There are various algorithms for finding a Bayesian networkstructure (BNS) that is optimal with respect to a given scoring function. No single algorithm dominates the others in speed, and, given a problem instance, it is a priori unclear which algorithm will perform best and how fast it will solve the problem. Estimating the runtimes directly is extremely difficult as they are complicated functions of the instance. The main contribution of this paper is characterization of the empirical hardness of an instance for a given algorithm based on a novel collection of non-trivial, yet efficiently computable features. Our empirical results, based on the largest evaluation of state-of-the-art BNS learning algorithms to date, demonstrate that we can predict the runtimes to a reasonable degree of accuracy, and effectively select algorithms that perform well on a particular instance. Moreover, we also show how the results can be utilized in building a portfolio algorithm that combines several individual algorithms in an almost optimal manner.

One-class classification approaches have been proposed in the literature to learn classifiers from examples of only one class. But these approaches are not directly applicable to relational domains due to their reliance on a feature vector or a distance measure. We propose a non-parametric relational one-class classification approach based on first-order trees. We learn a tree-based distance measure that iteratively introduces new relational features to differentiate relational examples. We update the distance measure so as to maximize the one-class classification performance of our model. We also relate our model definition to existing work on probabilistic combination functions and density estimation. We experimentally show that our approach can discover relevant features and outperform three baseline approaches.

A recent breadth-first branch and bound algorithm (BFBnB)for learning Bayesian network structures (Maloneet al. 2011) uses two bounds to prune the searchspace for better efficiency; one is a lower bound calculatedfrom pattern database heuristics, and the otheris an upper bound obtained by a hill climbing search.Whenever the lower bound of a search path exceeds theupper bound, the path is guaranteed to lead to suboptimalsolutions and is discarded immediately. This paperintroduces methods for tightening the bounds. Thelower bound is tightened by using more informed variablegroupings when creating the pattern databases, andthe upper bound is tightened using an anytime learningalgorithm. Empirical results show that these boundsimprove the efficiency of Bayesian network learning bytwo to three orders of magnitude.

In causal inference, all methods of model learning rely on testable implications, namely, properties of the joint distribution that are dictated by the model structure. These constraints, if not satisfied in the data, allow us to reject or modify the model. Most common methods of testing a linear structural equation model (SEM) rely on the likelihood ratio or chi-square test which simultaneously tests all of the restrictions implied by the model. Local constraints, on the other hand, offer increased power (Bollen and Pearl, 2013; McDonald, 2002) and, in the case of failure, provide the modeler with insight for revising the model specification. One strategy of uncovering local constraints in linear SEMs is to search for overidentified path coefficients. While these overidentifying constraints are well known, no method has been given for systematically discovering them. In this paper, we extend the half-trek criterion of (Foygel et al., 2012) to identify a larger set of structural coefficients and use it to systematically discover overidentifying constraints. Still open is the question of whether our algorithm is complete.

Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in either experimental or observational studies. In this paper, we provide complete graphical and algorithmic conditions for recovering conditional probabilities from selection biased data. We also provide graphical conditions for recoverability when unbiased data is available over a subset of the variables. Finally, we provide a graphical condition that generalizes the backdoor criterion and serves to recover causal effects when the data is collected under preferential selection.

Inference in large scale graphical models is an important task in many domains, and in particular probabilistic relational models (e.g. Markov logic networks). Such models often exhibit considerable symmetry, and it is a challenge to devise algorithms that exploit this symmetry to speed up inference. Recently, the automorphism group has been proposed to formalize mathematically what "exploiting symmetry" means. However, obtaining symmetry derived from automorphism is GI-hard, and consequently only a small fraction of the symmetry is easily available for effective employment. In this paper, we improve upon efficiency in two ways. First, we introduce the Cluster Signature Graph (CSG), a platform on which greater portions of the symmetries can be revealed and exploited. CSGs classify clusters of variables by projecting relations between cluster members onto a graph, allowing for the efficient pruning of symmetrical clusters even before their generation. Second, we introduce a novel framework based on CSGs for the Sherali-Adams hierarchy of linear program (LP) relaxations, dedicated to exploiting this symmetry for the benefit of tight Maximum A Posteriori (MAP) approximations. Combined with the pruning power of CSG, the framework quickly generates compact formulations for otherwise intractable LPs, as demonstrated by several empirical results.

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflict-free local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of flexibility due to decomposition. Here, flexibility roughly refers to the freedom in choosing suitable values for the variables in order to satisfy the constraints. In this paper, we concentrate on linear constraint systems and efficient decomposition techniques for them. Using a generalization of a flexibility metric developed for Simple Temporal Networks, we show how an efficient decomposition technique for linear constraint systems can be derived that minimizes the loss of flexibility. As a by-product of this decomposition technique, we propose an intuitively attractive flexibility metric for linear constraint systems where decomposition does not incur any loss of flexibility.

In many probabilistic planning scenarios, a system’s behavior needs to not only maximize the expected utility but also obey certain restrictions. This paper presents Saturated Path-Constrained Markov Decision Processes (SPC MDPs), a new MDP type for planning under uncertainty with deterministic model-checking constraints, e.g., "state s must be visited befores s'", "the system must end up in s", or "the system must never enter s". We present a mathematical analysis of SPCMDPs, showing that although SPC MDPs generally have no optimal policies, every instance of this class has an epsilon-optimal randomized policy for any > 0. We propose a dynamic programming-based algorithm for finding such policies, and empirically demonstrate this algorithm to be orders of magnitude faster than its next-best alternative.

Label reduction is a technique for simplifying families of labeled transition systems by dropping distinctions between certain transition labels. While label reduction is critical to the efficient computation of merge-and-shrink heuristics, current theory only permits reducing labels in a limited number of cases. We generalize this theory so that labels can be reduced in every intermediate abstraction of a merge-and-shrink tree. This is particularly important for efficiently computing merge-and-shrink abstractions based on non-linear merge strategies. As a case study, we implement a non-linear merge strategy based on the original work on merge-and-shrink heuristics in model checking by Dräger et al.

In this paper we investigate three different approaches to encoding domain-dependent control knowledge for Answer-Set Planning. Starting with a standard imple- mentation of the action description language B, we add control knowledge expressed in the GOLOG logic pro- gramming language. A naive encoding, following the original definitions of Levesque et al., is shown to scale poorly. We examine two alternative codings based on the transition semantics of ConGOLOG. We show that a speed increase of multiple orders of magnitude can be obtain by compiling the GOLOG program into a finite- state machine representation.