imPhy: Imputing Phylogenetic Trees with Missing Information Using Mathematical Programming.

Advances in modern genomics have allowed researchers to apply phylogenetic analyses on a genome-wide scale. While large volumes of genomic data can be generated cheaply and quickly, data missingness is a non-trivial and somewhat expected problem. Since the available information is often incomplete for a given set of genetic loci and individual organisms, a large proportion of trees that depict the evolutionary history of a single genetic locus, called gene trees, fail to contain all individuals.

Influence Function and Robust Variant of Kernel Canonical Correlation Analysis.

Many unsupervised kernel methods rely on the estimation of kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well-founded robust kernel methods for statistical unsupervised learning.

A Characterization of Minimum Spanning Tree-Like Metric Spaces.

Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms for this purpose, the goodness-of-fit of an MST to the data is often elusive because no quantitative criteria have been developed to measure it. Motivated by this, we provide a necessary and sufficient condition to ensure that a metric space on n points can be represented by a fully labeled tree on n vertices, and thereby determine when an MST preserves all pairwise distances between points in a finite metric space.

Filtering with State-Observation Examples via Kernel Monte Carlo Filter.

This letter addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e.

Kernel approximate Bayesian computation in population genetic inferences.

Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate.

Relation between weight size and degree of over-fitting in neural network regression.

This paper investigates the relation between over-fitting and weight size in neural network regression. The over-fitting of a network to Gaussian noise is discussed. Using re-parametrization, a network function is represented as a bounded function g multiplied by a coefficient c.

A Regularity Condition of the Information Matrix of a Multilayer Perceptron Network.

The Fisher information matrix of a multi-layer perceptron network can be singular at certain parameters, and in such cases many statistical techniques based on asymptotic theory cannot be applied properly. In this paper, we prove rigorously that the Fisher information matrix of a three-layer perceptron network is positive definite if and only if the network is irreducible; that is, if there is no hidden unit that makes no contribution to the output and there is no pair of hidden units that could be collapsed to a single unit without altering the input-output map. This implies that a network that has a singular Fisher information matrix can be reduced to a network with a positive definite Fisher information matrix by eliminating redundant hidden units.