Related papers: Learnability of Parameter-Bounded Bayes Nets

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability…

Building on the view of machine learning as search, we demonstrate the necessity of bias in learning, quantifying the role of bias (measured relative to a collection of possible datasets, or more generally, information resources) in…

In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier…

We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.

PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…

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…

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…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…

Parameter learning is the technique for obtaining the probabilistic parameters in conditional probability tables in Bayesian networks from tables with (observed) data --- where it is assumed that the underlying graphical structure is known.…

Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…

Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models…

We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the…

Bayesian belief network learning algorithms have three basic components: a measure of a network structure and a database, a search heuristic that chooses network structures to be considered, and a method of estimating the probability tables…

Graph contrastive learning has shown great promise when labeled data is scarce, but large unlabeled datasets are available. However, it often does not take uncertainty estimation into account. We show that a variational Bayesian neural…

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the…

A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network…

Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose…