MOTIVATION: Non-negative matrix factorization (NMF) is a powerful tool often applied to genomic data to identify non-negative latent components that constitute linearly mixed samples. It is useful when the observed signal combines contributions from multiple sources, such as cell types in bulk measurements of heterogeneous tissue. NMF accounts for two types of variation between samples - disparities in the proportions of sources and observation noise. However, in many settings, there is also a non-trivial variation between samples in the contribution of each source to the mixed data. This variation cannot be accurately modeled using the NMF framework. RESULTS: We present VarNMF, a probabilistic extension of NMF that explicitly models this variation in source values. We show that by modeling sources as non-negative distributions, we can recover source variation directly from mixed samples without observing any of the sources directly. We apply VarNMF to a cell-free ChIP-seq dataset of two cancer cohorts and a healthy cohort, demonstrating that VarNMF provides a better estimation of the data distribution. Moreover, VarNMF extracts cancer-associated source distributions that decouple the tumor characteristics from the amount of tumor contribution, and identify patient-specific disease behaviors. This decomposition highlights the inter-tumor variability that is obscured in the mixed samples. AVAILABILITY AND IMPLEMENTATION: Code is available at https://github.com/Nir-Friedman-Lab/VarNMF.

MOTIVATION: While growing numbers of T cell receptor (TCR) repertoires are being mapped by high-throughput sequencing, existing methods do not allow for computationally connecting a given TCR sequence to its target antigen, or relating it to a specific pathology. As an alternative, a manually-curated database can relate TCR sequences with their cognate antigens and associated pathologies based on published experimental data. RESULTS: We present McPAS-TCR, a manually curated database of TCR sequences associated with various pathologies and antigens based on published literature. Our database currently contains more than 5000 sequences of TCRs associated with various pathologic conditions (including pathogen infections, cancer and autoimmunity) and their respective antigens in humans and in mice. A web-based tool allows for searching the database based on different criteria, and for finding annotated sequences from the database in users' data. The McPAS-TCR website assembles information from a large number of studies that is very hard to dissect otherwise. Initial analyses of the data provide interesting insights on pathology-associated TCR sequences. AVAILABILITY AND IMPLEMENTATION: Free access at http://friedmanlab.weizmann.ac.il/McPAS-TCR/ . CONTACT: [email protected].

MOTIVATION: The clonal theory of adaptive immunity proposes that immunological responses are encoded by increases in the frequency of lymphocytes carrying antigen-specific receptors. In this study, we measure the frequency of different T-cell receptors (TcR) in CD4 + T cell populations of mice immunized with a complex antigen, killed Mycobacterium tuberculosis, using high throughput parallel sequencing of the TcRβ chain. Our initial hypothesis that immunization would induce repertoire convergence proved to be incorrect, and therefore an alternative approach was developed that allows accurate stratification of TcR repertoires and provides novel insights into the nature of CD4 + T-cell receptor recognition. RESULTS: To track the changes induced by immunization within this heterogeneous repertoire, the sequence data were classified by counting the frequency of different clusters of short (3 or 4) continuous stretches of amino acids within the antigen binding complementarity determining region 3 (CDR3) repertoire of different mice. Both unsupervised (hierarchical clustering) and supervised (support vector machine) analyses of these different distributions of sequence clusters differentiated between immunized and unimmunized mice with 100% efficiency. The CD4 + TcR repertoires of mice 5 and 14 days postimmunization were clearly different from that of unimmunized mice but were not distinguishable from each other. However, the repertoires of mice 60 days postimmunization were distinct both from naive mice and the day 5/14 animals. Our results reinforce the remarkable diversity of the TcR repertoire, resulting in many diverse private TcRs contributing to the T-cell response even in genetically identical mice responding to the same antigen. However, specific motifs defined by short stretches of amino acids within the CDR3 region may determine TcR specificity and define a new approach to TcR sequence classification. AVAILABILITY AND IMPLEMENTATION: The analysis was implemented in R and Python, and source code can be found in Supplementary Data. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Deciphering the complex mechanisms by which regulatory networks control gene expression remains a major challenge. While some studies infer regulation from dependencies between the expression levels of putative regulators and their targets, others focus on measured physical interactions. RESULTS: Here, we present Physical Module Networks, a unified framework that combines a Bayesian model describing modules of co-expressed genes and their shared regulation programs, and a physical interaction graph, describing the protein-protein interactions and protein-DNA binding events that coherently underlie this regulation. Using synthetic data, we demonstrate that a Physical Module Network model has similar recall and improved precision compared to a simple Module Network, as it omits many false positive regulators. Finally, we show the power of Physical Module Networks to reconstruct meaningful regulatory pathways in the genetically perturbed yeast and during the yeast cell cycle, as well as during the response of primary epithelial human cells to infection with H1N1 influenza. AVAILABILITY: The PMN software is available, free for academic use at http://www.compbio.cs.huji.ac.il/PMN/. CONTACT: [email protected]; [email protected].

