Related papers: Rule-based Bayesian regression
Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
This paper addresses the problem of resolving errors under uncertainty in a rule-based system. A new approach has been developed that reformulates this problem as a neural-network learning problem. The strength and the fundamental…
Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…
We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
Learning an explainable classifier often results in low accuracy model or ends up with a huge rule set, while learning a deep model is usually more capable of handling noisy data at scale, but with the cost of hard to explain the result and…
It is crucial for robots to be aware of the presence of constraints in order to acquire safe policies. However, explicitly specifying all constraints in an environment can be a challenging task. State-of-the-art constraint inference…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…