
An homotopy method for ℓ_p regression provably beyond selfconcordance and in inputsparsity time
We consider the problem of linear regression where the ℓ_2^n norm loss (...
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Subspace Embedding and Linear Regression with Orlicz Norm
We consider a generalization of the classic linear regression problem to...
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Estimation of the l_2norm and testing in sparse linear regression with unknown variance
We consider the related problems of estimating the l_2norm and the squa...
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Iterative Refinement for ℓ_pnorm Regression
We give improved algorithms for the ℓ_pregression problem, _xx_p such t...
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Efficient PerExample Gradient Computations
This technical report describes an efficient technique for computing the...
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Convergence Analysis of the Dynamics of a Special Kind of TwoLayered Neural Networks with ℓ_1 and ℓ_2 Regularization
In this paper, we made an extension to the convergence analysis of the d...
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Universal Streaming of Subset Norms
Most known algorithms in the streaming model of computation aim to appro...
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Efficient Symmetric Norm Regression via Linear Sketching
We provide efficient algorithms for overconstrained linear regression problems with size n × d when the loss function is a symmetric norm (a norm invariant under signflips and coordinatepermutations). An important class of symmetric norms are Orlicz norms, where for a function G and a vector y ∈R^n, the corresponding Orlicz norm y_G is defined as the unique value α such that ∑_i=1^n G(y_i/α) = 1. When the loss function is an Orlicz norm, our algorithm produces a (1 + ε)approximate solution for an arbitrarily small constant ε > 0 in inputsparsity time, improving over the previously bestknown algorithm which produces a d ·polylog napproximate solution. When the loss function is a general symmetric norm, our algorithm produces a √(d)·polylog n ·mmc(ℓ)approximate solution in inputsparsity time, where mmc(ℓ) is a quantity related to the symmetric norm under consideration. To the best of our knowledge, this is the first inputsparsity time algorithm with provable guarantees for the general class of symmetric norm regression problem. Our results shed light on resolving the universal sketching problem for linear regression, and the techniques might be of independent interest to numerical linear algebra problems more broadly.
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