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In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…
Multi-armed bandits are widely used for sequential experimentation in clinical trials, recommendation systems, and online platforms. While regret minimization and valid inference from adaptively collected data have each been studied…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
Uniqueness of solution is proved for any ptychographic scheme with a random masks under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas-Rachford (DR) algorithms.…
In the context of the graph matching problem we propose a novel method for projecting a matrix $Q$, which may be a doubly stochastic matrix, to a permutation matrix $P.$ We observe that there is an intuitve mapping, depending on a given…
The standard method for benchmarking quantum error-correction is randomized fault-injection testing. The state-of-the-art tool stim is efficient for error correction implementations with distances of up to 10, but scales poorly to larger…
Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds.…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
As large language models (LLMs) generate more human-like texts, concerns about the side effects of AI-generated texts (AIGT) have grown. So, researchers have developed methods for detecting AIGT. However, two challenges remain. First, the…
In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a…
Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…
Response adaptive randomization (RAR) is appealing from methodological, ethical, and pragmatic perspectives in the sense that subjects are more likely to be randomized to better performing treatment groups based on accumulating data.…
Adaptive radiation therapy (ART) seeks to maintain accurate dose delivery by monitoring anatomical changes during treatment and modifying plans accordingly, yet commonly used approaches for estimating cumulative dose rely on heuristic,…
Current interest in deep learning captures the attention of many programmers and researchers. Unfortunately, the lack of a unified schema for developing deep learning models results in methodological inconsistencies, unclear documentation,…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…
We study dynamic algorithms robust to adaptive input generated from sources with bounded capabilities, such as sparsity or limited interaction. For example, we consider robust linear algebraic algorithms when the updates to the input are…
Large language models (LLMs) have shown remarkable reasoning capabilities, yet aligning such abilities to small language models (SLMs) remains a challenge due to distributional mismatches and limited model capacity. Existing reasoning…
Self-Taught Reasoners (STaR), synonymously known as Rejection sampling Fine-Tuning (RFT), is an integral part of the training pipeline of self-improving reasoning Language Models (LMs). The self-improving mechanism often employs random…
Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from…
Retrieval Augmented Language Models (RALMs) have gained significant attention for their ability to generate accurate answer and improve efficiency. However, RALMs are inherently vulnerable to imperfect information due to their reliance on…