Related papers: Lossy Compression via Sparse Linear Regression: Pe…
The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…
The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…
Sparse coding is a proven principle for learning compact representations of images. However, sparse coding by itself often leads to very redundant dictionaries. With images, this often takes the form of similar edge detectors which are…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length $N$. For…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
Lossy gradient compression has become a practical tool to overcome the communication bottleneck in centrally coordinated distributed training of machine learning models. However, algorithms for decentralized training with compressed…
We evaluate typical performance of irregular low-density generator-matrix (LDGM) codes, which is defined by sparse matrices with arbitrary irregular bit degree distribution and arbitrary check degree distribution, for lossy compression. We…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the…
We address the problem of reconstructing sparse signals from noisy and compressive measurements using a feed-forward deep neural network (DNN) with an architecture motivated by the iterative shrinkage-thresholding algorithm (ISTA). We…
Dictionary learning methods continue to gain popularity for the solution of challenging inverse problems. In the dictionary learning approach, the computational forward model is replaced by a large dictionary of possible outcomes, and the…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$-norm minimization - a sparse quaternion signal from a limited number of its linear measurements,…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
We explore an error-bounded lossy compression approach for reducing scientific data associated with 2D/3D unstructured meshes. While existing lossy compressors offer a high compression ratio with bounded error for regular grid data,…
This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…