Related papers: The Bayesian Method of Tensor Networks

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…

Next-item prediction is a a popular problem in the recommender systems domain. As the name suggests, the task is to recommend subsequent items that a user would be interested in given contextual information and historical interaction data.…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

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 years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…

Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…

Artificial neural networks (ANNs) are powerful machine learning methods used in many modern applications such as facial recognition, machine translation, and cancer diagnostics. A common issue with ANNs is that they usually have millions or…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…