Related papers: Uncertainty Quantification for nonparametric regre…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…

We present a model-agnostic algorithm for generating post-hoc explanations and uncertainty intervals for a machine learning model when only a static sample of inputs and outputs from the model is available, rather than direct access to the…

Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…

We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model…

Frequentist and Bayesian methods differ in many aspects, but share some basic optimal properties. In real-life classification and regression problems, situations exist in which a model based on one of the methods is preferable based on some…

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods…

Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…

Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model's uncertainty is evaluated using…

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…

The willingness to trust predictions formulated by automatic algorithms is key in a vast number of domains. However, a vast number of deep architectures are only able to formulate predictions without an associated uncertainty. In this…