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We define "decision swap regret" which generalizes both prediction for downstream swap regret and omniprediction, and give algorithms for obtaining it for arbitrary multi-dimensional Lipschitz loss functions in online adversarial settings.…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…
We develop large sample theory including nonparametric confidence regions for $r$-dimensional ridges of probability density functions on $\mathbb{R}^d$, where $1\leq r<d$. We view ridges as the intersections of level sets of some special…
Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
We construct an optimal exponential tail decreasing confidence region for an unknown density of distribution in the Lebesgue-Riesz as well as in the uniform} norm, built on the sample of the random vectors based of the famous recursive…
Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the…
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…
We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data,…
Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk Coverage Curve (AURC), have been proposed for improving model calibration; yet their theoretical connections to calibration…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes…
We propose a new method called localized conformal prediction, where we can perform conformal inference using only a local region around a new test sample to construct its confidence interval. Localized conformal inference is a natural…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
This paper illustrates the central role of loss functions in data-driven decision making, providing a comprehensive survey on their influence in cost-sensitive classification (CSC) and reinforcement learning (RL). We demonstrate how…
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…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the…