Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the ‘bottleneck’ layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied.Peer ReviewedPostprint (published version

Neural Networks Principal Component Analysis for Estimating the Generative Multifactor Model of Returns under a Statistical Approach to the Arbitrage Pricing Theory: Evidence from the Mexican Stock Exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA's assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the 'bottleneck' layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied

Identification of neural networks that contribute to motion sickness through principal components analysis of fos labeling induced by galvanic vestibular stimulation

Motion sickness is a complex condition that includes both overt signs (e.g., vomiting) and more covert symptoms (e.g., anxiety and foreboding). The neural pathways that mediate these signs and symptoms are yet to identified. This study mapped the distribution of c-fos protein (Fos)-like immunoreactivity elicited during a galvanic vestibular stimulation paradigm that is known to induce motion sickness in felines. A principal components analysis was used to identify networks of neurons activated during this stimulus paradigm from functional correlations between Fos labeling in different nuclei. This analysis identified five principal components (neural networks) that accounted for greater than 95% of the variance in Fos labeling. Two of the components were correlated with the severity of motion sickness symptoms, and likely participated in generating the overt signs of the condition. One of these networks included neurons in locus coeruleus, medial, inferior and lateral vestibular nuclei, lateral nucleus tractus solitarius, medial parabrachial nucleus and periaqueductal gray. The second included neurons in the superior vestibular nucleus, precerebellar nuclei, periaqueductal gray, and parabrachial nuclei, with weaker associations of raphe nuclei. Three additional components (networks) were also identified that were not correlated with the severity of motion sickness symptoms. These networks likely mediated the covert aspects of motion sickness, such as affective components. The identification of five statistically independent component networks associated with the development of motion sickness provides an opportunity to consider, in network activation dimensions, the complex progression of signs and symptoms that are precipitated in provocative environments. Similar methodology can be used to parse the neural networks that mediate other complex responses to environmental stimuli. © 2014 Balaban et al

A Simulation Study on Nonlinear Principal Component Analysis

In statistical practice multicollinearity of predictor variables is rather the rule than the exception and appropriate models are needed to avoid instability of predictions. Feature extraction methods reflect the idea that latent variables not measurable directly are underlying the original data. They try to reduce the dimension of the data by constructing new independent variables which keep as much information as possible from the original measurements. A common feature extraction method is Principal Component Analysis (PCA), which in its classical form is restricted to linear relationships among predictor variables. This paper is concerned with nonlinear principal component analysis (NLPCA) as introduced by Kramer (1991), who modelled his approach with help of artificial neural networks. By means of first simulation studies data derived from semicircles and circles are investigated with respect to their ability to be described by nonlinear principal components among the predictors

Decorrelation of Lung and Heart Sound

Abstract— Signal separation is very useful where several signals have been mixed together to form combined signal and our objective is to recover individual original component signals from that combined signal. One of the major problem in neural network and research in other disciplines is finding a suitable representation of multivariate data, i.e. random vectors. For concept and computational simplicity representation is in terms of linear transformation of the original data. This means that each component of the representation is a linear combination of the original variables. There are linear transformation methods such as principal component analysis and Independent Component Analysis (ICA). ICA is a recently developed method in which the goal is to find a linear representation of non-gaussian data so that the components are statistically independent or as independent as possible. DOI: 10.17762/ijritcc2321-8169.150615

Dynamic Responses in Brain Networks to Social Feedback: A Dual EEG Acquisition Study in Adolescent Couples

abstract: Adolescence is a sensitive period for the development of romantic relationships. During this period the maturation of frontolimbic networks is particularly important for the capacity to regulate emotional experiences. In previous research, both functional magnetic resonance imaging (fMRI) and dense array electroencephalography (dEEG) measures have suggested that responses in limbic regions are enhanced in adolescents experiencing social rejection. In the present research, we examined social acceptance and rejection from romantic partners as they engaged in a Chatroom Interact Task. Dual 128-channel dEEG systems were used to record neural responses to acceptance and rejection from both adolescent romantic partners and unfamiliar peers (N = 75). We employed a two-step temporal principal component analysis (PCA) and spatial independent component analysis (ICA) approach to statistically identify the neural components related to social feedback. Results revealed that the early (288 ms) discrimination between acceptance and rejection reflected by the P3a component was significant for the romantic partner but not the unfamiliar peer. In contrast, the later (364 ms) P3b component discriminated between acceptance and rejection for both partners and peers. The two-step approach (PCA then ICA) was better able than either PCA or ICA alone in separating these components of the brain's electrical activity that reflected both temporal and spatial phases of the brain's processing of social feedback.View the article as published at https://www.frontiersin.org/articles/10.3389/fncom.2017.00046/ful

