Coronary Heart Disease can be diagnosed by assessing the regional motion of the heart walls in ultrasound images of the left ventricle. Even for experts, ultrasound images are difficult to interpret leading to high intra-observer variability. Previous work indicates that in order to approach this problem, the interactions between the different heart regions and their overall influence on the clinical condition of the heart need to be considered. To do this, we propose a method for jointly learning the structure and parameters of conditional random fields, formulating these tasks as a convex optimization problem. We consider block-L1 regularization for each set of features associated with an edge, and formalize an efficient projection method to find the globally optimal penalized maximum likelihood solution. We perform extensive numerical experiments comparing the presented method with related methods that approach the structure learning problem differently. We verify the robustness of our method on echocardiograms collected in routine clinical practice at one hospital. 1.

We present the first truly polynomial algorithm for PAC-learning the structure of bounded-treewidth junction trees – an attractive subclass of probabilistic graphical models that permits both the compact representation of probability distributions and efficient exact inference. For a constant treewidth, our algorithm has polynomial time and sample complexity. If a junction tree with sufficiently strong intraclique dependencies exists, we provide strong theoretical guarantees in terms of KL divergence of the result from the true distribution. We also present a lazy extension of our approach that leads to very significant speed ups in practice, and demonstrate the viability of our method empirically, on several real world datasets. One of our key new theoretical insights is a method for bounding the conditional mutual information of arbitrarily large sets of variables with only polynomially many mutual information computations on fixed-size subsets of variables, if the underlying distribution can be approximated by a bounded-treewidth junction tree. 1

Sparsity-promoting L1-regularization has recently been succesfully used to learn the structure of undirected graphical models. In this paper, we apply this technique to learn the structure of directed graphical models. Specifically, we make three contributions. First, we show how the decomposability of the MDL score, plus the ability to quickly compute entire regularization paths, allows us to efficiently pick the optimal regularization parameter on a per-node basis. Second, we show how to use L1 variable selection to select the Markov blanket, before a DAG search stage. Finally, we show how L1 variable selection can be used inside of an order search algorithm. The effectiveness of these L1-based approaches are compared to current state of the art methods on 10 datasets.

In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning. This problem is even more acute when learning networks with hidden variables. We present a general method for significantly speeding the structure search algorithm for continuous variable networks with common parametric distributions. Importantly, our method facilitates the addition of new hidden variables into the network structure efficiently. We demonstrate the method on several data sets, both for learning structure on fully observable data, and for introducing new hidden variables during structure search. 1

Abstract—The discovery of networks is a fundamental problem

This paper addresses exact learning of Bayesian network structure from data and expert’s knowledge based on score functions that are decomposable. First, it describes useful properties that strongly reduce the time and memory costs of many known methods such as hill-climbing, dynamic programming and sampling variable orderings. Secondly, a branch and bound algorithm is presented that integrates parameter and structural constraints with data in a way to guarantee global optimality with respect to the score function. It is an any-time procedure because, if stopped, it provides the best current solution and an estimation about how far it is from the global solution. We show empirically the advantages of the properties and the constraints, and the applicability of the algorithm to large data sets (up to one hundred variables) that cannot be handled by other current methods (limited to around 30 variables). 1.

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and parameters can be learned efficiently, even without restricting the size of the parent variable sets. We then consider the problem of optimizing the variable order for a given set of features. This is still a computationally hard problem, but we present a convex relaxation that yields an optimal “soft” ordering in polynomial time. One novel aspect of the approach is that we do not perform a discrete search over DAG structures, nor over variable orders, but instead solve a continuous convex relaxation that can then be rounded to obtain a valid network structure. We conduct an experimental comparison against standard structure search procedures over standard objectives, which cope with local minima, and evaluate the advantages of using convex relaxations that reduce the effects of local minima.

Structure learning algorithms usually focus on the compactness of the learned model. However, for general compact models, both exact and approximate inference are still NP-hard. Therefore, the focus only on compactness leads to learning models that require approximate inference techniques, thus reducing their prediction quality. In this paper, we propose a method for learning an attractive class of models: bounded-treewidth junction trees, which permit both compact representation of probability distributions and efficient exact inference. Using Bethe approximation of the likelihood, we transform the problem of finding a good junction tree separator into a minimum cut problem on a weighted graph. Using the graph cut intuition, we present an efficient algorithm with theoretical guarantees for finding good separators, which we recursively apply to obtain a thin junction tree. Our extensive empirical evaluation demonstrates the benefit of applying exact inference using our models to answer queries. We also extend our technique to learning low tree-width conditional random fields, and demonstrate significant improvements over state of the art block-L1 regularization techniques. 1

Abstract. Recently, there has been an increasing interest in directed probabilistic logical models and a variety of languages for describing such models has been proposed. Although many authors provide high-level arguments to show that in principle models in their language can be learned from data, most of the proposed learning algorithms have not yet been studied in detail. We introduce an algorithm, generalized ordering-search, to learn both structure and conditional probability distributions (CPDs) of directed probabilistic logical models. The algorithm upgrades the ordering-search algorithm for Bayesian networks. We use relational probability trees as a representation for the CPDs. We present experiments on blocks world domains, a gene domain and the Cora dataset. 1

Abstract. There is an increasing interest in upgrading Bayesian networks to the relational case, resulting in so-called directed probabilistic logical models. In this paper we discuss how to learn non-recursive directed probabilistic logical models from relational data. This problem has already been tackled before by upgrading the structure-search algorithm for learning Bayesian networks. In this paper we propose to upgrade another algorithm, namely ordering-search, since for Bayesian networks this was found to work better than structure-search. We have implemented both algorithms for the formalism Logical Bayesian Networks and are currently working on an experimental comparison of both algorithms.