Related papers: Linear Computation Coding: Exponential Search and …
Maximum Likelihood (ML) decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an Integer Programming (IP) problem. Feldman et al. relaxed this IP problem and presented Linear Programming (LP)…
This is a tale of two linear programming decoders, namely channel coding linear programming decoding (CC-LPD) and compressed sensing linear programming decoding (CS-LPD). So far, they have evolved quite independently. The aim of the present…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Slow working nodes, known as stragglers, can greatly reduce the speed of distributed computation. Coded matrix multiplication is a recently introduced technique that enables straggler-resistant distributed multiplication of large matrices.…
Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…