Related papers: Minimax Lower Bounds for Kronecker-Structured Dict…

When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative…

A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…

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…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Under a standard assumption in complexity theory (NP not in P/poly), we demonstrate a gap between the minimax prediction risk for sparse linear regression that can be achieved by polynomial-time algorithms, and that achieved by optimal…

Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a…

It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model.…

This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…

In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…

Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks. The standard setting of compressive sensing can not be immediately applied to…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

Kronecker compressed sensing refers to using Kronecker product matrices as sparsifying bases and measurement matrices in compressed sensing. This work focuses on the Kronecker compressed sensing problem, encompassing three sparsity…

We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

We develop lower bounds on communication in the memory hierarchy or between processors for nested bilinear algorithms, such as Strassen's algorithm for matrix multiplication. We build on a previous framework that establishes communication…