Early Stop Criterion from the Bootstrap Ensemble

This paper addresses the problem of generalization error estimation in neural networks. A new early stop criterion based on a Bootstrap estimate of the generlization error is suggested. The estimate does not require the network to be trained to the minimum of the cost function, as required by other methods based on asymptotic theory. Moreover, in constrast to methods based on cross-validation which require data left out for testing, and thus biasing the estimate, the Bootstrap technique does not have this disadvantage. The potential of the suggested technique is demonstrated on various time-series problems. 1. INTRODUCTION The goal of neural network learning in signal processing is to identify robust functional dependencies between input and output data (for an introduction see e.g., [3]). Such learning usually proceeds from a finite random sample of training data; hence, the functions implemented by neural networks are stochastic depending on the particular available training set. T..

An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, that can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine and bioinformatics within the past few years. High dimensional problems are common not only in genetics, but also in some areas of psychological research, where only few subjects can be measured due to time or cost constraints, yet a large amount of data is generated for each subject. Random forests have been shown to achieve a high prediction accuracy in such applications, and provide descriptive variable importance measures reflecting the impact of each variable in both main effects and interactions. The aim of this work is to introduce the principles of the standard recursive partitioning methods as well as recent methodological improvements, to illustrate their usage for low and high dimensional data exploration, but also to point out limitations of the methods and potential pitfalls in their practical application. Application of the methods is illustrated using freely available implementations in the R system for statistical computing

Time series classification based on fractal properties

The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification approaches based on different features is carried out. The results indicate the advantage of the machine learning methods over the traditional estimating the degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl

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

Pairwise meta-rules for better meta-learning-based algorithm ranking

In this paper, we present a novel meta-feature generation method in the context of meta-learning, which is based on rules that compare the performance of individual base learners in a one-against-one manner. In addition to these new meta-features, we also introduce a new meta-learner called Approximate Ranking Tree Forests (ART Forests) that performs very competitively when compared with several state-of-the-art meta-learners. Our experimental results are based on a large collection of datasets and show that the proposed new techniques can improve the overall performance of meta-learning for algorithm ranking significantly. A key point in our approach is that each performance figure of any base learner for any specific dataset is generated by optimising the parameters of the base learner separately for each dataset

Recurrent DNNs and its Ensembles on the TIMIT Phone Recognition Task

In this paper, we have investigated recurrent deep neural networks (DNNs) in combination with regularization techniques as dropout, zoneout, and regularization post-layer. As a benchmark, we chose the TIMIT phone recognition task due to its popularity and broad availability in the community. It also simulates a low-resource scenario that is helpful in minor languages. Also, we prefer the phone recognition task because it is much more sensitive to an acoustic model quality than a large vocabulary continuous speech recognition task. In recent years, recurrent DNNs pushed the error rates in automatic speech recognition down. But, there was no clear winner in proposed architectures. The dropout was used as the regularization technique in most cases, but combination with other regularization techniques together with model ensembles was omitted. However, just an ensemble of recurrent DNNs performed best and achieved an average phone error rate from 10 experiments 14.84 % (minimum 14.69 %) on core test set that is slightly lower then the best-published PER to date, according to our knowledge. Finally, in contrast of the most papers, we published the open-source scripts to easily replicate the results and to help continue the development.Comment: Submitted to SPECOM 2018, 20th International Conference on Speech and Compute

Human gesture classification by brute-force machine learning for exergaming in physiotherapy

In this paper, a novel approach for human gesture classification on skeletal data is proposed for the application of exergaming in physiotherapy. Unlike existing methods, we propose to use a general classifier like Random Forests to recognize dynamic gestures. The temporal dimension is handled afterwards by majority voting in a sliding window over the consecutive predictions of the classifier. The gestures can have partially similar postures, such that the classifier will decide on the dissimilar postures. This brute-force classification strategy is permitted, because dynamic human gestures show sufficient dissimilar postures. Online continuous human gesture recognition can classify dynamic gestures in an early stage, which is a crucial advantage when controlling a game by automatic gesture recognition. Also, ground truth can be easily obtained, since all postures in a gesture get the same label, without any discretization into consecutive postures. This way, new gestures can be easily added, which is advantageous in adaptive game development. We evaluate our strategy by a leave-one-subject-out cross-validation on a self-captured stealth game gesture dataset and the publicly available Microsoft Research Cambridge-12 Kinect (MSRC-12) dataset. On the first dataset we achieve an excellent accuracy rate of 96.72%. Furthermore, we show that Random Forests perform better than Support Vector Machines. On the second dataset we achieve an accuracy rate of 98.37%, which is on average 3.57% better then existing methods

The Theory Behind Overfitting, Cross Validation, Regularization, Bagging, and Boosting: Tutorial

In this tutorial paper, we first define mean squared error, variance, covariance, and bias of both random variables and classification/predictor models. Then, we formulate the true and generalization errors of the model for both training and validation/test instances where we make use of the Stein's Unbiased Risk Estimator (SURE). We define overfitting, underfitting, and generalization using the obtained true and generalization errors. We introduce cross validation and two well-known examples which are $K$-fold and leave-one-out cross validations. We briefly introduce generalized cross validation and then move on to regularization where we use the SURE again. We work on both $\ell_2$ and $\ell_1$ norm regularizations. Then, we show that bootstrap aggregating (bagging) reduces the variance of estimation. Boosting, specifically AdaBoost, is introduced and it is explained as both an additive model and a maximum margin model, i.e., Support Vector Machine (SVM). The upper bound on the generalization error of boosting is also provided to show why boosting prevents from overfitting. As examples of regularization, the theory of ridge and lasso regressions, weight decay, noise injection to input/weights, and early stopping are explained. Random forest, dropout, histogram of oriented gradients, and single shot multi-box detector are explained as examples of bagging in machine learning and computer vision. Finally, boosting tree and SVM models are mentioned as examples of boosting.Comment: 23 pages, 9 figure