MOTIVATION: The precise dynamics of gene expression is often crucial for proper response to stimuli. Time-course gene-expression profiles can provide insights about the dynamics of many cellular responses, but are often noisy and measured at arbitrary intervals, posing a major analysis challenge. RESULTS: We developed an algorithm that interleaves clustering time-course gene-expression data with estimation of dynamic models of their response by biologically meaningful parameters. In combining these two tasks we overcome obstacles posed in each one. Moreover, our approach provides an easy way to compare between responses to different stimuli at the dynamical level. We use our approach to analyze the dynamical transcriptional responses to inflammation and anti-viral stimuli in mice primary dendritic cells, and extract a concise representation of the different dynamical response types. We analyze the similarities and differences between the two stimuli and identify potential regulators of this complex transcriptional response. AVAILABILITY: The code to our method is freely available http://www.compbio.cs.huji.ac.il/DynaMiteC. CONTACT: [email protected].

MOTIVATION: Genetic interactions between genes reflect functional relationships caused by a wide range of molecular mechanisms. Large-scale genetic interaction assays lead to a wealth of information about the functional relations between genes. However, the vast number of observed interactions, along with experimental noise, makes the interpretation of such assays a major challenge. RESULTS: Here, we introduce a computational approach to organize genetic interactions and show that the bulk of observed interactions can be organized in a hierarchy of modules. Revealing this organization enables insights into the function of cellular machineries and highlights global properties of interaction maps. To gain further insight into the nature of these interactions, we integrated data from genetic screens under a wide range of conditions to reveal that more than a third of observed aggravating (i.e. synthetic sick/lethal) interactions are unidirectional, where one gene can buffer the effects of perturbing another gene but not vice versa. Furthermore, most modules of genes that have multiple aggravating interactions were found to be involved in such unidirectional interactions. We demonstrate that the identification of external stimuli that mimic the effect of specific gene knockouts provides insights into the role of individual modules in maintaining cellular integrity. AVAILABILITY: We designed a freely accessible web tool that includes all our findings, and is specifically intended to allow effective browsing of our results (http://compbio.cs.huji.ac.il/GIAnalysis). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Comparing the genomes from closely related species provides a powerful tool to identify functional elements in a reference genome. Many methods have been developed to identify conserved sequences across species; however, existing methods only model conservation as a decrease in the rate of mutation and have ignored selection acting on the pattern of mutations. RESULTS: We present a new approach that takes advantage of deeply sequenced clades to identify evolutionary selection by uncovering not only signatures of rate-based conservation but also substitution patterns characteristic of sequence undergoing natural selection. We describe a new statistical method for modeling biased nucleotide substitutions, a learning algorithm for inferring site-specific substitution biases directly from sequence alignments and a hidden Markov model for detecting constrained elements characterized by biased substitutions. We show that the new approach can identify significantly more degenerate constrained sequences than rate-based methods. Applying it to the ENCODE regions, we identify as much as 10.2% of these regions are under selection. AVAILABILITY: The algorithms are implemented in a Java software package, called SiPhy, freely available at http://www.broadinstitute.org/science/software/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The packaging of DNA around nucleosomes in eukaryotic cells plays a crucial role in regulation of gene expression, and other DNA-related processes. To better understand the regulatory role of nucleosomes, it is important to pinpoint their position in a high (5-10 bp) resolution. Toward this end, several recent works used dense tiling arrays to map nucleosomes in a high-throughput manner. These data were then parsed and hand-curated, and the positions of nucleosomes were assessed. RESULTS: In this manuscript, we present a fully automated algorithm to analyze such data and predict the exact location of nucleosomes. We introduce a method, based on a probabilistic graphical model, to increase the resolution of our predictions even beyond that of the microarray used. We show how to build such a model and how to compile it into a simple Hidden Markov Model, allowing for a fast and accurate inference of nucleosome positions. We applied our model to nucleosomal data from mid-log yeast cells reported by Yuan et al. and compared our predictions to those of the original paper; to a more recent method that uses five times denser tiling arrays as explained by Lee et al.; and to a curated set of literature-based nucleosome positions. Our results suggest that by applying our algorithm to the same data used by Yuan et al. our fully automated model traced 13% more nucleosomes, and increased the overall accuracy by about 20%. We believe that such an improvement opens the way for a better understanding of the regulatory mechanisms controlling gene expression, and how they are encoded in the DNA.

