22 accepted papers
We study the problem of generating structurally diverse graphs on $N$ unlabeled vertices. Given a space of such graphs $S_N$, a metric $d$, and a target cardinality $k$, the objective is to construct a set $\mathcal{G} \subset S_N$ that maximizes pairwise diversity under $d$. While neural generative…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by co…
We introduce nested diffusion models, an efficient and powerful hierarchical generative framework that substantially enhances the generation quality of diffusion models, particularly for images of complex scenes. Our approach employs a series of diffusion models to progressively generate latent vari…
Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative models for dynamic graphs is challenging due to the difficul…
Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three key challenges: (i) oversquashing of long-range information, (…
We propose a new framework for algorithmic stability in the context of multiclass classification. In practice, classification algorithms often operate by first assigning a continuous score (for instance, an estimated probability) to each possible label, then taking the maximizer---i.e., selecting th…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schrödinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit computational complexity that scales exponentially in the problem di…
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be ineffective for problems where the quantile regressors perform…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to repr…
This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a corresponding multi-channel time series. Our task is to accuratel…
As opaque predictive models increasingly impact many areas of modern life, interest in quantifying the importance of a given input variable for making a specific prediction has grown. Recently, there has been a proliferation of model-agnostic methods to measure variable importance (VI) that analyze…
This paper addresses the problem of localizing change points in high-dimensional linear regression models with piecewise constant regression coefficients. We develop a dynamic programming approach to estimate the locations of the change points whose performance improves upon the current state-of-the…
We study pure exploration in bandits, where the dimension of the feature representation can be much larger than the number of arms. To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each arm into a lower-dimensional space and carefully deal with th…
We give a tight characterization of the (vectorized Euclidean) norm of weights required to realize a function $f:\mathbb{R}\rightarrow \mathbb{R}^d$ as a single hidden-layer ReLU network with an unbounded number of units (infinite width), extending the univariate characterization of Savarese et al.…
We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbf{\Theta}…
Multivariate Bernoulli autoregressive (BAR) processes model time series of events in which the likelihood of current events is determined by the times and locations of past events. These processes can be used to model nonlinear dynamical systems corresponding to criminal activity, responses of patie…
We consider a non-linear generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e., each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly high-rank, but it becomes low-rank after mapping eac…
This paper describes a new parameter-free online learning algorithm for changing environments. In comparing against algorithms with the same time complexity as ours, we obtain a strongly adaptive regret bound that is a factor of at least $\sqrt\log(T)$ better, where $T$ is the time horizon. Empiri…
Generalized Linear Bandits (GLBs), a natural extension of the stochastic linear bandits, has been popular and successful in recent years. However, existing GLBs scale poorly with the number of rounds and the number of arms, limiting their utility in practice. This paper proposes new, scalable solu…
The last decade of John Cozzens's tenure at the NSF witnessed the advent of theory and methods at the heart of modern data science. These advances include (but are not limited to) compressed sensing, sparse coding, inference methods robust to outliers and missing data, and convex optimization tools…
Given samples lying on any of a number of subspaces, subspace clustering is the task of grouping the samples based on the their corresponding subspaces. Many subspace clustering methods operate by assigning a measure of affinity to each pair of points and feeding these affinities into a graph cluste…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This…