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The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
This paper explores the image synthesis capabilities of GPT-4, a leading multi-modal large language model. We establish a benchmark for evaluating the fidelity of texture features in images generated by GPT-4, comprising manually painted…
This paper investigates the distributionally robust filtering of signals generated by state-space models driven by exogenous disturbances with noisy observations in finite and infinite horizon scenarios. The exact joint probability…
We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval…
Data sets for statistical analysis become extremely large even with some difficulty of being stored on one single machine. Even when the data can be stored in one machine, the computational cost would still be intimidating. We propose a…
When primed with only a handful of training samples, very large, pretrained language models such as GPT-3 have shown competitive results when compared to fully-supervised, fine-tuned, large, pretrained language models. We demonstrate that…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
The integration of robots in chemical experiments has enhanced experimental efficiency, but lacking the human intelligence to comprehend literature, they seldom provide assistance in experimental design. Therefore, achieving full-process…
Data augmentation techniques are widely used for enhancing the performance of machine learning models by tackling class imbalance issues and data sparsity. State-of-the-art generative language models have been shown to provide significant…
We study robust regression under a contamination model in which covariates are clean while the responses may be corrupted in an adaptive manner. Unlike the classical Huber's contamination model, where both covariates and responses may be…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance,…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
Large Language Models (LLMs) are increasingly adopted for complex scientific text generation tasks, yet they often suffer from limitations in accuracy, consistency, and hallucination control. This thesis introduces a Parameter-Efficient…
Modern machine learning pipelines are increasingly combining and mixing data from diverse and disparate sources, e.g., pre-training large language models. Yet, finding the optimal data mixture is a challenging and open problem. We formalize…
The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem…
We demonstrate the power of human-LLM collaboration in tackling open problems in theoretical computer science. Focusing on combinatorial optimization, we refine outputs from the FunSearch algorithm [Romera-Paredes et al., Nature 2023] to…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
In August 2023, Scott Aaronson and I reported the results of testing GPT4 with the Wolfram Alpha and Code Interpreter plug-ins over a collection of 105 original high-school level and college-level science and math problems (Davis and…