Independent and Periodically Identically Distributed Processes (i.p.i.d.)
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d. processes. It is shown that the algorithms can be computed recursively and are asymptotically optimal. This problem has applications in anomaly detection in traffic data, social network data, and neural data, where periodic statistical behavior has been observed. …

C Math Library (CML)

Multiple Search Neuroevolution (MSN)
This paper presents an evolutionary metaheuristic called Multiple Search Neuroevolution (MSN) to optimize deep neural networks. The algorithm attempts to search multiple promising regions in the search space simultaneously, maintaining sufficient distance between them. It is tested by training neural networks for two tasks, and compared with other optimization algorithms. The first task is to solve Global Optimization functions with challenging topographies. We found to MSN to outperform classic optimization algorithms such as Evolution Strategies, reducing the number of optimization steps performed by at least 2X. The second task is to train a convolutional neural network (CNN) on the popular MNIST dataset. Using 3.33% of the training set, MSN reaches a validation accuracy of 90%. Stochastic Gradient Descent (SGD) was able to match the same accuracy figure, while taking 7X less optimization steps. Despite lagging, the fact that the MSN metaheurisitc trains a 4.7M-parameter CNN suggests promise for future development. This is by far the largest network ever evolved using a pool of only 50 samples. …

Nested Averaged Stochastic Approximation (NASA)
We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm has two auxiliary averaged sequences (filters) which estimate the gradient of the composite objective function and the inner function value. By using a special Lyapunov function, we show that NASA achieves the sample complexity of ${\cal O}(1/\epsilon^{2})$ for finding an $\epsilon$-approximate stationary point, thus outperforming all extant methods for nested stochastic approximation. Our method and its analysis are the same for both unconstrained and constrained problems, without any need of batch samples for constrained nonconvex stochastic optimization. We also present a simplified variant of the NASA method for solving constrained single level stochastic optimization problems, and we prove the same complexity result for both unconstrained and constrained problems. …