Wavelet Neural Networks: A Practical Guide

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications

BayesNAS: A Bayesian Approach for Neural Architecture Search

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian learning approach to alleviate these two issues by modeling architecture parameters using hierarchical automatic relevance determination (HARD) priors. Unlike other NAS methods, we train the over-parameterized network for only one epoch then update the architecture. Impressively, this enabled us to find the architecture on CIFAR-10 within only 0.2 GPU days using a single GPU. Competitive performance can be also achieved by transferring to ImageNet. As a byproduct, our approach can be applied directly to compress convolutional neural networks by enforcing structural sparsity which achieves extremely sparse networks without accuracy deterioration.Comment: International Conference on Machine Learning 201

Toward Optimal Run Racing: Application to Deep Learning Calibration

This paper aims at one-shot learning of deep neural nets, where a highly parallel setting is considered to address the algorithm calibration problem - selecting the best neural architecture and learning hyper-parameter values depending on the dataset at hand. The notoriously expensive calibration problem is optimally reduced by detecting and early stopping non-optimal runs. The theoretical contribution regards the optimality guarantees within the multiple hypothesis testing framework. Experimentations on the Cifar10, PTB and Wiki benchmarks demonstrate the relevance of the approach with a principled and consistent improvement on the state of the art with no extra hyper-parameter

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