Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models

Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.Comment: 19 pages, 16 figures, published versio

Inverse Statistical Physics of Protein Sequences: A Key Issues Review

In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques, sequence data accumulate at unprecedented pace. This provides large sets of so-called homologous, i.e.~evolutionarily related protein sequences, to which methods of inverse statistical physics can be applied. Using sequence data as the basis for the inference of Boltzmann distributions from samples of microscopic configurations or observables, it is possible to extract information about evolutionary constraints and thus protein function and structure. Here we give an overview over some biologically important questions, and how statistical-mechanics inspired modeling approaches can help to answer them. Finally, we discuss some open questions, which we expect to be addressed over the next years.Comment: 18 pages, 7 figure

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories

Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state-of-the-art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change-point models or Gaussian process priors. Change-point models suffer from computational issues when the number of change-points is unknown and needs to be estimated. Gaussian process-based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally-adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log-transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change-point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state-of-the-art methods.Comment: 36 pages, including supplementary informatio

Forecasting Long-Term Government Bond Yields: An Application of Statistical and AI Models

This paper evaluates several artificial intelligence and classical algorithms on their ability of forecasting the monthly yield of the US 10-year Treasury bonds from a set of four economic indicators. Due to the complexity of the prediction problem, the task represents a challenging test for the algorithms under evaluation. At the same time, the study is of particular significance for the important and paradigmatic role played by the US market in the world economy. Four data-driven artificial intelligence approaches are considered, namely, a manually built fuzzy logic model, a machine learned fuzzy logic model, a self-organising map model and a multi-layer perceptron model. Their performance is compared with the performance of two classical approaches, namely, a statistical ARIMA model and an econometric error correction model. The algorithms are evaluated on a complete series of end-month US 10-year Treasury bonds yields and economic indicators from 1986:1 to 2004:12. In terms of prediction accuracy and reliability of the modelling procedure, the best results are obtained by the three parametric regression algorithms, namely the econometric, the statistical and the multi-layer perceptron model. Due to the sparseness of the learning data samples, the manual and the automatic fuzzy logic approaches fail to follow with adequate precision the range of variations of the US 10-year Treasury bonds. For similar reasons, the self-organising map model gives an unsatisfactory performance. Analysis of the results indicates that the econometric model has a slight edge over the statistical and the multi-layer perceptron models. This suggests that pure data-driven induction may not fully capture the complicated mechanisms ruling the changes in interest rates. Overall, the prediction accuracy of the best models is only marginally better than the prediction accuracy of a basic one-step lag predictor. This result highlights the difficulty of the modelling task and, in general, the difficulty of building reliable predictors for financial markets.interest rates; forecasting; neural networks; fuzzy logic.

Probabilistic methods in the analysis of protein interaction networks

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