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Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Machine Learning · Computer Science 2024-08-20 Woojin Cho , Minju Jo , Haksoo Lim , Kookjin Lee , Dongeun Lee , Sanghyun Hong , Noseong Park

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Methodology · Statistics 2024-07-02 Thomas J. Loredo , Robert L. Wolpert

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

Computation · Statistics 2019-03-28 Matthew Parno , Tarek Moselhy , Youssef Marzouk

We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous…

Computational Complexity · Computer Science 2013-06-26 Hubie Chen , Moritz Müller

We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time…

Machine Learning · Computer Science 2012-07-09 Pieter Abbeel , Daphne Koller , Andrew Y. Ng

Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…

Statistics Theory · Mathematics 2014-06-04 Elizabeth S. Allman , John A. Rhodes , Elena Stanghellini , Marco Valtorta

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine Learning · Statistics 2020-02-27 Tim Pearce , Felix Leibfried , Alexandra Brintrup , Mohamed Zaki , Andy Neely

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…

Methodology · Statistics 2025-12-08 Lídia M. André , Jennifer L. Wadsworth , Raphaël Huser

This work introduces Bilinear Classes, a new structural framework, which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation. The framework incorporates nearly all existing…

Machine Learning · Computer Science 2021-07-13 Simon S. Du , Sham M. Kakade , Jason D. Lee , Shachar Lovett , Gaurav Mahajan , Wen Sun , Ruosong Wang

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

Machine Learning · Statistics 2020-11-09 Tom Charnock , Laurence Perreault-Levasseur , François Lanusse

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such…

Artificial Intelligence · Computer Science 2013-09-27 Denis D. Maua , Cassio Polpo de Campos , Alessio Benavoli , Alessandro Antonucci

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…

Artificial Intelligence · Computer Science 2012-12-12 Yong Gao

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…

Artificial Intelligence · Computer Science 2015-05-19 David Heckerman

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive…

Artificial Intelligence · Computer Science 2024-01-26 Jack Storror Carter

Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Sanyam Kapoor , Shikai Qiu , Andrew Gordon Wilson

In this paper, we show that Bandwidth is hard for the complexity class $W[t]$ for all $t\in {\bf N}$, even for caterpillars with hair length at most three. As intermediate problem, we introduce the Weighted Path Emulation problem: given a…

Computational Complexity · Computer Science 2020-12-03 Hans L. Bodlaender

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

Machine Learning · Computer Science 2021-06-28 Daniel T. Chang

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

Machine Learning · Computer Science 2025-12-02 Alfredo Reichlin , Miguel Vasco , Danica Kragic

Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by…

Machine Learning · Computer Science 2015-01-23 Diederik P. Kingma , Max Welling

Learning with neural networks relies on the complexity of the representable functions, but more importantly, the particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a…

Machine Learning · Statistics 2021-12-17 Hanna Tseran , Guido Montúfar