866 research outputs found
Testing the Martingale Difference Hypothesis Using Neural Network Approximations
The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a,b). However, unlike that work we can provide a formal theoretical justification for the validity of these tests using approximation results from Kapetanios and Blake (2007). These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a,b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have superior power performance to all existing tests of the martingale difference hypothesis we consider. An empirical application to the S&P500 constituents illustrates the usefulness of our new test.Martingale difference hypothesis, Neural networks, Boosting
Efficient Private ERM for Smooth Objectives
In this paper, we consider efficient differentially private empirical risk
minimization from the viewpoint of optimization algorithms. For strongly convex
and smooth objectives, we prove that gradient descent with output perturbation
not only achieves nearly optimal utility, but also significantly improves the
running time of previous state-of-the-art private optimization algorithms, for
both -DP and -DP. For non-convex but smooth
objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient
Descent) algorithm, which provably converges to a stationary point with privacy
guarantee. Besides the expected utility bounds, we also provide guarantees in
high probability form. Experiments demonstrate that our algorithm consistently
outperforms existing method in both utility and running time
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