Related papers: Bayesian Hierarchical Models and the Maximum Entro…
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…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power $\alpha$ as the prior distribution for the model parameters. The power parameter $\alpha$ is…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…
In this paper, we present an infinite hierarchical non-parametric Bayesian model to extract the hidden factors over observed data, where the number of hidden factors for each layer is unknown and can be potentially infinite. Moreover, the…
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…
Analyzing data collected from multiple sources to estimate common and heterogeneous structures through a hierarchical model is a central task in Bayesian inference, and to this end, Bayesian factor models are one of the most widely used…
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…
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…