Characterizing the DNA-binding specificities of transcription factors is a key problem in computational biology that has been addressed by multiple algorithms. These usually take as input sequences that are putatively bound by the same factor and output one or more DNA motifs. A common practice is to apply several such algorithms simultaneously to improve coverage at the price of redundancy. In interpreting such results, two tasks are crucial: clustering of redundant motifs, and attributing the motifs to transcription factors by retrieval of similar motifs from previously characterized motif libraries. Both tasks inherently involve motif comparison. Here we present a novel method for comparing and merging motifs, based on Bayesian probabilistic principles. This method takes into account both the similarity in positional nucleotide distributions of the two motifs and their dissimilarity to the background distribution. We demonstrate the use of the new comparison method as a basis for motif clustering and retrieval procedures, and compare it to several commonly used alternatives. Our results show that the new method outperforms other available methods in accuracy and sensitivity. We incorporated the resulting motif clustering and retrieval procedures in a large-scale automated pipeline for analyzing DNA motifs. This pipeline integrates the results of various DNA motif discovery algorithms and automatically merges redundant motifs from multiple training sets into a coherent annotated library of motifs. Application of this pipeline to recent genome-wide transcription factor location data in S. cerevisiae successfully identified DNA motifs in a manner that is as good as semi-automated analysis reported in the literature. Moreover, we show how this analysis elucidates the mechanisms of condition-specific preferences of transcription factors.

Distance-based methods for phylogeny reconstruction are the fastest and easiest to use, and their popularity is accordingly high. They are also the only known methods that can cope with huge datasets of thousands of sequences. These methods rely on evolutionary distance estimation and are sensitive to errors in such estimations. In this study, a novel Bayesian method for estimation of evolutionary distances is developed. The proposed method enables the use of a sophisticated evolutionary model that better accounts for among-site rate variation (ASRV), thereby improving the accuracy of distance estimation. Rate variations are estimated within a Bayesian framework by extracting information from the entire dataset of sequences, unlike standard methods that can only use one pair of sequences at a time. We compare the accuracy of a cascade of distance estimation methods, starting from commonly used methods and moving towards the more sophisticated novel method. Simulation studies show significant improvements in the accuracy of distance estimation by the novel method over the commonly used ones. We demonstrate the effect of the improved accuracy on tree reconstruction using both real and simulated protein sequence alignments. An implementation of this method is available as part of the SEMPHY package.

The information bottleneck (IB) method is an unsupervised model independent data organization technique. Given a joint distribution, p(X, Y), this method constructs a new variable, T, that extracts partitions, or clusters, over the values of X that are informative about Y. Algorithms that are motivated by the IB method have already been applied to text classification, gene expression, neural code, and spectral analysis. Here, we introduce a general principled framework for multivariate extensions of the IB method. This allows us to consider multiple systems of data partitions that are interrelated. Our approach utilizes Bayesian networks for specifying the systems of clusters and which information terms should be maintained. We show that this construction provides insights about bottleneck variations and enables us to characterize the solutions of these variations. We also present four different algorithmic approaches that allow us to construct solutions in practice and apply them to several real-world problems.

MOTIVATION: A key aspect of transcriptional regulation is the binding of transcription factors to sequence-specific binding sites that allow them to modulate the expression of nearby genes. Given models of such binding sites, one can scan regulatory regions for putative binding sites and construct a genome-wide regulatory network. In such genome-wide scans, it is crucial to control the amount of false positive predictions. Recently, several works demonstrated the benefits of modeling dependencies between positions within the binding site. Yet, computing the statistical significance of putative binding sites in this scenario remains a challenge. RESULTS: We present a general, accurate and efficient method for computing p-values of putative binding sites that is applicable to a large class of probabilistic binding site and background models. We demonstrate the accuracy of the method on synthetic and real-life data. AVAILABILITY: The procedure for scanning DNA sequences and computing the statistical significance of putative binding site scores is available upon request at http://compbio.cs.huji.ac.il/CIS/ CONTACT: [email protected].

