Least Squares and Minimum MSE Estimators of Variance Components in Mixed Linear Models

The paper deals with the quadratic invariant estimators of the linear functions of variance components in mixed linear model. The estimator with locally minimal mean square error with respect to a parameter ? is derived. Under the condition of normality of the vector Y the theoretical values of MSE of several types of estimators are compared in two different mixed models; under a different types of distributions a simulation study is carried out for the behaviour of derived estimators.     

Learning Bayesian network classifiers using ant colony optimization

Bayesian networks are knowledge representation tools that model the (in)dependency relationships among variables for probabilistic reasoning. Classification with Bayesian networks aims to compute the class with the highest probability given a case. This special kind is referred to as Bayesian network classifiers. Since learning the Bayesian network structure from a dataset can be viewed as an optimization problem, heuristic search algorithms may be applied to build high-quality networks in medium- or large-scale problems, as exhaustive search is often feasible only for small problems. In this paper, we present our new algorithm, ABC-Miner, and propose several extensions to it. ABC-Miner uses ant colony optimization for learning the structure of Bayesian network classifiers. We report extended computational results comparing the performance of our algorithm with eight other classification algorithms, namely six variations of well-known Bayesian network classifiers, cAnt-Miner for discovering classification rules and a support vector machine algorithm.     

Penalized Bregman divergence for large-dimensional regression and classification

Regularization methods are characterized by loss functions measuring data fits and penalty terms constraining model parameters. The commonly used quadratic loss is not suitable for classification with binary responses, whereas the loglikelihood function is not readily applicable to models where the exact distribution of observations is unknown or not fully specified. We introduce the penalized Bregman divergence by replacing the negative loglikelihood in the conventional penalized likelihood with Bregman divergence, which encompasses many commonly used loss functions in the regression analysis, classification procedures and machine learning literature. We investigate new statistical properties of the resulting class of estimators with the number p(n) of parameters either diverging with the sample size n or even nearly comparable with n, and develop statistical inference tools. It is shown that the resulting penalized estimator, combined with appropriate penalties, achieves the same oracle property as the penalized likelihood estimator, but asymptotically does not rely on the complete specification of the underlying distribution. Furthermore, the choice of loss function in the penalized classifiers has an asymptotically relatively negligible impact on classification performance. We illustrate the proposed method for quasilikelihood regression and binary classification with simulation evaluation and real-data application.     

A Bayesian network classification methodology for gene expression data.

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the absence of prior expert knowledge. Our classifiers are developed under a cross validation regimen and then validated on corresponding out-of-sample test sets. The classifiers attain a classification rate in excess of 90% on out-of-sample test sets for two publicly available datasets. We present an extensive compilation of results reported in the literature for other classification methods run against these same two datasets. Our results are comparable to, or better than, any we have found reported for these two sets, when a train-test protocol as stringent as ours is followed.     

On latent-variable model misspecification in structural measurement error models for binary response

Summary .  We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods.     

Shrinkage Pre-Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student-t Errors

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.     

Locally adaptive function estimation for binary regression models

In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.     

A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in MATLAB

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.     

Consensus methods based on machine learning techniques for marine phytoplankton presence–absence prediction

We performed different consensus methods by combining binary classifiers, mostly machine learning classifiers, with the aim to test their capability as predictive tools for the presence–absence of marine phytoplankton species. The consensus methods were constructed by considering a combination of four methods (i.e., generalized linear models, random forests, boosting and support vector machines). Six different consensus methods were analyzed by taking into account six different ways of combining single-model predictions. Some of these methods are presented here for the first time. To evaluate the performance of the models, we considered eight phytoplankton species presence–absence data sets and data related to environmental variables. Some of the analyzed species are toxic, whereas others provoke water discoloration, which can cause alarm in the population. Besides the phytoplankton data sets, we tested the models on 10 well-known open access data sets. We evaluated the models' performances over a test sample. For most (72%) of the data sets, a consensus method was the method with the lowest classification error. In particular, a consensus method that weighted single-model predictions in accordance with single-model performances (weighted average prediction error — WA-PE model) was the one that presented the lowest classification error most of the time. For the phytoplankton species, the errors of the WA-PE model were between 10% for the species Akashiwo sanguinea and 38% for Dinophysis acuminata. This study provides novel approaches to improve the prediction accuracy in species distribution studies and, in particular, in those concerning marine phytoplankton species.     

