A New Information Theoretic Approach Shows that Mixture Models Outperform Partitioned Models for Phylogenetic Analyses of Amino Acid Data

Machine learning for Big Data analytics in plants.

BackgroundThe genetic and molecular basis for many intermediate and end stage phenotypes in model systems such as C. elegans and D. melanogaster has long been known to involve pleiotropic effects and complex multigenic interactions. Gene sets are groups of genes that contribute to multiple biological or molecular phenomena. They have been used in the analysis of large molecular datasets such as microarray data, Next Generation sequencing, and other genomic datasets to reveal pleiotropic and multigenic contributions to phenotypic outcomes. Many model systems lack species specific organized phenotype based gene sets to enable high throughput analysis of large molecular datasets.Results and discussionHere, we describe two novel collections of gene sets in C. elegans and D. melanogaster that are based exclusively on genetically determined phenotypes and use a controlled phenotypic ontology. We use these collections to build genome-wide models of thousands of defined phenotypes in both model species. In addition, we demonstrate the utility of these gene sets in systems analysis and in analysis of gene expression-based molecular datasets and show how they are useful in analysis of genomic datasets connecting multigenic gene inputs to complex phenotypes.ConclusionsPhenotypic based gene sets in both C. elegans and D. melanogaster are developed, characterized, and shown to be useful in the analysis of large scale species-specific genomic datasets. These phenotypic gene set collections will contribute to the understanding of complex phenotypic outcomes in these model systems.

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \cite{FENN15} so that it can generate mixture models,in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.

Finite mixture models can provide the insights about behavioral patterns as a source of heterogeneity of the various dynamics of time course gene expression data by reducing the high dimensionality and making clear the major components of the underlying structure of the data in terms of the unobservable latent variables. The latent structure of the dynamic transition process of gene expression changes over time can be represented by Markov processes. This paper addresses key problems in the analysis of large gene expression data sets that describe systemic temporal response cascades and dynamic changes to therapeutic doses in multiple tissues, such as liver, skeletal muscle, and kidney from the same animals. Bayesian Finite Markov Mixture Model with a Dirichlet Prior is developed for the identifications of differentially expressed time related genes and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. The proposed Bayesian models are applied to multiple tissue polygenetic temporal gene expression data and compared to a Bayesian model-based clustering method, named CAGED. Results show that our proposed Bayesian Finite Markov Mixture model can well capture the dynamic changes and patterns for irregular complex temporal data.

The single-matrix amino acid (AA) substitution models are widely used in phylogenetic analyses; however, they are unable to properly model the heterogeneity of AA substitution rates among sites. The multi-matrix mixture models can handle the site rate heterogeneity and outperform the single-matrix models. Estimating multi-matrix mixture models is a complex process and no computer program is available for this task. In this study, we implemented a computer program of the so-called QMix based on the algorithm of LG4X and LG4M with several enhancements to automatically estimate multi-matrix mixture models from large datasets. QMix employs QMaker algorithm instead of XRATE algorithm to accurately and rapidly estimate the parameters of models. It is able to estimate mixture models with different number of matrices and supports multi-threading computing to efficiently estimate models from thousands of genes. We re-estimate mixture models LG4X and LG4M from 1471 HSSP alignments. The re-estimated models (HP4X and HP4M) are slightly better than LG4X and LG4M in building maximum likelihood trees from HSSP and TreeBASE datasets. QMix program required about 10 hours on a computer with 18 cores to estimate a mixture model with four matrices from 200 HSSP alignments. It is easy to use and freely available for researchers.

Astronomy datasets are generally terabytes in size and contain hundreds of millions of objects separated into millions of files-factors which makes many analyses impractical to perform on small computers. The key question we answer in this paper is: How can we leverage Grid resources to make the analysis of large astronomy datasets a reality for the astronomy community? To address this question, we have developed a Web Services-based system, AstroPortal, that uses grid computing to federate large computing and storage resources for dynamic analysis of large datasets. Building on the GT4, we have built a prototype and implemented a first analysis, stacking, that sums multiple regions of the sky, a function that can help both identify variable sources and detect faint objects. AstroPortal gives the astronomy community a new tool to advance their research and to open new doors to opportunities never before possible on such a large scale.

