Related papers: Backward Simulation in Bayesian Networks
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
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…
Bayesian inference without the likelihood evaluation, or likelihood-free inference, has been a key research topic in simulation studies for gaining quantitatively validated simulation models on real-world datasets. As the likelihood…
Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
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…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps…
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…
Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself --…
Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
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…