We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

can be formulated in terms of basis functions and discuss the dif culties in posterior simulations due to interdependence of these functions. Such interdependence affects the ef ciency of the sampling algorithms to draw from posterior distribution of the tree structures. Different strategies that are suggested in the literature for dealing with the sampling problem are discussed, and a detailed example using binary classi cation is presented to illustrate the Bayesian analysis. To alleviate the problems that arise in tree models, Chapter 7 introduces partition models. The partition models can be considered a generalization of tree models, and they allow for sampling from the posterior distributions of the tree structure. As noted by the authors, these models suffer from lack of interpretability in high dimensions. The authors present one-dimensional partition models whose analysis provides a general framework for the changepoint problems. Multidimensional partition models, where partitions are de ned by Dirichlet tessellations, are considered, and Bayesian inference for classi cation problems is discussed. Disease mapping models are presented as an application of partition models for spatial problems. Chapter 8 is a short chapter describing Bayesian nearest-neighbor modeling. The nearest-neighbor classi cation algorithm, which is used commonly in pattern recognition, is given a probabilistic formulation by introducing a parameter that controls the degree of association between the neighboring classes. In Chapter 9 the authors generalize the single-response case to multipleresponse models where the observed response is a collection of values. The chapter focuses on regression models and does not consider classi cation models such as the multivariate probit models. Multivariate Bayesian regression framework is introduced where basis functions can be determined from the data using methods of Chapter 3. A generalization is considered using seemingly unrelated regression (SUR) models and their Bayesian analysis is presented. Prior speci cation for basis function matrix are discussed, and computational details of the MCMC methods are given for both models. The book has a comprehensive bibliography, and each chapter (except Chap. 1) has a section on further reading. There are two appendixes at the end. Appendix B gives a summary of posterior inference results that are helpful for some of the development in the text. In summary, this book presents recent developments in Bayesian nonlinear modeling and provides a complete treatment of regression and classi cation problems by emphasizing a data-driven approach in determining appropriate models. Its in-depth coverage of implementation issues and detailed discussion of pros and cons of different modeling strategies make it attractive for many researchers. It de nitely makes my list of recommended texts in Bayesian statistics.

Resampling Methods for Dependent Data

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An Introduction To Genetic Analysis

Observability of Boolean networks: A graph-theoretic approach

A temporal constraint language is a set of relations that has a first-order definition in(Q;

/pdf/the-complexity-of-temporal-constraint-satisfaction-problems-5329j01r81.pdf

The complexity of temporal constraint satisfaction problems

Network inference algorithms can assist life scientists in unraveling gene-regulatory systems on a molecular level. In recent years, great attention has been drawn to the reconstruction of Boolean networks from time series. These need to be binarized, as such networks model genes as binary variables (either "expressed” or "not expressed”). Common binarization methods often cluster measurements or separate them according to statistical or information theoretic characteristics and may require many data points to determine a robust threshold. Yet, time series measurements frequently comprise only a small number of samples. To overcome this limitation, we propose a binarization that incorporates measurements at multiple resolutions. We introduce two such binarization approaches which determine thresholds based on limited numbers of samples and additionally provide a measure of threshold validity. Thus, network reconstruction and further analysis can be restricted to genes with meaningful thresholds. This reduces the complexity of network inference. The performance of our binarization algorithms was evaluated in network reconstruction experiments using artificial data as well as real-world yeast expression time series. The new approaches yield considerably improved correct network identification rates compared to other binarization techniques by effectively reducing the amount of candidate networks.

/pdf/multiscale-binarization-of-gene-expression-data-for-35959xisgs.pdf

Multiscale Binarization of Gene Expression Data for Reconstructing Boolean Networks

Boolean networks are a popular class of models for the description of gene-regulatory networks. They model genes as simple binary variables, being either expressed or not expressed. Simulations of Boolean networks can give insights into the dynamics of cellular systems. In particular, stable states and cycles in the networks are thought to correspond to phenotypes. This paper presents approaches to identify attractors in synchronous, asynchronous and probabilistic Boolean networks and gives examples of their usage in the BoolNet R package.

Attractors in Boolean networks: a tutorial

Motivation: Accurate, context-specific regulation of gene expression is essential for all organisms. Accordingly, it is very important to understand the complex relations within cellular gene regulatory networks. A tool to describe and analyze the behavior of such networks are Boolean models. The reconstruction of a Boolean network from biological data requires identification of dependencies within the network. This task becomes increasingly computationally demanding with large amounts of data created by recent high-throughput technologies. Thus, we developed a method that is especially suited for network structure reconstruction from large-scale data. In our approach, we took advantage of the fact that a specific transcription factor often will consistently either activate or inhibit a specific target gene, and this kind of regulatory behavior can be modeled using monotone functions.

Results: To detect regulatory dependencies in a network, we examined how the expression of different genes correlates to successive network states. For this purpose, we used Pearson correlation as an elementary correlation measure. Given a Boolean network containing only monotone Boolean functions, we prove that the correlation of successive states can identify the dependencies in the network. This method not only finds dependencies in randomly created artificial networks to very high percentage, but also reconstructed large fractions of both a published Escherichia coli regulatory network from simulated data and a yeast cell cycle network from real microarray data.

Contact: hans.kestler@uni-ulm.de

Supplementary information: Supplementary data are available at Bioinformatics online.

Inferring Boolean network structure via correlation

Setting the free parameters of classifiers to different values can have a profound impact on their performance. For some methods, specialized tuning algorithms have been developed. These approaches mostly tune parameters according to a single criterion, such as the cross-validation error. However, it is sometimes desirable to obtain parameter values that optimize several concurrent - often conflicting - criteria. The TunePareto package provides a general and highly customizable framework to select optimal parameters for classifiers according to multiple objectives. Several strategies for sampling and optimizing parameters are supplied. The algorithm determines a set of Pareto-optimal parameter configurations and leaves the ultimate decision on the weighting of objectives to the researcher. Decision support is provided by novel visualization techniques.

https://www.jstatsoft.org/article/view/v046i05/v46i05.pdf

Multi-Objective Parameter Selection for Classifiers

We investigate the problem of finding a total order of a finite set that satisfies various local ordering constraints. Depending on the admitted constraints, we provide an efficient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems.

/pdf/variations-on-an-ordering-theme-with-constraints-1o6acwtre5.pdf

Markus Maucher

Papers

Multiscale Binarization of Gene Expression Data for Reconstructing Boolean Networks

Attractors in Boolean networks: a tutorial

Inferring Boolean network structure via correlation

Multi-Objective Parameter Selection for Classifiers

Variations on an Ordering Theme with Constraints