相关论文: A robust parallel algorithm for combinatorial comp…

We propose $\beta$-graph embedding for robustly learning feature vectors from data vectors and noisy link weights. A newly introduced empirical moment $\beta$-score reduces the influence of contamination and robustly measures the difference…

Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…

Applications of compressed sensing motivate the possibility of using different operators to encode and decode a signal of interest. Since it is clear that the operators cannot be too different, we can view the discrepancy between the two…

We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…

Tensor train decomposition is one of the most powerful approaches for processing high-dimensional data. For low-rank tensor train decomposition of large tensors, the alternating least squares (ALS) algorithm is widely used by updating each…

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless,…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

State-of-the-art techniques for enhancing robustness of deep networks mostly rely on empirical risk minimization with suitable data augmentation. In this paper, we propose a complementary approach motivated by communication theory, aimed at…

This paper studies tensor-based Robust Principal Component Analysis (RPCA) using atomic-norm regularization. Given the superposition of a sparse and a low-rank tensor, we present conditions under which it is possible to exactly recover the…

In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…

We propose a prox-regular-type low-rank constrained nonconvex nonsmooth optimization model for Robust Low-Rank Matrix Recovery (RLRMR), i.e., estimate problem of low-rank matrix from an observed signal corrupted by outliers. For RLRMR, the…

We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…

The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…

Reinforcement learning algorithms are typically designed for discrete-time dynamics, even though the underlying real-world control systems are often continuous in time. In this paper, we study the problem of continuous-time reinforcement…

In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are called root-finding problems. Our first algorithm is…

Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two…

Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…

We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measurements. Our results are applicable for symmetric rank-one…