Machine learning methods for genomic high-content screen data analysis applied to deduce organization of endocytic network

High-content screens are widely used to get insight on mechanistic organization of biological systems. Chemical and/or genomic interferences are used to modulate molecular machinery, then light microscopy and quantitative image analysis yield a large number of parameters describing phenotype. However, extracting functional information from such high-content datasets (e.g. links between cellular processes or functions of unknown genes) remains challenging. This work is devoted to the analysis of a multi-parametric image-based genomic screen of endocytosis, the process whereby cells uptake cargoes (signals and nutrients) and distribute them into different subcellular compartments. The complexity of the quantitative endocytic data was approached using different Machine Learning techniques, namely, Clustering methods, Bayesian networks, Principal and Independent component analysis, Artificial neural networks. The main goal of such an analysis is to predict possible modes of action of screened genes and also to find candidate genes that can be involved in a process of interest. The degree of freedom for the multidimensional phenotypic space was identified using the data distributions, and then the high-content data were deconvolved into separate signals from different cellular modules. Some of those basic signals (phenotypic traits) were straightforward to interpret in terms of known molecular processes; the other components gave insight into interesting directions for further research. The phenotypic profile of perturbation of individual genes are sparse in coordinates of the basic signals, and, therefore, intrinsically suggest their functional roles in cellular processes. Being a very fundamental process, endocytosis is specifically modulated by a variety of different pathways in the cell; therefore, endocytic phenotyping can be used for analysis of non-endocytic modules in the cell. Proposed approach can be also generalized for analysis of other high-content screens.:Contents Objectives Chapter 1 Introduction 1.1 High-content biological data 1.1.1 Different perturbation types for HCS 1.1.2 Types of observations in HTS 1.1.3 Goals and outcomes of MP HTS 1.1.4 An overview of the classical methods of analysis of biological HT- and HCS data 1.2 Machine learning for systems biology 1.2.1 Feature selection 1.2.2 Unsupervised learning 1.2.3 Supervised learning 1.2.4 Artificial neural networks 1.3 Endocytosis as a system process 1.3.1 Endocytic compartments and main players 1.3.2 Relation to other cellular processes Chapter 2 Experimental and analytical techniques 2.1 Experimental methods 2.1.1 RNA interference 2.1.2 Quantitative multiparametric image analysis 2.2 Detailed description of the endocytic HCS dataset 2.2.1 Basic properties of the endocytic dataset 2.2.2 Control subset of genes 2.3 Machine learning methods 2.3.1 Latent variables models 2.3.2 Clustering 2.3.3 Bayesian networks 2.3.4 Neural networks Chapter 3 Results 3.1 Selection of labeled data for training and validation based on KEGG information about genes pathways 3.2 Clustering of genes 3.2.1 Comparison of clustering techniques on control dataset 3.2.2 Clustering results 3.3 Independent components as basic phenotypes 3.3.1 Algorithm for identification of the best number of independent components 3.3.2 Application of ICA on the full dataset and on separate assays of the screen 3.3.3 Gene annotation based on revealed phenotypes 3.3.4 Searching for genes with target function 3.4 Bayesian network on endocytic parameters 3.4.1 Prediction of pathway based on parameters values using Naïve Bayesian Classifier 3.4.2 General Bayesian Networks 3.5 Neural networks 3.5.1 Autoencoders as nonlinear ICA 3.5.2 siRNA sequence motives discovery with deep NN 3.6 Biological results 3.6.1 Rab11 ZNF-specific phenotype found by ICA 3.6.2 Structure of BN revealed dependency between endocytosis and cell adhesion Chapter 4 Discussion 4.1 Machine learning approaches for discovery of phenotypic patterns 4.1.1 Functional annotation of unknown genes based on phenotypic profiles 4.1.2 Candidate genes search 4.2 Adaptation to other HCS data and generalization Chapter 5 Outlook and future perspectives 5.1 Handling sequence-dependent off-target effects with neural networks 5.2 Transition between machine learning and systems biology models Acknowledgements References Appendix A.1 Full list of cellular and endocytic parameters A.2 Description of independent components of the full dataset A.3 Description of independent components extracted from separate assays of the HC