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Large-scale datasets have been pivotal to the advancements of deep learning models in recent years, but training on such large datasets invariably incurs substantial storage and computational overhead. Meanwhile, real-world datasets often…

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…

Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…

Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies…

This paper proposes a new robust smooth-threshold estimating equation to select important variables and automatically estimate parameters for high dimensional longitudinal data. A novel working correlation matrix is proposed to capture…

We give improved algorithms for the $\ell_{p}$-regression problem, $\min_{x} \|x\|_{p}$ such that $A x=b,$ for all $p \in (1,2) \cup (2,\infty).$ Our algorithms obtain a high accuracy solution in $\tilde{O}_{p}(m^{\frac{|p-2|}{2p + |p-2|}})…

We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…

Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By…

We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data, improving upon the previous best algorithm whose sampling complexity has at least cubic dependence on…

Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…

As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…

Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods…

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

We introduce a novel ensemble approach for feature selection based on hierarchical stacking for non-stationarity and/or a limited number of samples with a large number of features. Our approach exploits the co-dependency between features…

Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…

Traditional frameworks for dynamic graphs have relied on processing only the stream of edges added into or deleted from an evolving graph, but not any additional related information such as the degrees or neighbor lists of nodes incident to…

Hierarchical time series are common in several applied fields. The forecasts for these time series are required to be coherent, that is, to satisfy the constraints given by the hierarchy. The most popular technique to enforce coherence is…

Large language models (LLMs) are currently aligned using techniques such as reinforcement learning from human feedback (RLHF). However, these methods use scalar rewards that can only reflect user preferences on average. Pluralistic…

Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…