Related papers: Sample Complexity Bounds for Robust Mean Estimatio…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
We analyze the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of It\^o diffusions associated with weighted Poincar\'e inequalities. Based on a mean-square analysis, we establish the…
In this work, we introduce statistical testing under distributional shifts. We are interested in the hypothesis $P^* \in H_0$ for a target distribution $P^*$, but observe data from a different distribution $Q^*$. We assume that $P^*$ is…
In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are…
We present the first diffusion-based framework that can learn an unknown distribution using only highly-corrupted samples. This problem arises in scientific applications where access to uncorrupted samples is impossible or expensive to…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
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…
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…
Exposure measurement error is a ubiquitous but often overlooked challenge in causal inference with observational data. Existing methods accounting for exposure measurement error largely rely on restrictive parametric assumptions, while…
Contaminant observations and outliers often cause problems when estimating the parameters of cognitive models, which are statistical models representing cognitive processes. In this study, we test and improve the robustness of parameter…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode…
We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing…
A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…
Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…
Confidence estimation aims to quantify the confidence of the model prediction, providing an expectation of success. A well-calibrated confidence estimate enables accurate failure prediction and proper risk measurement when given noisy…