Related papers: Valid and efficient possibilistic structure learni…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…

Inferential models (IMs) represent a novel possibilistic approach for achieving provably valid statistical inference. This paper introduces a general framework for fusing independent IMs in a "black-box" manner, requiring no knowledge of…

Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…

Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown…

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…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

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…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through…

Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in…

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…

To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Modern large scale datasets are often plagued with missing entries. For tabular data with missing values, a flurry of imputation algorithms solve for a complete matrix which minimizes some penalized reconstruction error. However, almost…