A Bayesian method for comparing and combining binary classifiers in the absence of a gold standard

ABSTRACT: BACKGROUND: Many problems in bioinformatics involve classification based on features such as sequence, structure or morphology. Given multiple classifiers, two crucial questions arise: how does their performance compare, and how can they best be combined to produce a better classifier? A classifier can be evaluated in terms of sensitivity and specificity using benchmark, or gold standard, data, that is, data for which the true classification is known. However, a gold standard is not always available. Here we demonstrate that a Bayesian model for comparing medical diagnostics without a gold standard can be successfully applied in the bioinformatics domain, to genomic scale data sets. We present a new implementation, which unlike previous implementations is applicable to any number of classifiers. We apply this model, for the first time, to the problem of finding the globally optimal logical combination of classifiers. RESULTS: We compared three classifiers of protein subcellular localisation, and evaluated our estimates of sensitivity and specificity against estimates obtained using a gold standard. The method overestimated sensitivity and specificity with only a small discrepancy, and correctly ranked the classifiers. Diagnostic tests for swine flu were then compared on a small data set. Lastly, classifiers for a genome-wide association study of macular degeneration with 541094 SNPs were analysed. In all cases, run times were feasible, and results precise. The optimal logical combination of classifiers was also determined for all three data sets. Code and data are available from http://bioinformatics.monash.edu.au/downloads/. CONCLUSIONS: The examples demonstrate the methods are suitable for both small and large data sets, applicable to the wide range of bioinformatics classification problems, and robust to dependence between classifiers. In all three test cases, the globally optimal logical combination of the classifiers was found to be their union, according to three out of four ranking criteria. We propose as a general rule of thumb that the union of classifiers will be close to optimal.     

A comparison of several point estimators of the odds ratio in a single 2 x 2 contingency table.

The relative performance of the unconditioned maximum likelihood estimators (UMLEs), conditional MLEs (CMLEs), and Jewell-type estimators of the odds ratio (OR) and its logarithm were investigated in sets of single 2 x 2 contingency tables. The tables were generated by complete enumeration of all possible cell frequencies consistent with a single fixed margin. The bias, mean squared error (MSE), and average absolute error (AAE) were computed for all estimators using the individual table probabilities as weights. The results showed that, for the OR, Jewell's estimator usually had smaller bias, MSE, and AAE than either of the MLEs. While the differences were often slight for MSE and AAE, for bias it was sometimes substantial. For the log(OR), the UMLE usually had the lowest bias, and its MSE and AAE were only slightly greater than those for the other estimators. Overall, we recommend estimation on the log scale using the UMLE. If OR is to be estimated, Jewell's method had strong merit, although it is nonsymmetric with respect to the table orientation. In view of this, the UMLE may again be favoured in some situations.     

Correction for Covariate Measurement Error in Nonparametric Longitudinal Regression

Summary We introduce a correction for covariate measurement error in nonparametric regression applied to longitudinal binary data arising from a study on human sleep. The data have been surveyed to investigate the association of some hormonal levels and the probability of being asleep. The hormonal effect is modeled flexibly while we account for the error‐prone measurement of its concentration in the blood and the longitudinal character of the data. We present a fully Bayesian treatment utilizing Markov chain Monte Carlo inference techniques, and also introduce block updating to improve sampling and computational performance in the binary case. Our model is partly inspired by the relevance vector machine with radial basis functions, where usually very few basis functions are automatically selected for fitting the data. In the proposed approach, we implement such data‐driven complexity regulation by adopting the idea of Bayesian model averaging. Besides the general theory and the detailed sampling scheme, we also provide a simulation study for the Gaussian and the binary cases by comparing our method to the naive analysis ignoring measurement error. The results demonstrate a clear gain when using the proposed correction method, particularly for the Gaussian case with medium and large measurement error variances, even if the covariate model is misspecified.     