BackgroundTerminal restriction fragment length polymorphism (T-RFLP) analysis is a DNA-fingerprinting method that can be used for comparisons of the microbial community composition in a large number of samples. There is no consensus on how T-RFLP data should be treated and analyzed before comparisons between samples are made, and several different approaches have been proposed in the literature. The analysis of T-RFLP data can be cumbersome and time-consuming, and for large datasets manual data analysis is not feasible. The currently available tools for automated T-RFLP analysis, although valuable, offer little flexibility, and few, if any, options regarding what methods to use. To enable comparisons and combinations of different data treatment methods an analysis template and an extensive collection of macros for T-RFLP data analysis using Microsoft Excel were developed.ResultsThe Tools for T-RFLP data analysis template provides procedures for the analysis of large T-RFLP datasets including application of a noise baseline threshold and setting of the analysis range, normalization and alignment of replicate profiles, generation of consensus profiles, normalization and alignment of consensus profiles and final analysis of the samples including calculation of association coefficients and diversity index. The procedures are designed so that in all analysis steps, from the initial preparation of the data to the final comparison of the samples, there are various different options available. The parameters regarding analysis range, noise baseline, T-RF alignment and generation of consensus profiles are all given by the user and several different methods are available for normalization of the T-RF profiles. In each step, the user can also choose to base the calculations on either peak height data or peak area data.ConclusionsThe Tools for T-RFLP data analysis template enables an objective and flexible analysis of large T-RFLP datasets in a widely used spreadsheet application.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-014-0361-7) contains supplementary material, which is available to authorized users.

One of the most important and difficult challenges in the research of molecular evolution is modeling the process of amino acid substitutions. Although single-matrix models, such as the LG model, are popular, their capability to properly capture the heterogeneity of the substitution process across sites is still questioned. Several mixture models with multiple matrices have been introduced and shown to offer advantages over single-matrix models. Current general mixture models assume the reversibility of the evolutionary process, implying that substitution rates between any two amino acids are equal in both forward and backward directions. This assumption is not based on biological properties but rather on computational simplicity. The well-known hypothesis is that more realistic models can yield more accurate evolutionary inferences; therefore, our aim is to estimate more biologically realistic models. To this end, we relax the assumption of reversibility and introduce two new general non-reversible 4-matrix mixture models, called nT4M and nT4X. Using alignments from HSSP and TreeBASE databases as data, our newly estimated models outperformed all single-matrix models and almost all reversible mixture models. Moreover, the new non-reversible mixture models enable us to infer rooted trees.

Dimensionality-reduction methods are a fundamental tool in the analysis of large datasets. These algorithms work on the assumption that the intrinsic of the data is generally much smaller than the ambient dimension in which it is collected. Alongside their usual purpose of mapping data into a smaller-dimensional space with minimal information loss, dimensionality-reduction techniques implicitly or explicitly provide information about the dimension of the dataset.In this paper, we propose a new statistic that we call the kappa-profile for analysis of large datasets. The kappa-profile arises from a dimensionality-reduction optimization problem: namely that of finding a projection that optimally preserves the secants between points in the dataset. From this optimal projection we extract kappa, the norm of the shortest projected secant from among the set of all normalized secants. This kappa can be computed for any dimension k; thus the tuple of kappa values (indexed by dimension) becomes a kappa-profile. Algorithms such as the Secant-Avoidance Projection algorithm and the Hierarchical Secant-Avoidance Projection algorithm provide a computationally feasible means of estimating the kappa-profile for large datasets, and thus a method of understanding and monitoring their behavior. As we demonstrate in this paper, the kappa-profile serves as a useful statistic in several representative settings: weather data, soundscape data, and dynamical systems data.

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies.

We discuss the evaluation of subsets of variables for the discriminative evidence they provide in multivariate mixture modeling for classification. The novel development of Bayesian classification analysis presented is partly motivated by problems of design and selection of variables in biomolecular studies, particularly involving widely used assays of large-scale single-cell data generated using flow cytometry technology. For such studies and for mixture modeling generally, we define discriminative analysis that overlays fitted mixture models using a natural measure of concordance between mixture component densities, and define an effective and computationally feasible method for assessing and prioritizing subsets of variables according to their roles in discrimination of one or more mixture components. We relate the new discriminative information measures to Bayesian classification probabilities and error rates, and exemplify their use in Bayesian analysis of Dirichlet process mixture models fitted via Markov chain Monte Carlo methods as well as using a novel Bayesian expectation–maximization algorithm. We present a series of theoretical and simulated data examples to fix concepts and exhibit the utility of the approach, and compare with prior approaches. We demonstrate application in the context of automatic classification and discriminative variable selection in high-throughput systems biology using large flow cytometry datasets.

