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Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…
We consider learning to optimize a classification metric defined by a black-box function of the confusion matrix. Such black-box learning settings are ubiquitous, for example, when the learner only has query access to the metric of…
We study how we can adapt a predictor to a non-stationary environment with advises from multiple experts. We study the problem under complete feedback when the best expert changes over time from a decision theoretic point of view. Proposed…
Aggregating multiple learners through an ensemble of models aim to make better predictions by capturing the underlying distribution of the data more accurately. Different ensembling methods, such as bagging, boosting, and stacking/blending,…
Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…
A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression…
Sharpness-aware minimization (SAM), which searches for flat minima by min-max optimization, has been shown to be useful in improving model generalization. However, since each SAM update requires computing two gradients, its computational…
We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…
How to improve discriminative feature learning is central in classification. Existing works address this problem by explicitly increasing inter-class separability and intra-class similarity, whether by constructing positive and negative…
Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…
We propose a new, more general approach to the design of stochastic gradient-based optimization methods for machine learning. In this new framework, optimizers assume access to a batch of gradient estimates per iteration, rather than a…
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical…
Recently, invariant risk minimization (IRM) was proposed as a promising solution to address out-of-distribution (OOD) generalization. However, it is unclear when IRM should be preferred over the widely-employed empirical risk minimization…
In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…
The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size…
We address the problem of solving mixed random linear equations. We have unlabeled observations coming from multiple linear regressions, and each observation corresponds to exactly one of the regression models. The goal is to learn the…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…