
Decentralized Online Learning with Kernels
We consider multiagent stochastic optimization problems over reproducin...
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Stochastic Tverberg theorems and their applications in multiclass logistic regression, data separability, and centerpoints of data
We present new stochastic geometry theorems that give bounds on the prob...
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Stochastic DCA for minimizing a large sum of DC functions with application to Multiclass Logistic Regression
We consider the large sum of DC (Difference of Convex) functions minimiz...
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Indefinite Kernel Logistic Regression
Traditionally, kernel learning methods requires positive definitiveness ...
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Poisson intensity estimation with reproducing kernels
Despite the fundamental nature of the inhomogeneous Poisson process in t...
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Smoothed Online Optimization for Regression and Control
We consider Online Convex Optimization (OCO) in the setting where the co...
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Adaptive Kernel Learning in Heterogeneous Networks
We consider the framework of learning over decentralized networks, where...
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Sparse Representations of Positive Functions via Projected PseudoMirror Descent
We consider the problem of expected risk minimization when the population loss is strongly convex and the target domain of the decision variable is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. We restrict focus to the case that the decision variable belongs to a nonparametric Reproducing Kernel Hilbert Space (RKHS). To solve it, we consider stochastic mirror descent that employs (i) pseudogradients and (ii) projections. Compressive projections are executed via kernel orthogonal matching pursuit (KOMP), and overcome the fact that the vanilla RKHS parameterization grows unbounded with time. Moreover, pseudogradients are needed, e.g., when stochastic gradients themselves define integrals over unknown quantities that must be evaluated numerically, as in estimating the intensity parameter of an inhomogeneous Poisson Process, and multiclass kernel logistic regression with latent multikernels. We establish tradeoffs between accuracy of convergence in mean and the projection budget parameter under constant stepsize and compression budget, as well as nonasymptotic bounds on the model complexity. Experiments demonstrate that we achieve stateoftheart accuracy and complexity tradeoffs for inhomogeneous Poisson Process intensity estimation and multiclass kernel logistic regression.
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