A Modern Introduction to Online Learning

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.Comment: Fixed more typos, added more history bits, added local norms bounds for OMD and FTR

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

Photometric redshifts for Quasars in multi band Surveys

MLPQNA stands for Multi Layer Perceptron with Quasi Newton Algorithm and it is a machine learning method which can be used to cope with regression and classification problems on complex and massive data sets. In this paper we give the formal description of the method and present the results of its application to the evaluation of photometric redshifts for quasars. The data set used for the experiment was obtained by merging four different surveys (SDSS, GALEX, UKIDSS and WISE), thus covering a wide range of wavelengths from the UV to the mid-infrared. The method is able i) to achieve a very high accuracy; ii) to drastically reduce the number of outliers and catastrophic objects; iii) to discriminate among parameters (or features) on the basis of their significance, so that the number of features used for training and analysis can be optimized in order to reduce both the computational demands and the effects of degeneracy. The best experiment, which makes use of a selected combination of parameters drawn from the four surveys, leads, in terms of DeltaZnorm (i.e. (zspec-zphot)/(1+zspec)), to an average of DeltaZnorm = 0.004, a standard deviation sigma = 0.069 and a Median Absolute Deviation MAD = 0.02 over the whole redshift range (i.e. zspec <= 3.6), defined by the 4-survey cross-matched spectroscopic sample. The fraction of catastrophic outliers, i.e. of objects with photo-z deviating more than 2sigma from the spectroscopic value is < 3%, leading to a sigma = 0.035 after their removal, over the same redshift range. The method is made available to the community through the DAMEWARE web application.Comment: 38 pages, Submitted to ApJ in February 2013; Accepted by ApJ in May 201

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture