High-dimensional classification using features annealed independence rules

Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is poorly understood. In a seminal paper, Bickel and Levina [Bernoulli 10 (2004) 989--1010] show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that even for the independence classification rule, classification using all the features can be as poor as the random guessing due to noise accumulation in estimating population centroids in high-dimensional feature space. In fact, we demonstrate further that almost all linear discriminants can perform as poorly as the random guessing. Thus, it is important to select a subset of important features for high-dimensional classification, resulting in Features Annealed Independence Rules (FAIR). The conditions under which all the important features can be selected by the two-sample $t$-statistic are established. The choice of the optimal number of features, or equivalently, the threshold value of the test statistics are proposed based on an upper bound of the classification error. Simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure.Comment: Published in at http://dx.doi.org/10.1214/07-AOS504 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evolutionary algorithms for the selection of single nucleotide polymorphisms

BACKGROUND: Large databases of single nucleotide polymorphisms (SNPs) are available for use in genomics studies. Typically, investigators must choose a subset of SNPs from these databases to employ in their studies. The choice of subset is influenced by many factors, including estimated or known reliability of the SNP, biochemical factors, intellectual property, cost, and effectiveness of the subset for mapping genes or identifying disease loci. We present an evolutionary algorithm for multiobjective SNP selection. RESULTS: We implemented a modified version of the Strength-Pareto Evolutionary Algorithm (SPEA2) in Java. Our implementation, Multiobjective Analyzer for Genetic Marker Acquisition (MAGMA), approximates the set of optimal trade-off solutions for large problems in minutes. This set is very useful for the design of large studies, including those oriented towards disease identification, genetic mapping, population studies, and haplotype-block elucidation. CONCLUSION: Evolutionary algorithms are particularly suited for optimization problems that involve multiple objectives and a complex search space on which exact methods such as exhaustive enumeration cannot be applied. They provide flexibility with respect to the problem formulation if a problem description evolves or changes. Results are produced as a trade-off front, allowing the user to make informed decisions when prioritizing factors. MAGMA is open source and available at . Evolutionary algorithms are well suited for many other applications in genomics

Neuronal encoding of subjective value in dorsal and ventral anterior cingulate cortex

We examined the activity of individual cells in the primate anterior cingulate cortex during an economic choice task. In the experiments, monkeys chose between different juices offered in variables amounts and subjective values were inferred from the animals\u27 choices. We analyzed neuronal firing rates in relation to a large number of behaviorally relevant variables. We report three main results. First, there were robust differences between the dorsal bank (ACCd) and the ventral bank (ACCv) of the cingulate sulcus. Specifically, neurons in ACCd but not in ACCv were modulated by the movement direction. Furthermore, neurons in ACCd were most active before movement initiation, whereas neurons in ACCv were most active after juice delivery. Second, neurons in both areas encoded the identity and the subjective value of the juice chosen by the animal. In contrast, neither region encoded the value of individual offers. Third, the population of value-encoding neurons in both ACCd and ACCv underwent range adaptation. With respect to economic choice, it is interesting to compare these areas with the orbitofrontal cortex (OFC), previously examined. While neurons in OFC encoded both pre-decision and post-decision variables, neurons in ACCd and ACCv only encoded post-decision variables. Moreover, the encoding of the choice outcome (chosen value and chosen juice) in ACCd and ACCv trailed that found in OFC. These observations indicate that economic decisions (i.e., value comparisons) take place upstream of ACCd and ACCv. The coexistence of choice outcome and movement signals in ACCd suggests that this area constitutes a gateway through which the choice system informs motor systems

Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases, corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics, and may have applications in a variety of systems including social insects and microbial communities.Comment: 10 pages, 6 figure