A central challenge in learning probabilistic graphical models is dealing with domains that involve hidden variables. The common approach for learning model parameters in such domains is the expectation maximization (EM) algorithm. This algorithm, however, can easily get trapped in sub-optimal local maxima. Learning the model structure is even more challenging. The structural EM algorithm can adapt the structure in the presence of hidden variables, but usually performs poorly without prior knowledge about the cardinality and location of the hidden variables. In this work, we present a general approach for learning Bayesian networks with hidden variables that overcomes these problems. The approach builds on the information bottleneck framework of Tishby et al. (1999). We start by proving formal correspondence between the information bottleneck objective and the standard parametric EM functional. We then use this correspondence to construct a learning algorithm that combines an information-theoretic smoothing term with a continuation procedure. Intuitively, the algorithm bypasses local maxima and achieves superior solutions by following a continuous path from a solution of, an easy and smooth, target function, to a solution of the desired likelihood function. As we show, our algorithmic framework allows learning of the parameters as well as the structure of a network. In addition, it also allows us to introduce new hidden variables during model selection and learn their cardinality. We demonstrate the performance of our procedure on several challenging real-life data sets.

Methods for learning Bayesian networks can discover dependency structure between observed variables. Although these methods are useful in many applications, they run into computational and statistical problems in domains that involve a large number of variables. In this paper, we consider a solution that is applicable when many variables have similar behavior. We introduce a new class of models, module networks, that explicitly partition the variables into modules, so that the variables in each module share the same parents in the network and the same conditional probability distribution. We define the semantics of module networks, and describe an algorithm that learns the modules' composition and their dependency structure from data. Evaluation on real data in the domains of gene expression and the stock market shows that module networks generalize better than Bayesian networks, and that the learned module network structure reveals regularities that are obscured in learned Bayesian networks.

Current approaches for identification and detection of transcription factor binding sites rely on an extensive set of known target genes. Here we describe a novel structure-based approach applicable to transcription factors with no prior binding data. Our approach combines sequence data and structural information to infer context-specific amino acid-nucleotide recognition preferences. These are used to predict binding sites for novel transcription factors from the same structural family. We demonstrate our approach on the Cys(2)His(2) Zinc Finger protein family, and show that the learned DNA-recognition preferences are compatible with experimental results. We use these preferences to perform a genome-wide scan for direct targets of Drosophila melanogaster Cys(2)His(2) transcription factors. By analyzing the predicted targets along with gene annotation and expression data we infer the function and activity of these proteins.

MOTIVATION: Recent years' exponential increase in DNA microarrays experiments has motivated the development of many signal quantitation (SQ) algorithms. These algorithms perform various transformations on the actual measurements aimed to enable researchers to compare readings of different genes quantitatively within one experiment and across separate experiments. However, it is relatively unclear whether there is a 'best' algorithm to quantitate microarray data. The ability to compare and assess such algorithms is crucial for any downstream analysis. In this work, we suggest a methodology for comparing different signal quantitation algorithms for gene expression data. Our aim is to enable researchers to compare the effect of different SQ algorithms on the specific dataset they are dealing with. We combine two kinds of tests to assess the effect of an SQ algorithm in terms of signal to noise ratio. To assess noise, we exploit redundancy within the experimental dataset to test the variability of a given SQ algorithm output. For the effect of the SQ on the signal we evaluate the overabundance of differentially expressed genes using various statistical significance tests. RESULTS: We demonstrate our analysis approach with three SQ algorithms for oligonucleotide microarrays. We compare the results of using the dChip software and the RMAExpress software to the ones obtained by using the standard Affymetrix MAS5 on a dataset containing pairs of repeated hybridizations. Our analysis suggests that dChip is more robust and stable than the MAS5 tools for about 60% of the genes while RMAExpress is able to achieve an even greater improvement in terms of signal to noise, for more than 95% of the genes.

The availability of whole genome sequences and high-throughput genomic assays opens the door for in silico analysis of transcription regulation. This includes methods for discovering and characterizing the binding sites of DNA-binding proteins, such as transcription factors. A common representation of transcription factor binding sites is a position specific score matrix (PSSM). This representation makes the strong assumption that binding site positions are independent of each other. In this work, we explore Bayesian network representations of binding sites that provide different tradeoffs between complexity (number of parameters) and the richness of dependencies between positions. We develop the formal machinery for learning such models from data and for estimating the statistical significance of putative binding sites. We then evaluate the ramifications of these richer representations in characterizing binding site motifs and predicting their genomic locations. We show that these richer representations improve over the PSSM model in both tasks.

