Related papers: The Bayesian Method of Tensor Networks

Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

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…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

The lossless data compression algorithm based on Bayesian Attention Networks is derived from first principles. Bayesian Attention Networks are defined by introducing an attention factor per a training sample loss as a function of two sample…

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the…

Bayesian networks are graphical models to represent the probabilistic relationships between variables in the Bayesian framework. The knowledge of all variables can be updated using new information about some of the variables. We show that…

These lecture notes develop the theory of learning in deep and recurrent neuronal networks from the point of view of Bayesian inference. The aim is to enable the reader to understand typical computations found in the literature in this…

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

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…

Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…

We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of…

Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in…

Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

Model Compression has drawn much attention within the deep learning community recently. Compressing a dense neural network offers many advantages including lower computation cost, deployability to devices of limited storage and memories,…

Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…