5,870 research outputs found
Linear Convergence of Stochastic Iterative Greedy Algorithms with Sparse Constraints
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to the solution within a specified tolerance. This generalized framework applies to problems such as sparse signal recovery in compressed sensing, low-rank matrix recovery, and co-variance matrix estimation, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments which align with the theoretical analysis and demonstrate these improvements in several different settings
An Asynchronous Parallel Approach to Sparse Recovery
Asynchronous parallel computing and sparse recovery are two areas that have
received recent interest. Asynchronous algorithms are often studied to solve
optimization problems where the cost function takes the form , with a common assumption that each is sparse; that is, each
acts only on a small number of components of . Sparse
recovery problems, such as compressed sensing, can be formulated as
optimization problems, however, the cost functions are dense with respect
to the components of , and instead the signal is assumed to be sparse,
meaning that it has only non-zeros where . Here we address how one
may use an asynchronous parallel architecture when the cost functions are
not sparse in , but rather the signal is sparse. We propose an
asynchronous parallel approach to sparse recovery via a stochastic greedy
algorithm, where multiple processors asynchronously update a vector in shared
memory containing information on the estimated signal support. We include
numerical simulations that illustrate the potential benefits of our proposed
asynchronous method.Comment: 5 pages, 2 figure
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