Related papers: Tensor Data Scattering and the Impossibility of Sl…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
Industry-scale recommender systems face a core challenge: representing entities with high cardinality, such as users or items, using dense embeddings that must be accessible during both training and inference. However, as embedding sizes…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…
This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…
We investigate image segmentation of cells under the lens of scalar fields. Our goal is to learn a continuous scalar field on image domains such that its segmentation produces robust instances for cells present in images. This field is a…
Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…
We introduce a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a…
Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
Sparse tensor algebra computations have become important in many real-world applications like machine learning, scientific simulations, and data mining. Hence, automated code generation and performance optimizations for tensor algebra…
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…
Diffusion models demonstrate outstanding performance in image generation, but their multi-step inference mechanism requires immense computational cost. Previous works accelerate inference by leveraging layer or token cache techniques to…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information…
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with…
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…