arXiv research

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identic…

This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize bo…

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing un…

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One fami…

Recurrent Neural Networks (RNNs) are used in state-of-the-art models in domains such as speech recognition, machine translation, and language modelling. Sparsity is a technique to reduce compute and memory requirements of deep learning models. Sparse RNNs are easier to deploy on devices and high-end server processors. …

Two new methods improve block-sparse signal recovery from noisy data.

We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we d…

The performance of sparse signal recovery from noise corrupted, underdetermined measurements can be improved if both sparsity and correlation structure of signals are exploited. One typical correlation structure is the intra-block correlation in block sparse signals. To exploit this structure, a framework, called block…

Paper analyzes and improves GPSP algorithm for block sparse signal recovery.

Efficiently approximates Sparse PCA with significant speedups and minor error.

We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of…

GRRT recovers sparse signals without prior sparsity or noise variance knowledge.

Dealing with sparse rewards is a longstanding challenge in reinforcement learning. The recent use of hindsight methods have achieved success on a variety of sparse-reward tasks, but they fail on complex tasks such as stacking multiple blocks with a robot arm in simulation. Curiosity-driven exploration using the predict…

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest.…

In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes o…

We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-$\ell_1$ regularization. While the current theory provides promis…

Sparse deep neural networks(DNNs) are efficient in both memory and compute when compared to dense DNNs. But due to irregularity in computation of sparse DNNs, their efficiencies are much lower than that of dense DNNs on regular parallel hardware such as TPU. This inefficiency leads to poor/no performance benefits for s…

Proposes RBGP framework for efficient block sparse neural networks.

New method identifies latent variables with sparse perturbations.

Improved spectral clustering guarantees for dynamic stochastic block models.

Dynamic sparseness reduces neural network computation by selectively omitting parts of computations.

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion…

New method for community detection in sparse directed SBMs with exact recovery guarantees.

We introduce Block Sparse Canonical Correlation Analysis which estimates multiple pairs of canonical directions (together a "block") at once, resulting in significantly improved orthogonality of the sparse directions which, we demonstrate, translates to more interpretable solutions. Our approach builds on the sparse CC…

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed t…

Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization method for NCP that can impose sparsity efficiently is required. In this paper, we co…

Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.

We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual $\ell_1$ recovery," (b) block-sparsity with possibly overlapping blo…

New method finds linear relationships across multiple data blocks using proximal gradient descent with $\ell_1$ constraint.

The interaction between transitivity and sparsity, two common features in empirical networks, implies that there are local regions of large sparse networks that are dense. We call this the blessing of transitivity and it has consequences for both modeling and inference. Extant research suggests that statistical inferen…

Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization problem. In this paper, we reinterpret these results as performing MAP estimation u…

Sparse spectral decomposition identifies overlapping communities in networks.

In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …

Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.

The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these issues mean that the usual model-selection criteria do not work properly for networks…

In this paper, we study the information-theoretic limits of community detection in the symmetric two-community stochastic block model, with intra-community and inter-community edge probabilities $\frac{a}{n}$ and $\frac{b}{n}$ respectively. We consider the sparse setting, in which $a$ and $b$ do not scale with $n$, and…

New Bethe-Hessian method improves community detection in sparse networks.

Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.

Spectral method detects communities in sparse hypergraphs, achieving detection threshold.

The study extends stochastic block models to geometric settings, focusing on community detection and information flow.

Sparse activations in neural networks are hard to exploit but lead to advantages in learning.

STanHop predicts multivariate time series with memory-enhanced capabilities.

Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitr…

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 ascent (a variant of the tensor power method), and hard thresholding of the resid…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a fundamental challenge in bio-,astronomical imaging and speech processing. The problem abov…

Learning the "blocking" structure is a central challenge for high dimensional data (e.g., gene expression data). Recently, a sparse singular value decomposition (SVD) has been used as a biclustering tool to achieve this goal. However, this model ignores the structural information between variables (e.g., gene interacti…

Spectral algorithm recovers community structure in sparse hypergraphs.