机器学习

Operational disruptions can significantly impact companies performance. Ford, with its 37 plants globally, uses 17 billion parts annually to manufacture six million cars and trucks. With up to ten tiers of suppliers between the company and…

In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…

We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…

Bayesian optimization (BO) is a widely used iterative algorithm for optimizing black-box functions. Each iteration requires maximizing an acquisition function, such as the upper confidence bound (UCB) or a sample path from the Gaussian…

Spatio-temporal data, which consists of responses or measurements gathered at different times and positions, is ubiquitous across diverse applications of civil infrastructure. While SciML methods have made significant progress in tackling…

With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even…

In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this…

We address the problem of A/B testing, a widely used protocol for evaluating the potential improvement achieved by a new decision system compared to a baseline. This protocol segments the population into two subgroups, each exposed to a…

Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…

This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…

We study masked discrete diffusion models with classifier-free guidance (CFG). Assuming no score error nor discretization error, we derive an explicit solution to the guided reverse dynamics, so that how guidance influences the sampling…

It is well known that semantic and structural features of the generated images emerge at different times during the reverse dynamics of diffusion, a phenomenon that has been connected to physical phase transitions in magnets and other…

In this paper, we establish sample complexity bounds for learning high-dimensional simplices in $\mathbb{R}^K$ from noisy data. Specifically, we consider $n$ i.i.d. samples uniformly drawn from an unknown simplex in $\mathbb{R}^K$, each…

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…

We provide an overview of the diffusion model as a method to generate new samples. Generative models have been recently adopted for tasks such as art generation (Stable Diffusion, Dall-E) and text generation (ChatGPT). Diffusion models in…

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. We present a novel green/red list watermarking approach…

Classical results in statistical learning typically consider two extreme data-generating models: i.i.d. instances from an unknown distribution, or fully adversarial instances, often much more challenging statistically. To bridge the gap…

Causal mediation analyses investigate the mechanisms through which causes exert their effects, and are therefore central to scientific progress. The literature on the non-parametric definition and identification of mediational effects in…

Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…