Related papers: To ignore dependencies is perhaps not a sin
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
Recent work introduced loss functions which measure the error of a prediction based on multiple simultaneous observations or outcomes. In this paper, we explore the theoretical and practical questions that arise when using such…
Minimax $L_2$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$…
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…
Quantitative portfolio allocation requires the accurate and tractable estimation of covariances between a large number of assets, whose histories can greatly vary in length. Such data are said to follow a monotone missingness pattern, under…
Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged…
Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However,…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of probability distributions $\Gamma$ on $(X,Y)$, what is the optimal decision rule minimizing the worst-case expected loss over $\Gamma$? In this paper, we address…
Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
Inverse reinforcement learning (IRL), which infers reward functions from demonstrations, is a valuable tool for modeling and understanding decision-making behavior. Many variants of IRL have been developed to capture complexities of human…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
We present a convex optimization to reduce the impact of sensor falsification attacks in linear time invariant systems controlled by observer-based feedback. We accomplish this by finding optimal observer and controller gain matrices that…