Related papers: Likelihood Ratio Confidence Sets for Sequential De…
The statistical framework of Generalized Linear Models (GLM) can be applied to sequential problems involving categorical or ordinal rewards associated, for instance, with clicks, likes or ratings. In the example of binary rewards, logistic…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
We propose a likelihood ratio statistic for forming hypothesis tests and confidence intervals for a nonparametrically estimated univariate regression function, based on the shape restriction of concavity (alternatively, convexity). Dealing…
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
Contextual sequential decision problems with categorical or numerical observations are ubiquitous and Generalized Linear Bandits (GLB) offer a solid theoretical framework to address them. In contrast to the case of linear bandits, existing…
Selectivity estimation of a boolean query based on frequent itemsets can be solved by describing the problem by a linear program. However, the number of variables in the equations is exponential, rendering the approach tractable only for…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…
The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the…
We develop a general theory to optimize the frequentist regret for sequential learning problems, where efficient bandit and reinforcement learning algorithms can be derived from unified Bayesian principles. We propose a novel optimization…
To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score --…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
We introduce a unified probabilistic framework for solving sequential decision making problems ranging from Bayesian optimisation to contextual bandits and reinforcement learning. This is accomplished by a probabilistic model-based approach…
Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
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…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
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…