Related papers: Characterizing predictable classes of processes

This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter…

Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems,…

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

Predictions about people, such as their expected educational achievement or their credit risk, can be performative and shape the outcome that they aim to predict. Understanding the causal effect of these predictions on the eventual outcomes…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

Three events in a probability space form a conjunctive fork if they satisfy specific constraints on conditional independence and covariances. Patterns of conjunctive forks within collections of events are characterized by means of systems…

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…

Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…

This book is devoted to the problem of sequential probability forecasting, that is, predicting the probabilities of the next outcome of a growing sequence of observations given the past. This problem is considered in a very general setting…

We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…

Consider a predictor, a learner, whose input is a stream of discrete items. The predictor's task, at every time point, is probabilistic multiclass prediction, i.e. to predict which item may occur next by outputting zero or more candidate…

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

A set $P\subset \mathbb N$ is called predictive if for any zero entropy finite-valued stationary process $(X_i)_{i\in \mathbb Z}$, $X_0$ is measurable with respect to $(X_i)_{i\in P}$. We know that $\mathbb N$ is a predictive set. In this…

Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…

Though neural network models demonstrate impressive performance, we do not understand exactly how these black-box models make individual predictions. This drawback has led to substantial research devoted to understand these models in areas…

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…