We present a probabilistic framework that models the process by which transcriptional binding explains the mRNA expression of different genes. Our joint probabilistic model unifies the two key components of this process: the prediction of gene regulation events from sequence motifs in the gene's promoter region, and the prediction of mRNA expression from combinations of gene regulation events in different settings. Our approach has several advantages. By learning promoter sequence motifs that are directly predictive of expression data, it can improve the identification of binding site patterns. It is also able to identify combinatorial regulation via interactions of different transcription factors. Finally, the general framework allows us to integrate additional data sources, including data from the recent binding localization assays. We demonstrate our approach on the cell cycle data of Spellman et al., combined with the binding localization information of Simon et al. We show that the learned model predicts expression from sequence, and that it identifies coherent co-regulated groups with significant transcription factor motifs. It also provides valuable biological insight into the domain via these co-regulated "modules" and the combinatorial regulation effects that govern their behavior.

Query by melody is the problem of retrieving musical performances from melodies. Retrieval of real performances is complicated due to the large number of variations in performing a melody and the presence of colored accompaniment noise. We describe a simple yet effective probabilistic model for this task. We describe a generative model that is rich enough to capture the spectral and temporal variations of musical performances and allows for tractable melody retrieval. While most of previous studies on music retrieval from melodies were performed with either symbolic (e.g. MIDI) data or with monophonic (single instrument) performances, we performed experiments in retrieving live and studio recordings of operas that contain a leading vocalist and rich instrumental accompaniment. Our results show that the probabilistic approach we propose is effective and can be scaled to massive datasets.

We present a novel sequential clustering algorithm which is motivated by the Information Bottleneck (IB) method. In contrast to the agglomerative IB algorithm, the new sequential (sIB) approach is guaranteed to converge to a local maximum of the information with time and space complexity typically linear in the data size. information, as required by the original IB principle. Moreover, the time and space complexity are significantly improved. We apply this algorithm to unsupervised document classification. In our evaluation, on small and medium size corpora, the sIB is found to be consistently superior to all the other clustering methods we examine, typically by a significant margin. Moreover, the sIB results are comparable to those obtained by a supervised Naive Bayes classifier. Finally, we propose a simple procedure for trading cluster's recall to gain higher precision, and show how this approach can extract clusters which match the existing topics of the corpus almost perfectly.

MOTIVATION: We developed an algorithm to reconstruct ancestral sequences, taking into account the rate variation among sites of the protein sequences. Our algorithm maximizes the joint probability of the ancestral sequences, assuming that the rate is gamma distributed among sites. Our algorithm probably finds the global maximum. The use of 'joint' reconstruction is motivated by studies that use the sequences at all the internal nodes in a phylogenetic tree, such as, for instance, the inference of patterns of amino-acid replacement, or tracing the biochemical changes that occurred during the evolution of a given protein family. RESULTS: We give an algorithm that guarantees finding the global maximum. The efficient search method makes our method applicable to datasets with large number sequences. We analyze ancestral sequences of five gene families, exploring the effect of the amount of among-site-rate-variation, and the degree of sequence divergence on the resulting ancestral states. AVAILABILITY AND SUPPLEMENTARY INFORMATION: http://evolu3.ism.ac.jp/~tal/ CONTACT: [email protected]

The information bottleneck method is an unsupervised model independent data organization technique. Given a joint distribution peA, B), this method con(cid:173) structs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. In a recent paper, we introduced a general princi(cid:173) pled framework for multivariate extensions of the information bottleneck method that allows us to consider multiple systems of data partitions that are inter-related. In this paper, we present a new family of simple agglomerative algorithms to construct such systems of inter-related clusters. We analyze the behavior of these algorithms and apply them to several real-life datasets.

The recent growth in genomic data and measurement of genome-wide expression patterns allows to examine gene regulation by transcription factors using computational tools. In this work, we present a class of mathematical models that help in understanding the connections between transcription factors and functional classes of genes based on genetic and genomic data. These models represent the joint distribution of transcription factor binding sites and of expression levels of a gene in a single model. Learning a combined probability model of binding sites and expression patterns enables us to improve the clustering of the genes based on the discovery of putative binding sites and to detect which binding sites and experiments best characterize a cluster. To learn such models from data, we introduce a new search method that rapidly learns a model according to a Bayesian score. We evaluate our method on synthetic data as well as on real data and analyze the biological insights it provides.

