Related papers: Parameterized Complexity Results for Bayesian Infe…
We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…
Bayesian structure learning is the NP-hard 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 Bayesian structure learning…
We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
Algorithms for learning the conditional probabilities of Bayesian networks with hidden variables typically operate within a high-dimensional search space and yield only locally optimal solutions. One way of limiting the search space and…
In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…
The estimation of Bayesian networks given high-dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically…
The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading…
Qualitative probabilistic networks have been introduced as qualitative abstractions of Bayesian belief networks. One of the major drawbacks of these qualitative networks is their coarse level of detail, which may lead to unresolved…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…
We present the first results on the parameterized complexity of reconfiguration problems, where a reconfiguration version of an optimization problem $Q$ takes as input two feasible solutions $S$ and $T$ and determines if there is a sequence…