Related papers: Characterizing predictable classes of processes

In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

Bayesian filtering aims at tracking sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

A major limitation of machine learning (ML) prediction models is that they recover associational, rather than causal, predictive relationships between variables. In high-stakes automation applications of ML this is problematic, as the model…

In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model…

Given a c\`adl\`ag process $X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let $\mathfrak{P}_{sem}$ be the…

The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…

A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. Here we extend this idea by…

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…

Given a sequence $X=(X_1,X_2,\ldots)$ of random observations, a Bayesian forecaster aims to predict $X_{n+1}$ based on $(X_1,\ldots,X_n)$ for each $n\ge 0$. To this end, in principle, she only needs to select a collection…

We consider the well-posedness of Bayesian inverse problems when the prior measure has exponential tails. In particular, we consider the class of convex (log-concave) probability measures which include the Gaussian and Besov measures as…

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…

This paper reviews the growing field of Bayesian prediction. Bayes point and interval prediction are defined and exemplified and situated in statistical prediction more generally. Then, four general approaches to Bayes prediction are…