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Deep learning models in medical imaging often encounter challenges when adapting to new clinical settings unseen during training. Test-time adaptation offers a promising approach to optimize models for these unseen domains, yet its…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously…
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…
In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Data augmentation methods are indispensable heuristics to boost the performance of deep neural networks, especially in image recognition tasks. Recently, several studies have shown that augmentation strategies found by search algorithms…
Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees…
Backtracking line search is foundational in numerical optimization. The basic idea is to adjust the step-size of an algorithm by a constant factor until some chosen criterion (e.g. Armijo, Descent Lemma) is satisfied. We propose a novel way…
Self-supervised learning of convolutional neural networks can harness large amounts of cheap unlabeled data to train powerful feature representations. As surrogate task, we jointly address ordering of visual data in the spatial and temporal…
This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be…
In the big data era, the need to reevaluate traditional statistical methods is paramount due to the challenges posed by vast datasets. While larger samples theoretically enhance accuracy and hypothesis testing power without increasing false…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the…
It is widely believed that the backpropagation algorithm is essential for learning good feature detectors in early layers of artificial neural networks, so that these detectors are useful for the task performed by the higher layers of that…
Deep neural networks have demonstrated impressive performance in various machine learning tasks. However, they are notoriously sensitive to changes in data distribution. Often, even a slight change in the distribution can lead to drastic…