RNA-Seq Count Data Modelling by Grey Relational Analysis and Nonparametric Gaussian Process.

PurposeThe purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences.Design/methodology/approachThe definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied.FindingsThe negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility.Practical implicationsThe proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model.Originality/valueThe definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.

An expert system for automatically selecting stock portfolio is presented. The expert system involved Grey Relational Analysis (GRA) model, the VPRS-index clustering / classification method, and Variable Precision Rough Set (VPRS) theory. The GRA model is applied to consolidate the 53 financial indices into six financial ratios (Grey Relational Grades (GRGs)) for each stock item. The VPRS-index method is used to determine the optimal number of clusters per GRG. VPRS theory is then applied to identify the stocks within the -lower approximate sets. Finally, the GRGs of each candidate stock item are consolidated to a single GRG indicating the ability of the stock item to maximize the rate of return. The validity and effectiveness of the VPRS-index clustering / classification method is first evaluated prior to that of the expert system. After that, results of this study showed that this expert system yields a higher rate of return than those of several existing portfolio selection systems. Key words: Fuzzy C-Means, VPRS, VPRS-index method, classification, stock portfolio.

A stock portfolio selection system based on a Grey Relational Analysis (GRA) model, a Fuzzy C-Means (FCM) clustering scheme and Rough Set (RS) theory is proposed. In the proposed approach, 53 financial indices are collected automatically for each stock item every quarter and a GRA model is used to consolidate these indices into six predetermined financial ratios (Grey Relational Grades (GRGs)). The GRGs of the stock items are then clustered using a FCM scheme and the resulting cluster indices are processed using RS theory to identify the lower approximate set within the stock system. The stock items within the lower approximate set are filtered in accordance with established investment principles and the six GRGs of each surviving stock item are then consolidated to a single GRG indicating the overall merit of the corresponding stock item in terms of its ability to maximize the rate of return on the investment portfolio. The validity of the proposed approach is demonstrated using electronic stock data extracted from the financial database maintained by the Taiwan Economic Journal (TEJ). It is shown that the rate of return on the investment portfolio selected using the proposed GRA/FCM/RS system is higher than the average rate of return predicted by the variation in the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) over the same period. Thus, the feasibility of the GRA-based attribute reduction mechanism and the overall viability of the proposed portfolio selection system are confirmed. Introduction

This contribution presents a new development in the design of control system based on evolving Gaussian process (GP) models . GP models provide a probabilistic, nonparametric modelling approach for black-box identification of nonlinear dynamic systems. They can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. GP models contain noticeably less coefficients to be optimised than commonly used parametric models. While GP models are Bayesian models, their output is normal distribution, expressed in terms of mean and variance. Latter can be interpreted as a confidence in prediction and used in many fields, especially in control system. Evolving GP model is the concept approach within which various ways of model adaptations can be used. Successful control system needs as much as possible data about process to be controlled . If the prior knowledge about the system to be controlled is scarce or the system varies with time or operating region, this control problem can be solved with an iterative method which adapts model with information obtained with streaming data and concurrently optimises hyperparameter values. This contribution provides: a survey of adaptive control algorithms for dynamic systems described in publications where GP models have been used for control design, a novel and improved closed-loop controller with evolving GP models and an example for the illustration of proposed control algorithm.

Along with the development of the economy and society and the speedy increasing number of personal vehicles, especially motorcycles, many cities in developing countries like Hanoi (Vietnam) are facing many transportation problems, notably traffic accidents involving motorcyclists. Motorcycle accidents are caused by main human-error factors, and could be considered as the typical grey system with the features of complexity and imperfect information. In this study, a grey relational analysis (GRA) model of the human-error factors is presented to quickly explore the main human-error factors contributing to traffic accidents caused by motorcycles. In this model, the grey relational degree and the grey relational order of each human-error factor also are determined to rank the main contributing human-error factors. Taking the data of road traffic accidents caused by motorcycles in Hanoi, the capital of Vietnam between 2015 and 2017 as experimental data, the grey relational degrees of human-error factors have been analyzed quantitatively through the GRA model. The experimental results show the first three human-error factors include wrong lane shifting, poor road observation, and speeding, respectively. The results also help to conduct effective countermeasures for controlling human errors and reducing road traffic accidents.

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of inverse modeling. First, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Second, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of vegetation monitoring and atmospheric modeling.

Compared to state-of-the-art classifiers, the Gaussian process classifier (GPC) offers several attractive properties such as the possibility to estimate the hyperparameters or to learn the best input features in a fully automatic way. However, till now, the integration of spatial contextual information in a GPC model for classifying remote sensing imagery has not yet received a sufficient attention compared to other classification approaches for which it has been shown that the classification accuracy can benefit from the exploitation of such information. In this context, in order to improve the GPC capabilities, we propose here to reformulate the GPC learning model so as to integrate spatial contextual information. All the mathematical developments leading to the proposed spatial GPC (SGPC), which embeds iteratively the spatial contextual information in the classification process, is described. Experimental results show that the SGPC can help in improving the classification accuracy compared to the baseline GPC.

