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Sources of variability in experimentally derived data include measurement error in addition to the physical phenomena of interest. This measurement error is a combination of systematic components, originating from the measuring instrument,…
Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we…
In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable…
This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
Bayesian Optimization is a useful tool for experiment design. Unfortunately, the classical, sequential setting of Bayesian Optimization does not translate well into laboratory experiments, for instance battery design, where measurements may…
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
Batch effects represent a major confounder in genomic diagnostics. In copy number variant (CNV) detection from NGS, many algorithms compare read depth between test samples and a reference sample, assuming they are process-matched. When this…
We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
Many biological data analysis processes like Cytometry or Next Generation Sequencing (NGS) produce massive amounts of data which needs to be processed in batches for down-stream analysis. Such datasets are prone to technical variations due…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for…
Modern machine learning pipelines are increasingly combining and mixing data from diverse and disparate sources, e.g., pre-training large language models. Yet, finding the optimal data mixture is a challenging and open problem. We formalize…