相关论文: Joint Tensor Factorization and Outlying Slab Suppr…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
Methods exploiting sparsity have been popular in imaging and signal processing applications including compression, denoising, and imaging inverse problems. Data-driven approaches such as dictionary learning and transform learning enable one…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
Completing multidimensional tensor-structured data with missing entries is a fundamental task for many real-world applications involving incomplete or corrupted datasets. For data with spatial or temporal side information, low-rank…
In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…
Tensor factorization has received increasing interest due to its intrinsic ability to capture latent factors in multi-dimensional data with many applications such as recommender systems and Electronic Health Records (EHR) mining. PARAFAC2…
In this paper, we investigate the random subsampling method for tensor least squares problem with respect to the popular t-product. From the optimization perspective, we present the error bounds in the sense of probability for the residual…
The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
In many application areas we are faced with the following question: Can we recover a sparse vector $x_o \in \mathbb{R}^N$ from its undersampled set of noisy observations $y \in \mathbb{R}^n$, $y=A x_o+w$. The last decade has witnessed a…
We propose an algorithm for the non-negative factorization of an occurrence tensor built from heterogeneous networks. We use l0 norm to model sparse errors over discrete values (occurrences), and use decomposed factors to model the embedded…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Joint analysis of data from multiple sources has the potential to improve our understanding of the underlying structures in complex data sets. For instance, in restaurant recommendation systems, recommendations can be based on rating…
It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics.…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…
Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…