Related papers: Estimating the reciprocal of a binomial proportion
In capture-recapture experiments, individual covariates may be subject to missing, especially when the number of times of being captured is small. When the covariate information is missing at random, the inverse probability weighting method…
Clinical decision-making often involves selecting tests that are costly, invasive, or time-consuming, motivating individualized, sequential strategies for what to measure and when to stop ascertaining. We study the problem of learning…
This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the…
We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
Inverse reinforcement learning (IRL) addresses the problem of recovering a task description given a demonstration of the optimal policy used to solve such a task. The optimal policy is usually provided by an expert or teacher, making IRL…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic…
Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…
In this paper, we consider recent progress in estimating the average treatment effect when extreme inverse probability weights are present and focus on methods that account for a possible violation of the positivity assumption. These…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…
In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index and we provide its…
The purpose of modeling document relevance for search engines is to rank better in subsequent searches. Document-specific historical click-through rates can be important features in a dynamic ranking system which updates as we accumulate…
Learning near-optimal behaviour from an expert's demonstrations typically relies on the assumption that the learner knows the features that the true reward function depends on. In this paper, we study the problem of learning from…