Recent studies (Alizadeh et al, [1]; Bittner et al,[5]; Golub et al, [11]) demonstrate the discovery of putative disease subtypes from gene expression data. The underlying computational problem is to partition the set of sample tissues into statistically meaningful classes. In this paper we present a novel approach to class discovery and develop automatic analysis methods. Our approach is based on statistically scoring candidate partitions according to the overabundance of genes that separate the different classes. Indeed, in biological datasets, an overabundance of genes separating known classes is typically observed. we measure overabundance against a stochastic null model. This allows for highlighting subtle, yet meaningful, partitions that are supported on a small subset of the genes.

A central task in the study of evolution is the reconstruction of a phylogenetic tree from sequences of current-day taxa. A well supported approach to tree reconstruction performs maximum likelihood (ML) analysis. Unfortunately, searching for the maximum likelihood phylogenetic tree is computationally expensive. In this paper, we describe a new algorithm that uses Structural-EM for learning maximum likelihood trees. This algorithm is similar to the standard EM method for estimating branch lengths, except that during iterations of this algorithms the topology is improved as well as the branch length. The algorithm performs iterations of two steps. In the E-Step, we use the current tree topology and branch lengths to compute expected sufficient statistics, which summarize the data. In the M-Step, we search for a topology that maximizes the likelihood with respect to these expected sufficient statistics. As we show, searching for better topologies inside the M-step can be done efficiently, as opposed to standard search over topologies. We prove that each iteration of this procedure increases the likelihood of the topology, and thus the procedure must converge. We evaluate our new algorithm on both synthetic and real sequence data, and show that it is both dramatically faster and finds more plausible trees than standard search for maximum likelihood phylogenies.

We introduce a new approach to modeling uncertainty based onplausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. We focus on one application of plausibility measures in this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ε-semantics, possibilistic structures, and κ-rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature.

A serious problem in learning probabilistic models is the presence of hid(cid:173) den variables. These variables are not observed, yet interact with several of the observed variables. As such, they induce seemingly complex de(cid:173) pendencies among the latter. In recent years, much attention has been devoted to the development of algorithms for learning parameters, and in some cases structure, in the presence of hidden variables. In this pa(cid:173) per, we address the related problem of detecting hidden variables that interact with the observed variables. This problem is of interest both for improving our understanding of the domain and as a preliminary step that guides the learning procedure towards promising models. A very natural approach is to search for "structural signatures" of hidden variables - substructures in the learned network that tend to suggest the presence of a hidden variable. We make this basic idea concrete, and show how to integrate it with structure-search algorithms. We evaluate this method on several synthetic and real-life datasets, and show that it performs surpris(cid:173) ingly well.

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 and 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]).

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.

Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to confound statistical conditionals over the domain (such as “most birds fly”), and subjective conditionals over possible worlds (such as “I believe that Tweety is unlikely to fly”). We then address the issue of ascribing semantics to first-order conditional logic. As in the propositional case, there are many possible semantics. To study the problem in a coherent way, we use plausibility structures . These provide us with a general framework in which many of the standard approaches can be embedded. We show that while these standard approaches are all the same at the propositional level, they are significantly different in the context of a first-order language. Furthermore, we show that plausibilities provide the most natural extension of conditional logic to the first-order case:we provide a sound and complete axiomatization that contains only the KLM properties and standard axioms of first-order modal logic. We show that most of the other approaches have additional properties, which result in an inappropriate treatment of an infinitary version of the lottery paradox .

We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. We then consider one application of plausibility measures: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, /spl epsiv/-semantics, possibilistic structures, and /spl kappa/-rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Finally, we show that plausibility measures provide an appropriate basis for examining first-order default logics.

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.

Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes Φ if he knows that Φ is more plausible than ¬Φ. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin for modeling knowledge in multi-agent systems. We then examine the problem of “minimal change”. This notion can be captured by using prior plausibilities, an analogue to prior probabilities, which can be updated by “conditioning”. We show by example that conditioning on a plausibility measure can capture many scenarios of interest. In a companion paper, we show how the two best-studied scenarios of belief change, belief revision and belief update, fit into our framework.