Related papers: Unbiased risk estimation method for covariance est…
In contrast to the standard learning paradigm where all classes can be observed in training data, learning with augmented classes (LAC) tackles the problem where augmented classes unobserved in the training data may emerge in the test…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
We construct an unbiased estimator for function value evaluated at the solution of a partial differential equation with random coefficients. We show that the variance and expected computational cost of our estimator are finite and our…
Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
To facilitate robust and trustworthy deployment of large language models (LLMs), it is essential to quantify the reliability of their generations through uncertainty estimation. While recent efforts have made significant advancements by…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
We propose a novel approach to select the best model of the data. Based on the exclusive properties of the nested models, we find the most parsimonious model containing the risk minimizer predictor. We prove the existence of probable…
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…
In this paper for the first time the nonparametric autoregression estimation problem for the quadratic risks is considered. To this end we develop a new adaptive sequential model selection method based on the efficient sequential kernel…
We examine the problem of estimating the trace of a matrix $A$ when given access to an oracle which computes $x^\dagger A x$ for an input vector $x$. We make use of the basis vectors from a set of mutually unbiased bases, widely studied in…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the…
We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more…
There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…
Reward models (RMs) are essential for aligning large language models (LLM) with human expectations. However, existing RMs struggle to capture the stochastic and uncertain nature of human preferences and fail to assess the reliability of…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Multi-fidelity methods that use an ensemble of models to compute a Monte Carlo estimator of the expectation of a high-fidelity model can significantly reduce computational costs compared to single-model approaches. These methods use oracle…
Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…