Related papers: On tensor rank of conditional probability tables i…

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…

Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…

Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…

Decision Trees are some of the most popular machine learning models today due to their out-of-the-box performance and interpretability. Often, Decision Trees models are constructed greedily in a top-down fashion via heuristic search…

Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…

This paper presents analytical and experimental results on the ranked nodes method (RNM) that is used to construct conditional probability tables for Bayesian networks by expert elicitation. The majority of the results are focused on a…

In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…

There is evidence that the numbers in probabilistic inference don't really matter. This paper considers the idea that we can make a probabilistic model simpler by making fewer distinctions. Unfortunately, the level of a Bayesian network…

Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…

When expert systems based on causal probabilistic networks (CPNs) reach a certain size and complexity, the "combinatorial explosion monster" tends to be present. We propose an approximation scheme that identifies rarely occurring cases and…

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

We describe a graphical model for probabilistic relationships---an alternative to the Bayesian network---called a dependency network. The graph of a dependency network, unlike a Bayesian network, is potentially cyclic. The probability…