245,912 research outputs found
Second-Order Stochastic Optimization for Machine Learning in Linear Time
First-order stochastic methods are the state-of-the-art in large-scale
machine learning optimization owing to efficient per-iteration complexity.
Second-order methods, while able to provide faster convergence, have been much
less explored due to the high cost of computing the second-order information.
In this paper we develop second-order stochastic methods for optimization
problems in machine learning that match the per-iteration cost of gradient
based methods, and in certain settings improve upon the overall running time
over popular first-order methods. Furthermore, our algorithm has the desirable
property of being implementable in time linear in the sparsity of the input
data
Stochastic Dominance Efficiency Tests under Diversification
This paper focuses on Stochastic Dominance (SD) efficiency in a finite empirical panel data. We analytically characterize the sets of unsorted time series that dominate a given evaluated distribution by the First, Second, and Third order SD. Using these insights, we develop simple Linear Programming and 0-1 Mixed Integer Linear Programming tests of SD efficiency. The advantage to the earlier efficiency tests is that the proposed approach explicitly accounts for diversification. Allowing for diversification can both improve the power of the empirical SD tests, and enable SD based portfolio optimization. A simple numerical example illustrates the SD efficiency tests. Discussion on the application potential and the future research directions concludes.Stochastic Dominance, Protfolio Choice, Efficiency, Diversification, Mathematical Programming
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