Related papers: Near-Universal Multiplicative Updates for Nonnegat…

Neural abstractive summarization models are prone to generate summaries which are factually inconsistent with their source documents. Previous work has introduced the task of recognizing such factual inconsistency as a downstream…

Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…

There are increasing demands for understanding deep neural networks' (DNNs) behavior spurred by growing security and/or transparency concerns. Due to multi-layer nonlinearity of the deep neural network architectures, explaining DNN…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to…

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

We generalize the non-negative matrix factorization algorithm of Lee and Seung to accept a weighted norm, and to support ridge and Lasso regularization. We recast the Lee and Seung multiplicative update as an additive update which does not…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

Counterfactual examples identify how inputs can be altered to change the predicted class of a classifier, thus opening up the black-box nature of, e.g., deep neural networks. We propose a method, ECINN, that utilizes the generative…

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…

Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete,…

In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian…

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…