Optimal number of features as a function of sample size for various classification rules

MOTIVATION: Given the joint feature-label distribution, increasing the number of features always results in decreased classification error; however, this is not the case when a classifier is designed via a classification rule from sample data. Typically (but not always), for fixed sample size, the error of a designed classifier decreases and then increases as the number of features grows. The potential downside of using too many features is most critical for small samples, which are commonplace for gene-expression-based classifiers for phenotype discrimination. For fixed sample size and feature-label distribution, the issue is to find an optimal number of features. RESULTS: Since only in rare cases is there a known distribution of the error as a function of the number of features and sample size, this study employs simulation for various feature-label distributions and classification rules, and across a wide range of sample and feature-set sizes. To achieve the desired end, finding the optimal number of features as a function of sample size, it employs massively parallel computation. Seven classifiers are treated: 3-nearest-neighbor, Gaussian kernel, linear support vector machine, polynomial support vector machine, perceptron, regular histogram and linear discriminant analysis. Three Gaussian-based models are considered: linear, nonlinear and bimodal. In addition, real patient data from a large breast-cancer study is considered. To mitigate the combinatorial search for finding optimal feature sets, and to model the situation in which subsets of genes are co-regulated and correlation is internal to these subsets, we assume that the covariance matrix of the features is blocked, with each block corresponding to a group of correlated features. Altogether there are a large number of error surfaces for the many cases. These are provided in full on a companion website, which is meant to serve as resource for those working with small-sample classification. AVAILABILITY: For the companion website, please visit http://public.tgen.org/tamu/ofs/ CONTACT: e-dougherty@ee.tamu.edu.     

Using hierarchical text classification to investigate the utility of machine learning in automating online analyses of wildlife exploitation

Expanding digital data sources, including social media, online news articles and blogs, provide an opportunity to understand better the context and intensity of human-nature interactions, such as wildlife exploitation. However, online searches encompassing large taxonomic groups can generate vast datasets, which can be overwhelming to filter for relevant content without the use of automated tools. The variety of machine learning models available to researchers, and the need for manually labelled training data with an even balance of labels, can make applying these tools challenging. Here, we implement and evaluate a hierarchical text classification pipeline which brings together three binary classification tasks with increasingly specific relevancy criteria. Crucially, the hierarchical approach facilitates the filtering and structuring of a large dataset, of which relevant sources make up a small proportion. Using this pipeline, we also investigate how the accuracy with which text classifiers identify relevant and irrelevant texts is influenced by the use of different models, training datasets, and the classification task. To evaluate our methods, we collected data from Facebook, Twitter, Google and Bing search engines, with the aim of identifying sources documenting the hunting and persecution of bats (Chiroptera). Overall, the ‘state-of-the-art’ transformer-based models were able to identify relevant texts with an average accuracy of 90%, with some classifiers achieving accuracy of >95%. Whilst this demonstrates that application of more advanced models can lead to improved accuracy, comparable performance was achieved by simpler models when applied to longer documents and less ambiguous classification tasks. Hence, the benefits from using more computationally expensive models are dependent on the classification context. We also found that stratification of training data, according to the presence of key search terms, improved classification accuracy for less frequent topics within datasets, and therefore improves the applicability of classifiers to future data collection. Overall, whilst our findings reinforce the usefulness of automated tools for facilitating online analyses in conservation and ecology, they also highlight that the effectiveness and appropriateness of such tools is determined by the nature and volume of data collected, the complexity of the classification task, and the computational resources available to researchers.     

Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials

Cluster randomized trials (CRTs) frequently recruit a small number of clusters, therefore necessitating the application of small-sample corrections for valid inference. A recent systematic review indicated that CRTs reporting right-censored, time-to-event outcomes are not uncommon and that the marginal Cox proportional hazards model is one of the common approaches used for primary analysis. While small-sample corrections have been studied under marginal models with continuous, binary, and count outcomes, no prior research has been devoted to the development and evaluation of bias-corrected sandwich variance estimators when clustered time-to-event outcomes are analyzed by the marginal Cox model. To improve current practice, we propose nine bias-corrected sandwich variance estimators for the analysis of CRTs using the marginal Cox model and report on a simulation study to evaluate their small-sample properties. Our results indicate that the optimal choice of bias-corrected sandwich variance estimator for CRTs with survival outcomes can depend on the variability of cluster sizes and can also slightly differ whether it is evaluated according to relative bias or type I error rate. Finally, we illustrate the new variance estimators in a real-world CRT where the conclusion about intervention effectiveness differs depending on the use of small-sample bias corrections. The proposed sandwich variance estimators are implemented in an R package CoxBcv .     

