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We consider the minimization of a function defined on a Riemannian manifold M accessible only through unbiased estimates of its gradients. We develop a geometric framework to transform a sequence of slowly converging iterates generated from stochastic gradi ...
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is well-clustered. ...
We propose an estimator for the mean of a random vector in Rd that can be computed in time O(n3.5 + n2d) for n i.i.d. samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has ...
