Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

The Analysis of Time Series: An Introduction, 4th edn. By C. Chatfield. ISBN 0 412 31820 2. Chapman and Hall, London, 1989. 242 pp. £13.50.

The Analysis of Time Series: An Introduction

There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research.

Why most published research findings are false

Time-Frequency Analysis.

Choosing a model with too few parameters can involve making unrealistically simple assumptions and lead to high bias, poor prediction, and missed opportunities for insight. Such models are not flexible enough to describe the sample or the population well. A model with too many parameters can fit the observed data very well, but be too closely tailored to it. Such models may generalize poorly. Penalizedlikelihood information criteria, such as Akaike’s Information Criterion (AIC), the Bayesian Information Criterion (BIC), the Consistent AIC, and the Adjusted BIC, are widely used for model selection. However, different criteria sometimes support different models, leading to uncertainty about which criterion is the most trustworthy. In some simple cases the comparison of two models using information criteria can be viewed as equivalent to a likelihood ratio test, with the different models representing different alpha levels (i.e., different emphases on sensitivity or specificity; Lin & Dayton 1997). This perspective may lead to insights about how to interpret the criteria in less simple situations. For example, AIC or BIC could be preferable, depending on sample size and on the relative importance one assigns to sensitivity versus specificity. Understanding the differences among the criteria may make it easier to compare their results and to use them to make informed decisions.

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Sensitivity and specificity of information criteria.

In the era of big data, analysts usually explore various statistical models or machine-learning methods for observed data to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are employed, a crucial step is to select the most appropriate model or method from a set of candidates. Model selection is a key ingredient in data analysis for reliable and reproducible statistical inference or prediction, and thus it is central to scientific studies in such fields as ecology, economics, engineering, finance, political science, biology, and epidemiology. There has been a long history of model selection techniques that arise from researches in statistics, information theory, and signal processing. A considerable number of methods has been proposed, following different philosophies and exhibiting varying performances. The purpose of this article is to provide a comprehensive overview of them, in terms of their motivation, large sample performance, and applicability. We provide integrated and practically relevant discussions on theoretical properties of state-of-the-art model selection approaches. We also share our thoughts on some controversial views on the practice of model selection.

Model Selection Techniques: An Overview

Federated Learning (FL) is a method of training machine learning models on private data distributed over a large number of possibly heterogeneous clients such as mobile phones and IoT devices. In this work, we propose a new federated learning framework named HeteroFL to address heterogeneous clients equipped with very different computation and communication capabilities. Our solution can enable the training of heterogeneous local models with varying computation complexities and still produce a single global inference model. For the first time, our method challenges the underlying assumption of existing work that local models have to share the same architecture as the global model. We demonstrate several strategies to enhance FL training and conduct extensive empirical evaluations, including five computation complexity levels of three model architecture on three datasets. We show that adaptively distributing subnetworks according to clients' capabilities is both computation and communication efficient.

HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients

Speech Emotion Recognition (SER) has emerged as a critical component of the next generation of human-machine interfacing technologies. In this work, we propose a new dual-level model that predicts emotions based on both MFCC features and mel-spectrograms produced from raw audio signals. Each utterance is preprocessed into MFCC features and two mel-spectrograms at different time-frequency resolutions. A standard LSTM processes the MFCC features, while a novel LSTM architecture, denoted as Dual-Sequence LSTM (DS-LSTM), processes the two mel-spectrograms simultaneously. The outputs are later averaged to produce a final classification of the utterance. Our proposed model achieves, on average, a weighted accuracy of 72.7% and an unweighted accuracy of 73.3%—a 6% improvement over current state-of-the-art unimodal models—and is comparable with multimodal models that leverage textual information as well as audio signals.

Speech Emotion Recognition with Dual-Sequence LSTM Architecture

Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for sparse approximation. Previous studies of OMP have considered the recovery of a sparse signal through Φ and y = Φx + b, where is a matrix with more columns than rows and denotes the measurement noise. In this paper, based on Restricted Isometry Property (RIP), the performance of OMP is analyzed under general perturbations, which means both y and Φ are perturbed. Though the exact recovery of an almost sparse signal x is no longer feasible, the main contribution reveals that the support set of the best k-term approximation of x can be recovered under reasonable conditions. The error bound between x and the estimation of OMP is also derived. By constructing an example it is also demonstrated that the sufficient conditions for support recovery of the best k-term approximation of are rather tight. When x is strong-decaying, it is proved that the sufficient conditions for support recovery of the best k-term approximation of x can be relaxed, and the support can even be recovered in the order of the entries' magnitude. Our results are also compared in detail with some related previous ones.

Perturbation Analysis of Orthogonal Matching Pursuit

To address order selection for an autoregressive model fitted to time series data, we propose a new information criterion. It has the benefits of the two well-known model selection techniques: the Akaike information criterion and the Bayesian information criterion. When the data are generated from a finite-order autoregression, the Bayesian information criterion is known to be consistent, and so is the new criterion. When the true order is infinity or suitably high with respect to the sample size, the Akaike information criterion is known to be efficient in the sense that its predictive performance is asymptotically equivalent to the best offered by the candidate models; in this case, the new criterion behaves in a similar manner. Different from the two classical criteria, the proposed criterion adaptively achieves either consistency or efficiency depending on the underlying true model. In practice, where the observed time series is given without any prior information about the model specification, the proposed order selection criterion is more flexible and reliable compared with classical approaches. Numerical results are presented, demonstrating the adaptivity of the proposed technique when applied to various data sets.

Jie Ding

Papers

Model Selection Techniques: An Overview

HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients

Speech Emotion Recognition with Dual-Sequence LSTM Architecture

Perturbation Analysis of Orthogonal Matching Pursuit

Bridging AIC and BIC: A New Criterion for Autoregression