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Machine learning pipelines that include a combinatorial optimization layer can give surprisingly efficient heuristics for difficult combinatorial optimization problems. Three questions remain open: which architecture should be used, how…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Predicting flood for any location at times of extreme storms is a longstanding problem that has utmost importance in emergency management. Conventional methods that aim to predict water levels in streams use advanced hydrological models…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
We propose two novel samplers to generate high-quality samples from a given (un-normalized) probability density. Motivated by the success of generative adversarial networks, we construct our samplers using deep neural networks that…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…
We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…
Probabilistic generative neural networks are useful for many applications, such as image classification, speech recognition and occlusion removal. However, the power budget for hardware implementations of neural networks can be extremely…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
The default approach to deal with the enormous size and limited accessibility of many Web and social media networks is to sample one or more subnetworks from a conceptually unbounded unknown network. Clearly, the extracted subnetworks will…
In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing $\textit{bottlenecks}$ of the variety. Using geometric information such as the…
Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…