DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graph-based model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cell-cycle measurements of Spellman et al. (1998). Key words: gene expression, microarrays, Bayesian methods. 1.

A reliable and precise classification of tumors is essential for successful diagnosis and treatment of cancer. cDNA microarrays and high-density oligonucleotide chips are novel biotechnologies increasingly used in cancer research. By allowing the monitoring of expression levels in cells for thousands of genes simultaneously, microarray experiments may lead to a more complete understanding of the molecular variations among tumors and hence to a finer and more informative classification. The ability to successfully distinguish between tumor classes (already known or yet to be discovered) using gene expression data is an important aspect of this novel approach to cancer classification. This article compares the performance of different discrimination methods for the classification of tumors based on gene expression data. The methods include nearest-neighbor classifiers, linear discriminant analysis, and classification trees. Recent machine learning approaches, such as bagging and boosting, are also considered. The discrimination methods are applied to datasets from three recently published cancer gene expression studies.

Recent advances in biotechnology allow researchers to measure expression levels for thousands of genes simultaneously, across different conditions and over time. Analysis of data produced by such experiments offers potential insight into gene function and regulatory mechanisms. A key step in the analysis of gene expression data is the detection of groups of genes that manifest similar expression patterns. The corresponding algorithmic problem is to cluster multi-condition gene expression patterns. In this paper we describe a novel clustering algorithm that was developed for analysis of gene expression data. We define an appropriate stochastic error model on the input, and prove that under the conditions of the model, the algorithm recovers the cluster structure with high probability. The running time of the algorithm on an n-gene dataset is O(n 2 (log(n)) c ). We also present a practical heuristic based on the same algorithmic ideas. The heuristic was implemented and its p...

Motivation: DNA microarray experiments generating thousands of gene expression measurements, are being used to gather information from tissue and cell samples regarding gene expression differences that will be useful in diagnosing disease. We have developed a new method to analyse this kind of data using support vector machines (SVMs). This analysis consists of both classification of the tissue samples, and an exploration of the data for mis-labeled or questionable tissue results. Results: We demonstrate the method in detail on samples consisting of ovarian cancer tissues, normal ovarian tissues, and other normal tissues. The dataset consists of expression experiment results for 97 802 cDNAs for each tissue. As a result of computational analysis, a tissue sample is discovered and confirmed to be wrongly labeled. Upon correction of this mistake and the removal of an outlier, perfect classification of tissues is achieved, but not with high confidence. We identify and analyse a subset of genes from the ovarian dataset whose expression is highly differentiated between the types of tissues. To show robustness of the SVM method, two previously published datasets from other types of tissues or cells are analysed. The results are comparable to those previously obtained. We show that other machine learning methods also perform comparably to the SVM on many of those datasets. Availability: The SVM software is available at http:// www. cs.columbia.edu/#bgrundy/svm. Contact: booch@cse.ucsc.edu

Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and K-means clustering are not robust to missing data, and may lose effectiveness even with a few missing values. Methods for imputing missing data are needed, therefore, to minimize the effect of incomplete data sets on analyses, and to increase the range of data sets to which these algorithms can be applied. In this report, we investigate automated methods for estimating missing data.

Motivation: DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. Results: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t-test, provide a systematic inference approach that compares favorably with simple t-test or fold methods, and partly compensate for the lack of replication. Availability: The approach is implemented in a software called Cyber-T accessible through a Web interface at www.genomics.uci.edu/software.html. The code is available as Open Source and is written in the freely available statistical language R. and Department of Biological Chemistry, College of Medicine, University of California, Irvine. To whom all correspondence should be addressed. Contact: pfbaldi@ics.uci.edu, tdlong@uci.edu. 1

DNA microarrays are a new and promising biotechnology whichallows the monitoring of expression levels in cells for thousands of genes simultaneously. The present paper describes statistical methods for the identification of differentially expressed genes in replicated cDNA microarray experiments. Although it is not the main focus of the paper, new methods for the important pre-processing steps of image analysis and normalization are proposed. Given suitably normalized data, the biological question of differential expression is restated as a problem in multiple hypothesis testing: the simultaneous test for each gene of the null hypothesis of no association between the expression levels and responses or covariates of interest. Di erentially expressed genes are identified based on adjusted p-values for a multiple testing procedure which strongly controls the family-wise Type I error rate and takes into account the dependence structure between the gene expression levels. No specific parametric form is assumed for the distribution of the test statistics and a permutation procedure is used to estimate adjusted p-values. Several data displays are suggested for the visual identification of differentially expressed genes and of important features of these genes. The above methods are applied to microarray data from a study of gene expression in the livers of mice with very low HDL cholesterol levels. The genes identified using data from multiple slides are compared to those identified by recently published single-slide methods.

motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.

Constantly improving gene expression profiling technologies are expected to provide understanding and insight into cancer related cellular processes. Gene expression data is also expected to significantly aid in the development of efficient cancer diagnosis and classification platforms. In this work we examine two sets of gene expression data measured across sets of tumor and normal clinical samples. One set consists of 2,000 genes, measured in 62 epithelial colon samples [1]. The second consists of 100,000 clones, measured in 32 ovarian samples (unpublished, extension of data set described in [26]). We examine the use of scoring methods, measuring separation of tumors from normals using individual gene expression levels. These are then coupled with high dimensional classification methods to assess the classification power of complete expression profiles. We present results of performing leave-one-out cross validation (LOOCV) experiments on the two data sets, employing SVM [8], AdaB...

... for inferring genetic network architectures from state transition tables which correspond to time series of gene expression patterns, using the Boolean network model. Their results of computational experiments suggested that a small number of state transition (INPUT/OUTPUT) pairs are sufficient in order to infer the original Boolean network correctly. This paper gives a mathematical proof for their observation. Precisely, this paper devises a much simpler algorithm for the same problem and proves that, if the indegree of each node (i.e., the number of input nodes to each node) is bounded by a constant, only O(log n) state transition pairs (from 2n pairs) are necessary and sufficient to identify the original Boolean network of n nodes correctly with high probability. We made computational experiments in order to expose the constant factor involved in O(log n) notation. The computational results show that the Boolean network of size 100,000 can be identified by our algorithm from about 100 INPUT/OUTPUT pairs if the maximum indegree is bounded by 2. It is also a merit of our algorithm that the algorithm is conceptually so simple that it is extensible for more realistic network models.