based representation using regression trees and forests whose parameter spaces grow linearly in the number of node splits. Using a multiplicative assumption we show how to update the forest likelihood in closed form, producing efficient model updates. Our results show multiplicative forests can be learned from few temporal trajectories with large gains in performance and scalability.

We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus cannot represent relations between multiple similar objects in multiple contexts. Several researchers have thus proposed first-order languages to describe such networks. Namely, one very successful example of this approach are the Probabilistic Relational Models (PRMs), that combine Bayesian networks with relational database technology. The key difficulty that we had to address when designing CLP(cal{BN}) is that logic based representations use ground terms to denote objects. With probabilitic data, we need to be able to uniquely represent an object whose value we are not sure about. We use {sl Skolem functions} as unique new symbols that uniquely represent objects with unknown value. The semantics of CLP(cal{BN}) programs then naturally follow from the general framework of constraint logic programming, as applied to a specific domain where we have probabilistic data. This paper introduces and defines CLP(cal{BN}), and it describes an implementation and initial experiments. The paper also shows how CLP(cal{BN}) relates to Probabilistic Relational Models (PRMs), Ngo and Haddawys Probabilistic Logic Programs, AND Kersting AND De Raedts Bayesian Logic Programs.

The pharmaceutical industry, consumer protection groups, users of medications and government oversight agencies are all strongly interested in identifying adverse reactions to drugs. While a clinical trial of a drug may use only a thousand patients, once a drug is released on the market it may be taken by millions of patients. As a result, in many cases adverse drug events (ADEs) are observed in the broader population that were not identified during clinical trials. Therefore, there is a need for continued, postmarketing surveillance of drugs to identify previously-unanticipated ADEs. This paper casts this problem as a reverse machine learning task, related to relational subgroup discovery and provides an initial evaluation of this approach based on experiments with an actual EMR/EHR and known adverse drug events.

Precision-recall (PR) curves and the areas under them are widely used to summarize machine learning results, especially for data sets exhibiting class skew. They are often used analogously to ROC curves and the area under ROC curves. It is known that PR curves vary as class skew changes. What was not recognized before this paper is that there is a region of PR space that is completely unachievable, and the size of this region depends only on the skew. This paper precisely characterizes the size of that region and discusses its implications for empirical evaluation methodology in machine learning.