Related papers: Sparse Approximation, List Decoding, and Uncertain…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…
In our recent work \cite{StojnicCSetam09} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved that if the number of equations in the system is…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same…
Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…