Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

NEAR-OPTIMALITY AND ROBUSTNESS OF GREEDY ALGORITHMS FOR BAYESIAN POOL-BASED ACTIVE LEARNING

Ph.DDOCTOR OF PHILOSOPH

Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

CAD Tools for DNA Micro-Array Design, Manufacture and Application

Motivation: As the human genome project progresses and some microbial and eukaryotic genomes are recognized, numerous biotechnological processes have attracted increasing number of biologists, bioengineers and computer scientists recently. Biotechnological processes profoundly involve production and analysis of highthroughput experimental data. Numerous sequence libraries of DNA and protein structures of a large number of micro-organisms and a variety of other databases related to biology and chemistry are available. For example, microarray technology, a novel biotechnology, promises to monitor the whole genome at once, so that researchers can study the whole genome on the global level and have a better picture of the expressions among millions of genes simultaneously. Today, it is widely used in many fields- disease diagnosis, gene classification, gene regulatory network, and drug discovery. For example, designing organism specific microarray and analysis of experimental data require combining heterogeneous computational tools that usually differ in the data format; such as, GeneMark for ORF extraction, Promide for DNA probe selection, Chip for probe placement on microarray chip, BLAST to compare sequences, MEGA for phylogenetic analysis, and ClustalX for multiple alignments. Solution: Surprisingly enough, despite huge research efforts invested in DNA array applications, very few works are devoted to computer-aided optimization of DNA array design and manufacturing. Current design practices are dominated by ad-hoc heuristics incorporated in proprietary tools with unknown suboptimality. This will soon become a bottleneck for the new generation of high-density arrays, such as the ones currently being designed at Perlegen [109]. The goal of the already accomplished research was to develop highly scalable tools, with predictable runtime and quality, for cost-effective, computer-aided design and manufacturing of DNA probe arrays. We illustrate the utility of our approach by taking a concrete example of combining the design tools of microarray technology for Harpes B virus DNA data

Information geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

Reinforcement Learning

Brains rule the world, and brain-like computation is increasingly used in computers and electronic devices. Brain-like computation is about processing and interpreting data or directly putting forward and performing actions. Learning is a very important aspect. This book is on reinforcement learning which involves performing actions to achieve a goal. The first 11 chapters of this book describe and extend the scope of reinforcement learning. The remaining 11 chapters show that there is already wide usage in numerous fields. Reinforcement learning can tackle control tasks that are too complex for traditional, hand-designed, non-learning controllers. As learning computers can deal with technical complexities, the tasks of human operators remain to specify goals on increasingly higher levels. This book shows that reinforcement learning is a very dynamic area in terms of theory and applications and it shall stimulate and encourage new research in this field

Robust hand pose recognition from stereoscopic capture

Hand pose is emerging as an important interface for human-computer interaction. The problem of hand pose estimation from passive stereo inputs has received less attention in the literature compared to active depth sensors. This thesis seeks to address this gap by presenting a data-driven method to estimate a hand pose from a stereoscopic camera input, with experimental results comparable to more expensive active depth sensors. The frameworks presented in this thesis are based on a two camera stereo rig capture as it yields a simpler and cheaper set-up and calibration. Three frameworks are presented, describing the sequential steps taken to solve the problem of depth and pose estimation of hands. The first is a data-driven method to estimate a high quality depth map of a hand from a stereoscopic camera input by introducing a novel regression framework. The method first computes disparity using a robust stereo matching technique. Then, it applies a machine learning technique based on Random Forest to learn the mapping between the estimated disparity and depth given ground truth data. We introduce Eigen Leaf Node Features (ELNFs) that perform feature selection at the leaf nodes in each tree to identify features that are most discriminative for depth regression. The system provides a robust method for generating a depth image with an inexpensive stereo camera. The second framework improves on the task of hand depth estimation from stereo capture by introducing a novel superpixel-based regression framework that takes advantage of the smoothness of the depth surface of the hand. To this end, it introduces Conditional Regressive Random Forest (CRRF), a method that combines a Conditional Random Field (CRF) and a Regressive Random Forest (RRF) to model the mapping from a stereo RGB image pair to a depth image. The RRF provides a unary term that adaptively selects different stereo-matching measures as it implicitly determines matching pixels in a coarse-to-fine manner. While the RRF makes depth prediction for each super-pixel independently, the CRF unifies the prediction of depth by modeling pair-wise interactions between adjacent superpixels. The final framework introduces a stochastic approach to propose potential depth solutions to the observed stereo capture and evaluate these proposals using two convolutional neural networks (CNNs). The first CNN, configured in a Siamese network architecture, evaluates how consistent the proposed depth solution is to the observed stereo capture. The second CNN estimates a hand pose given the proposed depth. Unlike sequential approaches that reconstruct pose from a known depth, this method jointly optimizes the hand pose and depth estimation through Markov-chain Monte Carlo (MCMC) sampling. This way, pose estimation can correct for errors in depth estimation, and vice versa. Experimental results using an inexpensive stereo camera show that the proposed system measures pose more accurately than competing methods. More importantly, it presents the possibility of pose recovery from stereo capture that is on par with depth based pose recovery

Generalization and robustness of batched weighted average algorithm with V-geometrically ergodic Markov data

We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from overfitting or when optimizing the empirical risk is hard. For the generalization of the algorithm, we prove a PAC-style bound on the training sample size for the expected L1-loss to converge to the optimal loss when training data are V-geometrically ergodic Markov chains. For the robustness, we show that if the training target variable's values contain bounded noise, then the generalization bound of the algorithm deviates at most by the range of the noise. Our results can be applied to the regression problem, the classification problem, and the case where there exists an unknown deterministic target hypothesis. © 2013 Springer-Verlag