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Convergence analysis of inexact proximal Newtontype methods
"... We study inexact proximal Newtontype methods to solve convex optimization problems in composite form: minimize x∈Rn f(x): = g(x) + h(x), where g is convex and continuously differentiable and h: Rn → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated ef ..."
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We study inexact proximal Newtontype methods to solve convex optimization problems in composite form: minimize x∈Rn f(x): = g(x) + h(x), where g is convex and continuously differentiable and h: Rn → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated
Proximal Newtontype methods for convex optimization
"... We seek to solve convex optimization problems in composite form: minimize x∈R n f(x): = g(x) + h(x), where g is convex and continuously differentiable and h: R n → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. We derive a generalizatio ..."
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Cited by 15 (0 self)
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generalization of Newtontype methods to handle such convex but nonsmooth objective functions. We prove such methods are globally convergent and achieve superlinear rates of convergence in the vicinity of an optimal solution. We also demonstrate the performance of these methods using problems of relevance
Projected Newtontype Methods in Machine Learning
"... We consider projected Newtontype methods for solving largescale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newtontype methods by reviewing a canonical projected (quasi)Newton method. This method, while conceptua ..."
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Cited by 10 (1 self)
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conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are more scalable, namely, twometric projection and inexact projection methods. Finally, we show how to apply the Newtontype framework to handle nonsmooth objectives. Examples are provided throughout
11 Projected Newtontype Methods in Machine Learning
"... We consider projected Newtontype methods for solving largescale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newtontype methods by reviewing a canonical projected (quasi)Newton method. This method, while concep ..."
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conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are more scalable, namely, twometric projection and inexact projection methods. Finally, we show how to apply the Newtontype framework to handle nonsmooth objectives. Examples are provided through
A family of algorithms for approximate Bayesian inference
, 2001
"... One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," ..."
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Cited by 369 (11 self)
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distribution with a simpler distribution, which is close in the sense of KLdivergence. Expectation Propagation exploits the best of both algorithms: the generality of assumeddensity filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M ..."
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Cited by 270 (33 self)
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dimensional source signal s(t). Many natural signals can be sparsely represented in a proper signal dictionary s i (t) = K X k=1 C ik ' k (t) (1.2) The scalar functions ' k
Results 11  20
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13,744