Related papers: Polyhedral aspects of score equivalence in Bayesia…

We introduce Selective Greedy Equivalence Search (SGES), a restricted version of Greedy Equivalence Search (GES). SGES retains the asymptotic correctness of GES but, unlike GES, has polynomial performance guarantees. In particular, we show…

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…

We present a novel metric designed, among other applications, to quantify biased behaviors of machine learning models. As its core, the metric consists of a new similarity metric between score distributions that balances both their general…

Comparing representations of complex stimuli in neural network layers to human brain representations or behavioral judgments can guide model development. However, even qualitatively distinct neural network models often predict similar…

Many algorithms for score-based Bayesian network structure learning (BNSL), in particular exact ones, take as input a collection of potentially optimal parent sets for each variable in the data. Constructing such collections naively is…

We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and…

The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions…

Polyhedra and spectrahedra over the real numbers, or more generally their images under linear maps, are respectively the feasible sets of linear and semidefinite programming, and form the family of semidefinite-representable sets. This…

Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the…

Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set,…

For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each…

The objective of this work is set-based verification, e.g. to decide if two sets of images of a face are of the same person or not. The traditional approach to this problem is to learn to generate a feature vector per image, aggregate them…

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

Score-based algorithms that learn the structure of Bayesian networks can be used for both exact and approximate solutions. While approximate learning scales better with the number of variables, it can be computationally expensive in the…

Recently, there has been a panoptic segmentation task combining semantic and instance segmentation, in which the goal is to classify each pixel with the corresponding instance ID. In this work, we propose a solution to tackle the panoptic…

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of…

Various hand-crafted features and metric learning methods prevail in the field of person re-identification. Compared to these methods, this paper proposes a more general way that can learn a similarity metric from image pixels directly. By…

Classification by neural nets and by tree-based methods are powerful tools of machine learning. There exist interesting visualizations of the inner workings of these and other classifiers. Here we pursue a different goal, which is to…

This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…