Related papers: Universality of Bayesian mixture predictors

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…

Predictive mean matching (PMM) is a popular imputation strategy that imputes missing values by borrowing observed values from other cases with similar expectations. We show that, unlike other imputation strategies, PMM is not guaranteed to…

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…

The article considers semi-supervised multitask learning on a Gaussian mixture model (GMM). Using methods from statistical physics, we compute the asymptotic Bayes risk of each task in the regime of large datasets in high dimension, from…

We propose a method for combining probabilistic outputs of classifiers to make a single consensus class prediction when no further information about the individual classifiers is available, beyond that they have been trained for the same…

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov…

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes…

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

This paper establishes the theoretical foundations for the asymptotic separability of Gaussian Mixture Models (GMMs) in high dimensions by extending the classical Feldman-H\'ajek theorem. We first prove that a countable mixture of Gaussian…

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…