Stochastic Optimization and Sparse Statistical Recovery: An Optimal Algorithm for High Dimensions

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We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures, yielding an O(d/T) convergence rate for strongly convex objectives in d dimensions, and an O(sqrt(s log d)/T) convergence rate when the optimum is s-sparse. Our algorithm is based on successively solving a series of regularized optimization problems using Nesterov’s dual averaging algorithm. We establish that the error of our solution after T iterations is at most O((s log d)/T), with natural extensions to approximate sparsity. Our results apply to locally Lipschitz losses including the logistic, exponential, hinge and least-squares losses. By recourse to statistical minimax results, we show that our convergence rates are optimal up to multiplicative constant factors. The effectiveness of our approach is also confirmed in numerical simulations, in which we compare to several baselines on a least-squares regression problem. [Joint work with Sahand Negahban and Martin Wainwright]

Most Accurate Stochastic Settings, Stochastic Optimization and Sparse Statistical Recovery: An Optimal Algorithm for High Dimensions.

Forex Trend Following – Catching The Big Trends

This identifies whether the time frame required is per hour, everyday or annual. What it implies is that when an existing pattern ends, a new trend starts. The technical analysis needs to also be determined by the Forex trader.

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What’s Your Trading Strategy?

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Swing Stochastic Trading systems feature different indications however the objective is always the very same, to take advantage of short term cost spikes, offer or purchase them and try to find a go back to a moving average.

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