Related papers: Covariance Eigenvector Sparsity for Compression an…

Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…

In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} =…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…

The discontinuous operations inherent in quantization and sparsification introduce a long-standing obstacle to backpropagation, particularly in ultra-low precision and sparse regimes. While the community has long viewed quantization as…

Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but…

Learning a generative model of visual information with sparse and compositional features has been a challenge for both theoretical neuroscience and machine learning communities. Sparse coding models have achieved great success in explaining…

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

This paper introduces a new method for learning and inferring sparse representations of depth (disparity) maps. The proposed algorithm relaxes the usual assumption of the stationary noise model in sparse coding. This enables learning from…

In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is…

Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors…

Cosmological covariance matrices are fundamental for parameter inference, since they are responsible for propagating uncertainties from the data down to the model parameters. However, when data vectors are large, in order to estimate…

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…

This paper investigates the signal detection problem in colored Gaussian noise with an unknown covariance matrix. To be specific, we consider a sample deficient scenario in which the number of signal bearing samples ($n$) is strictly…