A probabilistic framework with concurrent analytics of Gaussian process regression and classification for multivariate control performance assessment

We present an interactive perception model for object sorting based on Gaussian Process (GP) classification that is capable of recognizing objects categories from point cloud data. In our approach, FPFH features are extracted from point clouds to describe the local 3D shape of objects and a Bag-of-Words coding method is used to obtain an object-level vocabulary representation. Multi-class Gaussian Process classification is employed to provide and probable estimation of the identity of the object and serves a key role in the interactive perception cycle – modelling perception confidence. We show results from simulated input data on both SVM and GP based multi-class classifiers to validate the recognition accuracy of our proposed perception model. Our results demonstrate that by using a GP-based classifier, we obtain true positive classification rates of up to 80%. Our semi-autonomous object sorting experiments show that the proposed GP based interactive sorting approach outperforms random sorting by up to 30% when applied to scenes comprising configurations of household objects.

This paper presents a comparison of four predictive models for classification tasks: logistic regression, support vector machines (SVM), Gaussian process (GP) classification, and a model based on partial exchangeability. The models were evaluated using a dataset with 7 binary covariates, where 70% of the sample was used for training and the remaining 30% for testing. Predictive performance was assessed through three metrics: the area under the receiver operating characteristic curve (AUC), Brier score, and logarithmic score. Results show that, while the SVM model performed distinctly, the other three models exhibited similar performance, with logistic regression demonstrating the best overall results, though not by a large margin. Theoretical insights from de Finetti’s representation theorem for partially exchangeable data suggest that logistic regression can be seen as a specific case of a more general model, which captures the influence of covariates on the outcome probabilities. Furthermore, we explored the Bayesian counterpart of logistic regression, using a flat prior on the model coefficients, and found that its predictive performance was almost identical to the frequentist approach. Although logistic regression was the most effective model for this dataset, the paper discusses the advantages of more flexible models, like SVM and GP classification, which may be better suited for capturing complex nonlinear relationships in data. The results indicate that while logistic regression is a reliable, fast, and interpretable model, alternative models may outperform it in cases where complex interactions between covariates and the target variable exist.

Quantitative prediction of subjective pain intensity from whole-brain fMRI data using Gaussian processes

We propose an iterative method to safely learn the unmodeled dynamics of a control-affine nonlinear system using Bayesian Gaussian process (GP) models with polynomial kernel functions. The method maintains safety by ensuring that the system state stays within the region of attraction (ROA) of a stabilizing control policy while collecting data. A quadratic programming based exploration control policy is computed to keep the exploration trajectory inside an inner-approximation of the ROA and to maximize the information gained from the trajectory. A prior GP model, which incorporates prior information about the unknown dynamics, is used to construct an initial stabilizing policy. As the GP model is updated with data, it is used to synthesize a new policy and a larger ROA, which increases the range of safe exploration. The use of polynomial kernels allows us to compute ROA inner-approximations and stabilizing control laws for the model using sum-of-squares programming. We also provide a probabilistic guarantee of safety which ensures that the policy computed using the learned model stabilizes the true dynamics with high confidence.

While machine learning algorithms are able to detect subtle patterns of interest in data, expert knowledge may contain crucial information that is not easily extracted from a given dataset, especially when the latter is small or noisy. In this paper we investigate the suitability of Gaussian Process Classification (GPC) as an effective model to implement the domain knowledge in an algorithm's training phase. Building on their Bayesian nature, we proceed by injecting problem- specific domain knowledge in the form of an a-priori distribution on the GPC latent function. We do this by extracting handcrafted features from the input data, and correlating them to the logits of the classification problem through fitting a prior function informed by the physiology of the problem. The physiologically-informed prior of the GPC is then updated through the Bayes formula using the available dataset. We apply the methods discussed here to a two-class classification problem associated to a dataset comprising Heart Rate Variability (HRV) and Electrodermal Activity (EDA) signals collected from 26 subjects who were exposed to a physical stressor aimed at altering their autonomic nervous systems dynamics. We provide comparative computational experiments on the selection of appropriate physiologically-inspired GPC prior functions. We find that the recognition of the presence of the physical stressor is significantly enhanced when the physiologically-inspired prior knowledge is injected into the GPC model.

In the contemporary educational landscape, proactively engaging in predictive assessment has become indispensable for academic institutions. This strategic imperative involves evaluating students based on their innate aptitude, preparing them adequately for impending examinations, and fostering both academic and personal development. Alarming statistics underscore a notable failure rate among students, particularly in courses. This article aims to employ predictive methodologies to assess and anticipate the academic performance of students in language courses during the G2 and G3 academic exams. The study utilizes the Gaussian Process Classification (GPC) model in conjunction with two optimization algorithms, the Population-based Vortex Search Algorithm (PVS) and the COOT Optimization Algorithm (COA), resulting in the creation of GPPV and GPCO models. The classification of students into distinct performance categories based on their language scores reveals that the GPPV model exhibits the highest concordance between measured and predicted outcomes. In G2, the GPPV model demonstrated the notable 51.1% correct categorization of students as Poor, followed by 25.57% in the Acceptable category, 14.17% in the good category, and 7.7% in the Excellent category. This performance surpasses both the optimized GPCO model and the singular GPC model, signifying its efficacy in predictive analysis and educational advancement.