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Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
Piecewise deterministic Markov processes provide scalable methods for sampling from the posterior distributions in big data settings by admitting principled sub-sampling strategies that do not bias the output. An important example is the…
This paper investigates estimation and inference for average treatment effects in completely randomized experiments when researchers observe potentially many covariates. Within Neyman's (1923) design-based framework, allowing the number of…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked…
Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…
In this paper, we study the problem of mean estimation under 1-bit communication constraints. We propose a novel adaptive mean estimator based solely on randomized threshold queries, where each 1-bit outcome indicates whether a given sample…
In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal non-private…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
Bernstein's condition is a key assumption that guarantees fast rates in machine learning. For example, the Gibbs algorithm with prior $\pi$ has an excess risk in $O(d_{\pi}/n)$, as opposed to the standard $O(\sqrt{d_{\pi}/n})$, where $n$…
In this paper, we consider the related problems of multicalibration -- a multigroup fairness notion and omniprediction -- a simultaneous loss minimization paradigm, both in the distributional and online settings. The recent work of Garg et…
While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…
In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…
The Gibbs sampler (GS) is a crucial algorithm for approximating complex calculations, and it is justified by Markov chain theory, the alternating projection theorem, and $I$-projection, separately. We explore the equivalence between these…
Replicability requires that algorithmic conclusions remain consistent when rerun on independently drawn data. A central structural question is composition: given $k$ problems each admitting a $\rho$-replicable algorithm with sample…