基于优化核参数支持向量机的意识任务分类

根据支持向量机的基本原理,给出一种推广误差上界估计判据,并利用该判据进行最优核参数的自动选取。对三种不同意识任务的脑电信号进行多变量自回归模型参数估计,作为意识任务的特征向量,利用支持向量机进行训练和分类测试。分类结果表明,优化核参数的支持向量机分类器取得了最佳的分类效果,分类正确率明显高于径向基函数神经网络。     

StAR: a simple tool for the statistical comparison of ROC curves

Background  

As in many different areas of science and technology, most important problems in bioinformatics rely on the proper development and assessment of binary classifiers. A generalized assessment of the performance of binary classifiers is typically carried out through the analysis of their receiver operating characteristic (ROC) curves. The area under the ROC curve (AUC) constitutes a popular indicator of the performance of a binary classifier. However, the assessment of the statistical significance of the difference between any two classifiers based on this measure is not a straightforward task, since not many freely available tools exist. Most existing software is either not free, difficult to use or not easy to automate when a comparative assessment of the performance of many binary classifiers is intended. This constitutes the typical scenario for the optimization of parameters when developing new classifiers and also for their performance validation through the comparison to previous art.     

Random projection ensemble classification with high-dimensional time series

Multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. We propose new random projection ensemble classifiers with high-dimensional MTS. The method first applies dimension reduction in the time domain via randomly projecting the time-series variables into some low-dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space. Our contributions are twofold: (i) We derive optimal weighted majority voting schemes for pooling information from the base classifiers for multiclass classification and (ii) we introduce new base frequency-domain classifiers based on Whittle likelihood (WL), Kullback-Leibler (KL) divergence, eigen-distance (ED), and Chernoff (CH) divergence. Both simulations for binary and multiclass problems, and an Electroencephalogram (EEG) application demonstrate the efficacy of the proposed methods in constructing accurate classifiers with high-dimensional MTS.     

Robust two-gene classifiers for cancer prediction

Two-gene classifiers have attracted a broad interest for their simplicity and practicality. Most existing two-gene classification algorithms were involved in exhaustive search that led to their low time-efficiencies. In this study, we proposed two new two-gene classification algorithms which used simple univariate gene selection strategy and constructed simple classification rules based on optimal cut-points for two genes selected. We detected the optimal cut-point with the information entropy principle. We applied the two-gene classification models to eleven cancer gene expression datasets and compared their classification performance to that of some established two-gene classification models like the top-scoring pairs model and the greedy pairs model, as well as standard methods including Diagonal Linear Discriminant Analysis, k-Nearest Neighbor, Support Vector Machine and Random Forest. These comparisons indicated that the performance of our two-gene classifiers was comparable to or better than that of compared models.     

Multitrait Bayesian shrinkage and variable selection models with the BGLR-R package

The BGLR-R package implements various types of single-trait shrinkage/variable selection Bayesian regressions. The package was first released in 2014, since then it has become a software very often used in genomic studies. We recently develop functionality for multitrait models. The implementation allows users to include an arbitrary number of random-effects terms. For each set of predictors, users can choose diffuse, Gaussian, and Gaussian–spike–slab multivariate priors. Unlike other software packages for multitrait genomic regressions, BGLR offers many specifications for (co)variance parameters (unstructured, diagonal, factor analytic, and recursive). Samples from the posterior distribution of the models implemented in the multitrait function are generated using a Gibbs sampler, which is implemented by combining code written in the R and C programming languages. In this article, we provide an overview of the models and methods implemented BGLR’s multitrait function, present examples that illustrate the use of the package, and benchmark the performance of the software.