Machine LearningEmphasizing theory and
algorithms for learning from highdimensional data, and reasoning under
uncertainty. 
Computational BiologyEmphasizing
developing formal models and algorithms that address problems of
practical biological and medical concerns. 



Machine LearningEmphasizing theory and algorithms for learning complex probabilistic models, learning with prior knowledge, and reasoning under uncertainty. 
In this project we develop methodologies for estimating and analyzing varyingcoefficient models with structural changes occurring at unknown times or locations. Instances of such models are frequently encountered in social and biological problems where data are structured and longitudinal, and the iid assumptions on sample with respect to an invariant underlying model no longer hold. For example, at each time point, the observation (such as a single snapshot of social state of all actors) is distributed according to a model (such as a network) specific to that time, and therefore can not be directly used for estimating models underlying other time points. The main issues we concern in this project include estimating the changing model structures and parameters, number of structural changes, the change times, and the unknown coefficient functions. We will develop efficient and scalable algorithms for addressing these problems under "small n large p" scenarios based on techniques such as sparse regression under various regularization and structuredconstraint schemes, convex optimization, and Bayesian inference. We will also focus on asymptotic analysis of the procedure and give conditions under which it is able to correctly estimate the structural changes and the model coefficients.
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In many highdimensional structured I/O problems, such as genomephenome association analysis and image segmentation, where both input and output can contain tens of thousands, sometimes even millions of interrelated features, learning a sparse and consistent structured predictive function can be of paramount importance for both robustness and interpretability of the model. In this project, we attack this problem from two directions. One direction we will pursue to learn sparse structured I/O models is to extend the l1regularized regression model (i.e., the lasso method) to a family of sparse "structured" regression models in the contexts of uncovering true associations between linked genetic variations (inputs) and networked phenotypes (outputs), which can be cast as efficiently solvable convex optimization problems and yield parsimonious and possibly consistent maximum likelihood estimates of the model. Another direction we are exploring is based on a new statistical formalism known as the maximum entropy discrimination Markov networks, which address the problem of estimating sparse structured I/O models under a maximum margin framework, but using a entropic regularizer that leads to a distribution of structured prediction functions that are simultaneously primal and dual sparse (i.e., with few support vectors, and of low effective feature dimension), and can be efficiently solved via a novel algorithm that builds on variational inference and existing solvers for the maximum margin Markov network (which is a special case of our proposed model). We will also investigate the theoretical guarantee of these methods such as generalization bounds, sample complexity, convergence behavior.
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A plausible representation of the relational information among entities in dynamic systems such as a living cell, or a social community, or the internet, is a stochastic network which is topologically rewiring and semantically evolving over time (or space). In this project we develop probabilistic generative models for the formation, growth, evolution, and dynamics of networks and relational data in general, and inference/learning algorithms for node labeling, link prediction, latent theme extraction, etc., for network and relational data. We also work on theoretical issues, such as bounds, complexity, related to our models and algorithms, and applications to the analysis of sociocultural networks, authorcitation networks, the blogosphere, and biological networks.
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In this project we develop nonparametric and semiparametric Bayesian models (based on the Dirichlet process and extensions, sometimes known as the generalized Polya urn schemes) for analyzing time series data, hierarchical data, and other complex inputs with uncertain internal structure, which arise from temporal text mining (e.g., emails, news streams), object tracking (e.g., video surveillance, navigation and control) and biological data analysis. We develop formal probabilistic formalisms, sampling and variational inference algorithms, and also address theoretical issues such as consistence, bounds and convergence of our models and algorithms.
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This is a "googlestyle" project in which we develop formal methods for visualizing, categorizing, and tracking contentrich multimedia and network datastreams in an arbitrarydimension "tomographic" space of latent semantic topics, where each entity can be represented by a humanperceivable and interpretable "semantic" coordinates or trajectory, so that one can succinctly browse the complex multimodal and timeevolving data in a direct, global and online fashion. Such display of complex data complements the current Google representation of webinformation, which is onedimensional (in terms of a rank list), static (no change in the topical content of the media can be traced), and unimodal (only one type of media can be displayed as a time, such as text only, or image only). One can use our system to directly visualize in the topic space a much larger amount of media or web information, rather than via pages of orderedlists of subjects as in current Google interface. One can detect bias, ideological perspective, or other subtle information, which hide beneath the topical contents in news article or other media. One can directly measure (by eye) the distance between query and related entities rather than following a rank list, which offer more flexibility and higher accuracy. One can also track the trajectories of evolving entities and detection events such as birth/death of themes/topics using our system, which is not possible under Google.
