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Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…

Big data analytics on geographically distributed datasets (across data centers or clusters) has been attracting increasing interests from both academia and industry, but also significantly complicates the system and algorithm designs. In…

Traditionally, fault detection and isolation community has used system dynamic equations to generate diagnosers and to analyze detectability and isolability of the dynamic systems. Model-based fault detection and isolation methods use…

Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…

Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…

Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…

The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Learning discriminative global features plays a vital role in semantic segmentation. And most of the existing methods adopt stacks of local convolutions or non-local blocks to capture long-range context. However, due to the absence of…

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…

This paper explores object detection in the small data regime, where only a limited number of annotated bounding boxes are available due to data rarity and annotation expense. This is a common challenge today with machine learning being…

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

In this work we propose a distributed randomized block coordinate descent method for minimizing a convex function with a huge number of variables/coordinates. We analyze its complexity under the assumption that the smooth part of the…

Image classification is an essential task in computer vision, which aims to categorise a set of images into different groups based on some visual criteria. Existing methods, such as convolutional neural networks, have been successfully…

Collision detection is a core component of robotics applications such as simulation, control, and planning. Traditional algorithms like GJK+EPA compute witness points (i.e., the closest or deepest-penetration pairs between two objects) but…