The mixture model is known as model-based clustering that is used to model a mixture of unknown distributions. The clustering of mixture model is based on four important criteria, including the number of components in the mixture model, clustering kernel (such as Gaussian mixture models, Dirichlet, etc.), estimation methods, and dimensionality (Lai et al., 2019). Finite mixture model is a finite dimensional of a hierarchical model. It is useful in modeling the data with outliers, non-normal distributed or heavy tails. Furthermore, finite mixture model is flexible when fitted with the models that have multiple modes or skewed distribution. The flexibility depends on the increasing number of parameters with the existence of a number of components. The finite mixture model is a flexible model family and widely applied for large heterogeneous datasets. In addition, the finite mixture model is a probabilistic model that is used to examine the presence of unobserved situations or groups and to measure the distinct parameters or distribution. The situations, such as trend, seasoning, crisis time, normal situation, etc., might affect the number of components that exist for a probabilistic distribution. Furthermore, the finite mixture model is essential for time series data because these data exhibit nonlinearity properties and may have missing data or a jump-diffusion situation (Gensler, 2017; McLachlan and Lee, 2019). Keywords: Bayesian method; Finite Mixture Model; Maximum Likelihood Estimation; Prior distribution; Likelihood Function.

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone.

Loosely speaking, clustering refers to the problem of grouping data, and plays a central role in statistical machine learning and data analysis. One way in which to formalize the clustering problem is in terms of a mixture model, where the mixture components represent clusters within the data. We consider a semi-parametric formulation, in which a random vector X isin Ropf <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> is modeled as a distribution Fx(x)=Sigma <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> omega <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> (x-mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> ). (1) with m components. Here omega <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> isin (0, 1) is the weight on mixture component alpha. The mean vectors mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> isin Ropf <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> are the (parametric) component of interest, whereas the dispersion distributions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> are a non-parametric nuisance component, on which we impose only tail conditions (e.g., sub-Gaussian or sub-exponential tail decay). Given n independent and identically distributed samples from the mixture model (1), we consider the problem of "learning" the mixture. More formally, for parameters (delta, epsi) isin (0, 1) times (0, 1), we say that a method (epsi, delta)-learns the mixture if it correctly determines the mixture label of all n samples with probability greater than 1 - delta, and estimates the mean vectors to accuracy epsi with high probability. This conference abstract provides an overview of the results in our full-length paper. We derive both necessary and sufficient conditions on the scaling of the sample size n as a function of the ambient dimension d, the minimum separation r(d) = min <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alphanebeta</sub> parmu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> - mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">beta</sub> par <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> between mixture components, and tail decay parameters. All of our analysis is high-dimensional in nature, meaning that we allow the sample size n, ambient dimension d and other parameters to scale in arbitrary ways. Our necessary conditions are information-theoretic in nature, and provide lower bounds on the performance of any algorithm, regardless of its computational complexity. Our sufficient conditions are based on analyzing a particular form of spectral clustering. For mixture models without any constraints on the mean vectors mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> we show that standard spectral clustering-that is, based on sample means and covariance matrices-can achieve the information-theoretic limits. We also analyze mixture models in which the mean vectors are ldquosparse", and derive information-theoretic lower bounds. For such models, spectral clustering based on sample means/covariances is highly sub-optimal, but modified spectral clustering algorithms using thresholding estimators are nearly optimal.

Introduction: In real-world datasets, outliers are a common occurrence that can have a significant impact on the accuracy and reliability of statistical analyses. Detecting these outliers and developing robust models to handle their presence is a crucial challenge in data analysis. For instance, natural images may have complex distributions of values due to environmental factors like noise and illumination, resulting in objects with overlapping regions and non-trivial contours that cannot be accurately described by Gaussian mixture models. In many real life applications, observed data always fall in bounded support regions. This leads to the idea of bounded support mixture models. Motivated by the aforementioned observations, we introduce a bounded multivariate cntaminated normal distribution for fitting data with non-Gaussian distributions, asymmetry, and bounded support which makes finite mixture models more robust to fitting, since rare observations are given less importance in calculations. Methods: A family of finite mixtures of bounded multivariate contaminated normal distributions is introduced. The model is well-suited for computer vision and pattern recognition problems due to its heavily-tailed and bounded nature, providing flexibility in modeling data in the presence of outliers. A feasible expectation- maximization algorithm is developed to compute the maximum likelihood estimates of the model parameters using a selection mechanism. Results: The proposed methodology is validated by conducting experiments on both simulated data and two real natural skin cancer images. We estimate the parameters by the proposed expectation-maximization algorithm. The obtained results shown that the proposed model has successfully enhanced accuracy in segmenting skin lesions. Conclusion: The reliable model-based clustering using finite mixtures of bounded multivariate contaminated normal distributions is introduced. An expectation-maximization algorithm was created to estimate parameters, with closed-form expressions utilized at the E-step. Practical tests on images for skin cancer detection showed enhanced accuracy in delineating skin lesions.