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We design various taskspecific generative, discriminative, and hybrid graphical models and algorithms for various biological and genetic problems (see bellow), for NLP problems such as statistical machine translation, for comprehending and categorizing text corpus, for segmenting, tracking and interpreting video and caption streams from various sources (e.g., surveillance system, robots), and for decision making and active learning in dynamic environments.
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Computational BiologyWith an emphasis on developing formal models and algorithms that address problems of practical biological and medical concerns. 
Many complex disease syndromes consist of a large number of related, rather than independent, clinical phenotypes. Differences between these syndromes involve the complex interplay of a large number of genomic variations that perturb the function of diseaserelated genes in the context of a regulatory network, rather than individually. The current stateoftheart in genomewideassociation studies (GWAS) is a singlegene association approach. A major challenge for the immediate future is therefore to transcend the onegene/onedisease approach with a suite of approaches that account for pathway and network structure. In this project, we aim at developing algorithms and software to enable nextgeneration association analysis addressing these problems, in the context of asthma disease. We are developing methodologies for the largely unexplored but practically important problem of structured associations between elements in the genome, transcriptome, and the phenome. This research will open a new paradigm for association studies of complex diseases, which facilitates: 1) Intra and interomic integration of data for association mapping and disease gene/pathway discovery, 2) Thorough explorations of the internal structures within different omic data, so that cryptic associations that are not possibly detectable in unstructured analysis due to their weak statistical power can be now inferred. 3) Joint statistical inference of mechanisms and pathways of how variations in DNA lead to variations in complex traits flows through molecular networks, and inference of conditionspecific state of gene function in the molecular networks, and 4) Development of faster and automated computational algorithm with greater scalability and robustness to largescale interomic analysis, and more convenient software package and user interface.
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Due to the dynamic nature of biological systems, biological networks underlying temporal process such as development, immunoresponse, and disease progression can exhibit significant topological changes to facilitate dynamic regulatory functions. The latent functionality or membership undertaken by the biomolecules as determined by these dynamic interactions will also exhibit rich temporal behaviors, assuming a distinct function at one point while leaning more towards a second function at an another point. In this project, we focus on two dynamic processes, the life cycle of Drosophila melanogaster, and the progress of asthma in human, for which we develop methodologies to, 1) reverseengineer latent timeevolving gene networks based on either microimages of spatial pattern of gene expressions in Drosophila embryos, or genomewide microarray profile of gene expression intensities; 2) recover the transcriptional activation/repression functions from temporal/spatial patterns of gene expressions; 3) estimate embeddings of every genes into a latent function space and track its mixed membership of functions in the latent space across time. The goal is to understand the driving forces underlying dynamic rewiring of gene regulation circuity, and to predict future network structures.
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In this project we
analyze the molecular abundance profiles
(e.g., microarray, CGH, ChIpChip) measured in a "designer
microenvironment", realized in 3D culture model that imitates the in
vivo cellular context and dynamics of cancer progression, reversion and
apoptosis. We will develop algorithms to identify molecular
determinants and
markers of cancer states and categorize cancers on the basis of
signaling pathway
characteristics. Using probabilistic graphical modeling approaches, we
hope to infer stochastic network models for transcriptional regulation
in
response to combinations of signaling inhibitions in cancer cells.
Selected Reading:
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In this project we study the evolutionary relationships reflected in the sequence, ordering, position, spacing and function of the regulatory motifs controlling body segmentation during early embryogenesis in multiple species of the Drosophila. We are interested in understanding the biological driving forces, molecular mechanisms and functional implications of motif evolution in general from this biological model, and in developing comparative genomic algorithms for motif finding from unaligned noncoding sequences.
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In this project we develop novel statistical models and computational algorithms based on formalisms such as the coalescent process, Bayesian nonparametrics, admixture models, and various temporal/spatial stochastic processes for uncovering the chromosomal association (i.e., haplotypes), population distribution (i.e., diversity and frequency) inheritance process (i.e., recombination/substitution/selection), and migration history of genetics polymorphisms such as SNPs, to address problems such as ancestry reconstruction, diseaserelated gene flow, chromosomal evolution and genetic demography in human or organismal populations.
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In this project we develop models and algorithms for understanding and uncovering the structure of genomic sequences of higher organisms. We develop Bayesian models for DNA/protein motif detection and gene finding based on both sequencelevel signatures and metasequencelevel structural information reflecting proteinDNA binding, transcript stability, and prior knowledge of the organization rules of regulatory modules. We intend to integrate motif finding with the system biology research of gene regulatory network.
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Last updated 02/1/2009 