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The $k$-$\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\mathcal{X} \subset \mathbb{R} ^d$ into $k$ clusters. The…
We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by observing only $m < K$ of its entries in each round. We propose two MSE estimators, and…
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…
We extend methods for finite-sample inference about the average treatment effect (ATE) in randomized experiments with binary outcomes to accommodate stratification (blocking). We present three valid methods that differ in their…
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…
The present study discuss the problem of estimating the finite population mean using auxiliary attribute in stratified random sampling. In this paper taking the advantage of point bi-serial correlation between the study variable and…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
Motivated by emerging technologies for energy efficient analog computing and continuous-time processing, this paper proposes continuous-time minimum mean squared error estimation for multiple-input multiple-output (MIMO) systems based on an…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
Many datasets such as market basket data, text or hypertext documents, and sensor observations recorded in different locations or time periods, are modeled as a collection of sets over a ground set of keys. We are interested in basic…
This paper presents a novel approach to level set estimation for any function/simulation with an arbitrary number of continuous inputs and arbitrary numbers of continuous responses. We present a method that uses existing data from computer…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…
This article introduces a subbagging (subsample aggregating) approach for variable selection in regression within the context of big data. The proposed subbagging approach not only ensures that variable selection is scalable given the…
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical…
Given a set of $n$ input integers, the Equal Subset Sum problem asks us to find two distinct subsets with the same sum. In this paper we present an algorithm that runs in time $O^*(3^{0.387n})$ in the~average case, significantly improving…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…