Related papers: SWIFT: Scalable Wasserstein Factorization for Spar…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
We present a new algorithm for transposing sparse tensors called Quesadilla. The algorithm converts the sparse tensor data structure to a list of coordinates and sorts it with a fast multi-pass radix algorithm that exploits knowledge of the…
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Tabular learning transforms raw features into optimized spaces for downstream tasks, but its effectiveness deteriorates under distribution shifts between training and testing data. We formalize this challenge as the Distribution Shift…
Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive latent distributions using…
The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…
Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…
We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some $N$-length input vector in the presence of noise, where the $N$-point Walsh spectrum is $K$-sparse with $K = {O}(N^{\delta})$ scaling sub-linearly in the input…
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e.g.…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsify the separators in a Nested Dissection based Householder QR…
The Wasserstein metric is broadly used in optimal transport for comparing two probabilistic distributions, with successful applications in various fields such as machine learning, signal processing, seismic inversion, etc. Nevertheless, the…
The quadratic Wasserstein metric has shown its power in measuring the difference between probability densities, which benefits optimization objective function with better convexity and is insensitive to data noise. Nevertheless, it is…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
This paper presents a new method, which we call SUSTain, that extends real-valued matrix and tensor factorizations to data where values are integers. Such data are common when the values correspond to event counts or ordinal measures. The…