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It has been postulated and observed in practice that for prediction problems in which covariate data can be naturally partitioned into clusters, ensembling algorithms based on suitably aggregating models trained on individual clusters often…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…

The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…

We analyze the convergence rate of the random reshuffling (RR) method, which is a randomized first-order incremental algorithm for minimizing a finite sum of convex component functions. RR proceeds in cycles, picking a uniformly random…

In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…

We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…

Neural network (NN) ensembles can reduce large prediction variance of NN and improve prediction accuracy. For highly nonlinear problems with insufficient data set, the prediction accuracy of NN models becomes unstable, resulting in a…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…

A novel approach is suggested for improving the accuracy of fault detection in distribution networks. This technique combines adaptive probability learning and waveform decomposition to optimize the similarity of features. Its objective is…

The study of adaptive data analysis examines how many statistical queries can be answered accurately using a fixed dataset while avoiding false discoveries (statistically inaccurate answers). In this paper, we tackle a question that…

We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…

Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent…

Balancing influential covariates is crucial for valid treatment comparisons in clinical studies. While covariate-adaptive randomization is commonly used to achieve balance, its performance can be inadequate when the number of baseline…

In recent years the importance of finding a meaningful pattern from huge datasets has become more challenging. Data miners try to adopt innovative methods to face this problem by applying feature selection methods. In this paper we propose…

In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary…

We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…