Related papers: Near-Optimal Procedures for Model Discrimination w…
Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…
Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…
Local differential privacy (LDP) is a model where users send privatized data to an untrusted central server whose goal it to solve some data analysis task. In the non-interactive version of this model the protocol consists of a single round…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
We consider infinite-horizon $\gamma$-discounted (linear) constrained Markov decision processes (CMDPs) where the objective is to find a policy that maximizes the expected cumulative reward subject to expected cumulative constraints. Given…
We propose a framework to convert $(\varepsilon, \delta)$-approximate Differential Privacy (DP) mechanisms into $(\varepsilon', 0)$-pure DP mechanisms under certain conditions, a process we call ``purification.'' This algorithmic technique…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…
In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…