Related papers: Suboptimal behaviour of Bayes and MDL in classific…

Machine learning (ML) models are typically optimized for their accuracy on a given dataset. However, this predictive criterion rarely captures all desirable properties of a model, in particular how well it matches a domain expert's…

Meta learning uses information from base learners (e.g. classifiers or estimators) as well as information about the learning problem to improve upon the performance of a single base learner. For example, the Bayes error rate of a given…

We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a…

Supervised machine learning (ML) and deep learning (DL) algorithms excel at predictive tasks, but it is commonly assumed that they often do so by exploiting non-causal correlations, which may limit both interpretability and…

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…

Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying…

Inverse reinforcement learning (IRL) aims to infer an agent's preferences (represented as a reward function $R$) from their behaviour (represented as a policy $\pi$). To do this, we need a behavioural model of how $\pi$ relates to $R$. In…

Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…

This paper introduces a new method for model selection and more generally hyperparameter selection in machine learning. Minimum description length (MDL) is an established method for model selection, which is however not directly aimed at…

Parametric complexity is a central concept in MDL model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…

In this study, both Bayesian classifiers and mutual information classifiers are examined for binary classifications with or without a reject option. The general decision rules in terms of distinctions on error types and reject types are…

While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior.…

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and…

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…