相关论文: Bayes without Underfitting: Fully Correlated Deep …

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…

Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\text{ -- }$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges…

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…

Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node.…

We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…

Estimated uncertainty by approximate posteriors in Bayesian neural networks are prone to miscalibration, which leads to overconfident predictions in critical tasks that have a clear asymmetric cost or significant losses. Here, we extend the…

Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…

Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime where classical learning theory would instead predict that they would severely overfit. While many…

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While…

Despite the dominant role of deep models in machine learning, limitations persist, including overconfident predictions, susceptibility to adversarial attacks, and underestimation of variability in predictions. The Bayesian paradigm provides…

Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…

General Bayesian updating replaces the likelihood with a loss scaled by a learning rate, but posterior uncertainty can depend sharply on that scale. We propose a simple post-processing that aligns generalized posterior draws with their…