Accuracy bounds for ensembles under 0 - 1 loss.

This paper is an attempt to increase the understanding in the behavior of ensembles for discrete variables in a quantitative way. A set of tight upper and lower bounds for the accuracy of an ensemble is presented for wide classes of ensemble algorithms, including bagging and boosting. The ensemble accuracy is expressed in terms of the accuracies of the members of the ensemble. Since those bounds represent best and worst case behavior only, we study typical behavior as well, and discuss its properties. A parameterised bound is presented which describes ensemble bahavior as a mixture of dependent base classifier and independent base classifier areas. Some empirical results are presented to support our conclusions

Efficient algorithms for conditional independence inference

The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method

StarBEAST2 Brings Faster Species Tree Inference and Accurate Estimates of Substitution Rates

Fully Bayesian multispecies coalescent (MSC) methods like *BEAST estimate species trees from multiple sequence alignments. Today thousands of genes can be sequenced for a given study, but using that many genes with *BEAST is intractably slow. An alternative is to use heuristic methods which compromise accuracy or completeness in return for speed. A common heuristic is concatenation, which assumes that the evolutionary history of each gene tree is identical to the species tree. This is an inconsistent estimator of species tree topology, a worse estimator of divergence times, and induces spurious substitution rate variation when incomplete lineage sorting is present. Another class of heuristics directly motivated by the MSC avoids many of the pitfalls of concatenation but cannot be used to estimate divergence times. To enable fuller use of available data and more accurate inference of species tree topologies, divergence times, and substitution rates, we have developed a new version of *BEAST called StarBEAST2. To improve convergence rates we add analytical integration of population sizes, novel MCMC operators and other optimizations. Computational performance improved by 13.5× and 13.8× respectively when analyzing two empirical data sets, and an average of 33.1× across 30 simulated data sets. To enable accurate estimates of per-species substitution rates, we introduce species tree relaxed clocks, and show that StarBEAST2 is a more powerful and robust estimator of rate variation than concatenation. StarBEAST2 is available through the BEAUTi package manager in BEAST 2.4 and above.This work was supported by a Rutherford Discovery Fellowship awarded to A.J.D. by the Royal Society of New Zealand. H.A.O. was supported by an Australian Laureate Fellowship awarded to Craig Moritz by the Australian Research Council (FL110100104)

Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

Multidimensional Phylogenetic Metrics Identify Class I Aminoacyl-tRNA Synthetase Evolutionary Mosaicity and Inter-Modular Coupling

The role of aminoacyl-tRNA synthetases (aaRS) in the emergence and evolution of genetic coding poses challenging questions concerning their provenance. We seek evidence about their ancestry from curated structure-based multiple sequence alignments of a structurally invariant “scaffold” shared by all 10 canonical Class I aaRS. Three uncorrelated phylogenetic metrics—mutation frequency, its uniformity, and row-by-row cladistic congruence—imply that the Class I scaffold is a mosaic assembled from successive genetic sources. Metrics for different modules vary in accordance with their presumed functionality. Sequences derived from the ATP– and amino acid– binding sites exhibit specific two-way coupling to those derived from Connecting Peptide 1, a third module whose metrics suggest later acquisition. The data help validate: (i) experimental fragmentations of the canonical Class I structure into three partitions that retain catalytic activities in proportion to their length; and (ii) evidence that the ancestral Class I aaRS gene also encoded a Class II ancestor in frame on the opposite strand. A 46-residue Class I “protozyme” roots the Class I tree prior to the adaptive radiation of the Rossmann dinucleotide binding fold that refined substrate discrimination. Such rooting implies near simultaneous emergence of genetic coding and the origin of the proteome, resolving a conundrum posed by previous inferences that Class I aaRS evolved after the genetic code had been implemented in an RNA world. Further, pinpointing discontinuous enhancements of aaRS fidelity establishes a timeline for the growth of coding from a binary amino acid alphabet

BEAST 2:A Software Platform for Bayesian Evolutionary Analysis

We present a new open source, extensible and flexible software platform for Bayesian evolutionary analysis called BEAST 2. This software platform is a re-design of the popular BEAST 1 platform to correct structural deficiencies that became evident as the BEAST 1 software evolved. Key among those deficiencies was the lack of post-deployment extensibility. BEAST 2 now has a fully developed package management system that allows third party developers to write additional functionality that can be directly installed to the BEAST 2 analysis platform via a package manager without requiring a new software release of the platform. This package architecture is showcased with a number of recently published new models encompassing birth-death-sampling tree priors, phylodynamics and model averaging for substitution models and site partitioning. A second major improvement is the ability to read/write the entire state of the MCMC chain to/from disk allowing it to be easily shared between multiple instances of the BEAST software. This facilitates checkpointing and better support for multi-processor and high-end computing extensions. Finally, the functionality in new packages can be easily added to the user interface (BEAUti 2) by a simple XML template-based mechanism because BEAST 2 has been re-designed to provide greater integration between the analysis engine and the user interface so that, for example BEAST and BEAUti use exactly the same XML file format