机器学习

We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback,…

The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation. This work attempts to provide a…

Most existing multitask learning approaches are limited by their reliance on task-specific loss functions tailored to the scale and type of each outcome. When outcomes differ across tasks, these losses are generally not directly comparable,…

Traditional variational Kalman filtering with unknown noise statistics suffers from inconsistent process covariance estimation and slow convergence speed, limiting its practical utility. To address these issues, we introduce a surrogate…

We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a…

We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time-$T$ solution operators of dissipative evolution equations. The analysis builds on the premise that FNOs can efficiently approximate and…

While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost. Recent methods, including Jackknife+ and Jackknife-minmax, achieve…

The classical $k$-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of $k$-means to missing data is to involve only the observed…

Gaussian process inference is often limited by cubic computational costs, a challenge that becomes more pronounced in spatio-temporal settings where posterior inference is required over dense grids. While state-space SPDE formulations…

Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory. Most prior analyses of the edge of stability phenomenon focus on…

Alternating recurrent events -- event-times of a specific nature that trigger a secondary refractory period -- occur in a wide-range of fields, including behavioral science, criminal justice, and biostatistics. Analysis of these events…

In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory. Specifically,…

Contrastive embedding models trained with scale-invariant losses are typically paired with distance metrics like cosine similarity, effectively ignoring embedding magnitudes. However, surprisingly, empirical studies reveal that despite…

We propose doubly robust adaptive conformal inference (DR-ACI), which constructs prediction intervals for doubly robust pseudo-outcomes under temporal dependence.

Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a…

We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data. This…

Neural networks are known to be susceptible to over-reliance on spurious correlations. However, the precise mechanism by which models exploit shortcut features is not fully understood, and algorithms to mitigate this behavior rely on as yet…

Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged delay, often through an abrupt transition. Despite extensive…

Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which -- while potentially sub-optimal for the task at hand -- can be…

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections. Standard estimators of the SW distance rely…