Adaptive Seeding for Gaussian Mixture Models

We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2016. The final publication is available at link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2 24

A statistical framework for integrating two microarray data sets in differential expression analysis

<p>Abstract</p> <p>Background</p> <p>Different microarray data sets can be collected for studying the same or similar diseases. We expect to achieve a more efficient analysis of differential expression if an efficient statistical method can be developed for integrating different microarray data sets. Although many statistical methods have been proposed for data integration, the genome-wide concordance of different data sets has not been well considered in the analysis.</p> <p>Results</p> <p>Before considering data integration, it is necessary to evaluate the genome-wide concordance so that misleading results can be avoided. Based on the test results, different subsequent actions are suggested. The evaluation of genome-wide concordance and the data integration can be achieved based on the normal distribution based mixture models.</p> <p>Conclusion</p> <p>The results from our simulation study suggest that misleading results can be generated if the genome-wide concordance issue is not appropriately considered. Our method provides a rigorous parametric solution. The results also show that our method is robust to certain model misspecification and is practically useful for the integrative analysis of differential expression.</p

Implicitly Constrained Semi-Supervised Least Squares Classification

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, our approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. We show this approach can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a certain way, our method never leads to performance worse than the supervised classifier. Experimental results corroborate this theoretical result in the multidimensional case on benchmark datasets, also in terms of the error rate.Comment: 12 pages, 2 figures, 1 table. The Fourteenth International Symposium on Intelligent Data Analysis (2015), Saint-Etienne, Franc

Markov propagation of allosteric effects in biomolecular systems: application to GroEL–GroES

We introduce a novel approach for elucidating the potential pathways of allosteric communication in biomolecular systems. The methodology, based on Markov propagation of ‘information' across the structure, permits us to partition the network of interactions into soft clusters distinguished by their coherent stochastics. Probabilistic participation of residues in these clusters defines the communication patterns inherent to the network architecture. Application to bacterial chaperonin complex GroEL–GroES, an allostery-driven structure, identifies residues engaged in intra- and inter-subunit communication, including those acting as hubs and messengers. A number of residues are distinguished by their high potentials to transmit allosteric signals, including Pro33 and Thr90 at the nucleotide-binding site and Glu461 and Arg197 mediating inter- and intra-ring communication, respectively. We propose two most likely pathways of signal transmission, between nucleotide- and GroES-binding sites across the cis and trans rings, which involve several conserved residues. A striking observation is the opposite direction of information flow within cis and trans rings, consistent with negative inter-ring cooperativity. Comparison with collective modes deduced from normal mode analysis reveals the propensity of global hinge regions to act as messengers in the transmission of allosteric signals

Unsupervised Bayesian linear unmixing of gene expression microarrays

Background: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Results: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. Conclusions: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor

Incorporating predicted functions of nonsynonymous variants into gene-based analysis of exome sequencing data: a comparative study

Next-generation sequencing has opened up new avenues for the genetic study of complex traits. However, because of the small number of observations for any given rare allele and high sequencing error, it is a challenge to identify functional rare variants associated with the phenotype of interest. Recent research shows that grouping variants by gene and incorporating computationally predicted functions of variants may provide higher statistical power. On the other hand, many algorithms are available for predicting the damaging effects of nonsynonymous variants. Here, we use the simulated mini-exome data of Genetic Analysis Workshop 17 to study and compare the effects of incorporating the functional predictions of single-nucleotide polymorphisms using two popular algorithms, SIFT and PolyPhen-2, into a gene-based association test. We also propose a simple mixture model that can effectively combine test results based on different functional prediction algorithms

Improved analysis of bacterial CGH data beyond the log-ratio paradigm

<p>Abstract</p> <p>Background</p> <p>Existing methods for analyzing bacterial CGH data from two-color arrays are based on log-ratios only, a paradigm inherited from expression studies. We propose an alternative approach, where microarray signals are used in a different way and sequence identity is predicted using a supervised learning approach.</p> <p>Results</p> <p>A data set containing 32 hybridizations of sequenced versus sequenced genomes have been used to test and compare methods. A ROC-analysis has been performed to illustrate the ability to rank probes with respect to Present/Absent calls. Classification into Present and Absent is compared with that of a gaussian mixture model.</p> <p>Conclusion</p> <p>The results indicate our proposed method is an improvement of existing methods with respect to ranking and classification of probes, especially for multi-genome arrays.</p

A Comparison of Machine Learning Methods for Cross-Domain Few-Shot Learning

We present an empirical evaluation of machine learning algorithms in cross-domain few-shot learning based on a fixed pre-trained feature extractor. Experiments were performed in five target domains (CropDisease, EuroSAT, Food101, ISIC and ChestX) and using two feature extractors: a ResNet10 model trained on a subset of ImageNet known as miniImageNet and a ResNet152 model trained on the ILSVRC 2012 subset of ImageNet. Commonly used machine learning algorithms including logistic regression, support vector machines, random forests, nearest neighbour classification, naïve Bayes, and linear and quadratic discriminant analysis were evaluated on the extracted feature vectors. We also evaluated classification accuracy when subjecting the feature vectors to normalisation using p-norms. Algorithms originally developed for the classification of gene expression data—the nearest shrunken centroid algorithm and LDA ensembles obtained with random projections—were also included in the experiments, in addition to a cosine similarity classifier that has recently proved popular in few-shot learning. The results enable us to identify algorithms, normalisation methods and pre-trained feature extractors that perform well in cross-domain few-shot learning. We show that the cosine similarity classifier and ℓ² -regularised 1-vs-rest logistic regression are generally the best-performing algorithms. We also show that algorithms such as LDA yield consistently higher accuracy when applied to ℓ² -normalised feature vectors. In addition, all classifiers generally perform better when extracting feature vectors using the ResNet152 model instead of the ResNet10 model

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio