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777798

Context Effects in Category Learning: An Investigation of Four Probabilistic Models

Categorization is a central activity of human cognition. When an individual is asked to categorize a sequence of items, context effects arise: categorization of one item influences category decisions for subsequent items. Specifically, when experimental subjects are shown an exemplar of some target category, the category prototype appears to be pulled toward the exemplar, and the prototypes of all nontarget categories appear to be pushed away. These push and pull effects diminish with experience, and likely reflect long-term learning of category boundaries. We propose and evaluate four principled probabilistic (Bayesian) accounts of context effects in categorization. In all four accounts, the probability of an exemplar given a category is encoded as a Gaussian density in feature space, and categorization involves computing category posteriors given an exemplar. The models differ in how the uncertainty distribution of category prototypes is represented (localist or distributed), and how it is updated following each experience (using a maximum likelihood gradient ascent, or a Kalman filter update). We find that the distributed maximum-likelihood model can explain the key experimental phenomena. Further, the model predicts other phenomena that were confirmed via reanalysis of the experimental data.

2709712

Learning from Multiple Sources

We consider the problem of learning accurate models from multiple sources of "nearby" data. Given distinct samples from multiple data sources and estimates of the dissimilarities between these sources, we provide a general theory of which samples should be used to learn models for each source. This theory is applicable in a broad decision-theoretic learning framework, and yields results for classification and regression generally, and for density estimation within the exponential family. A key component of our approach is the development of approximate triangle inequalities for expected loss, which may be of independent interest.

9139882

Conditional mean field

Despite all the attention paid to variational methods based on sum-product message passing (loopy belief propagation, tree-reweighted sum-product), these methods are still bound to inference on a small set of probabilistic models. Mean field approximations have been applied to a broader set of problems, but the solutions are often poor. We propose a new class of conditionally-specified variational approximations based on mean field theory. While not usable on their own, combined with sequential Monte Carlo they produce guaranteed improvements over conventional mean field. Moreover, experiments on a well-studied problem— inferring the stable configurations of the Ising spin glass—show that the solutions can be significantly better than those obtained using sum-product-based methods.

7665438

Relational Learning with Gaussian Processes

Correlation between instances is often modelled via a kernel function using input attributes of the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relational information and input attributes using Gaussian process techniques. This approach provides a novel non-parametric Bayesian framework with a data-dependent covariance function for supervised learning tasks. We also apply this framework to semi-supervised learning. Experimental results on several real world data sets verify the usefulness of this algorithm.

63191

Chained Boosting

We describe a method to learn to make sequential stopping decisions, such as those made along a processing pipeline. We envision a scenario in which a series of decisions must be made as to whether to continue to process. Further processing costs time and resources, but may add value. Our goal is to create, based on historic data, a series of decision rules (one at each stage in the pipeline) that decide, based on information gathered up to that point, whether to continue processing the part. We demonstrate how our framework encompasses problems from manufacturing to vision processing. We derive a quadratic (in the number of decisions) bound on testing performance and provide empirical results on object detection.

2618641

Fast Iterative Kernel PCA

We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic Meta-Descent (SMD) to KHA/et; this further speeds convergence by performing gain adaptation in RKHS. Experimental results for kernel PCA and spectral clustering of USPS digits as well as motion capture and image de-noising problems confirm that our methods converge substantially faster than conventional KHA.

6130767

Comparative Gene Prediction using Conditional Random Fields

Computational gene prediction using generative models has reached a plateau, with several groups converging to a generalized hidden Markov model (GHMM) incorporating phylogenetic models of nucleotide sequence evolution. Further improvements in gene calling accuracy are likely to come through new methods that incorporate additional data, both comparative and species specific. Conditional Random Fields (CRFs), which directly model the conditional probability P(y|x) of a vector of hidden states conditioned on a set of observations, provide a unified framework for combining probabilistic and non-probabilistic information and have been shown to outperform HMMs on sequence labeling tasks in natural language processing. We describe the use of CRFs for comparative gene prediction. We implement a model that encapsulates both a phylogenetic-GHMM (our baseline comparative model) and additional non-probabilistic features. We tested our model on the genome sequence of the fungal human pathogen Cryptococcus neoformans. Our baseline comparative model displays accuracy comparable to the the best available gene prediction tool for this organism. Moreover, we show that discriminative training and the incorporation of non-probabilistic evidence significantly improve performance. Our software implementation, Conrad, is freely available with an open source license at http://www.broad.mit.edu/annotation/conrad/.

1467337

Scalable Discriminative Learning for Natural Language Parsing and Translation

Parsing and translating natural languages can be viewed as problems of predicting tree structures. For machine learning approaches to these predictions, the diversity and high dimensionality of the structures involved mandate very large training sets. This paper presents a purely discriminative learning method that scales up well to problems of this size. Its accuracy was at least as good as other comparable methods on a standard parsing task. To our knowledge, it is the first purely discriminative learning algorithm for translation with tree-structured models. Unlike other popular methods, this method does not require a great deal of feature engineering a priori, because it performs feature selection over a compound feature space as it learns. Experiments demonstrate the method's versatility, accuracy, and efficiency. Relevant software is freely available at http://nlp.cs.nyu.edu/parser and http://nlp.cs.nyu.edu/GenPar.

2727

Fundamental Limitations of Spectral Clustering

Spectral clustering methods are common graph-based approaches to clustering of data. Spectral clustering algorithms typically start from local information encoded in a weighted graph on the data and cluster according to the global eigenvectors of the corresponding (normalized) similarity matrix. One contribution of this paper is to present fundamental limitations of this general local to global approach. We show that based only on local information, the normalized cut functional is not a suitable measure for the quality of clustering. Further, even with a suitable similarity measure, we show that the first few eigenvectors of such adjacency matrices cannot successfully cluster datasets that contain structures at different scales of size and density. Based on these findings, a second contribution of this paper is a novel diffusion based measure to evaluate the coherence of individual clusters. Our measure can be used in conjunction with any bottom-up graph-based clustering method, it is scale-free and can determine coherent clusters at all scales. We present both synthetic examples and real image segmentation problems where various spectral clustering algorithms fail. In contrast, using this coherence measure finds the expected clusters at all scales.

13045437

Using Combinatorial Optimization within Max-Product Belief Propagation

In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or close-to-optimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as sub-networks, but also other non-complying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for sub-networks within the context of a max-product belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact max-marginals for an entire sub-network; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing max-marginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higher-scoring assignments.

7711172

Clustering appearance and shape by learning jigsaws

Patch-based appearance models are used in a wide range of computer vision applications. To learn such models it has previously been necessary to specify a suitable set of patch sizes and shapes by hand. In the jigsaw model presented here, the shape, size and appearance of patches are learned automatically from the repeated structures in a set of training images. By learning such irregularly shaped 'jigsaw pieces', we are able to discover both the shape and the appearance of object parts without supervision. When applied to face images, for example, the learned jigsaw pieces are surprisingly strongly associated with face parts of different shapes and scales such as eyes, noses, eyebrows and cheeks, to name a few. We conclude that learning the shape of the patch not only improves the accuracy of appearance-based part detection but also allows for shape-based part detection. This enables parts of similar appearance but different shapes to be distinguished; for example, while foreheads and cheeks are both skin colored, they have markedly different shapes.

70831

Correcting Sample Selection Bias by Unlabeled Data

We consider the scenario where training and test data are drawn from different distributions, commonly referred to as sample selection bias. Most algorithms for this setting try to first recover sampling distributions and then make appropriate corrections based on the distribution estimate. We present a nonparametric method which directly produces resampling weights without distribution estimation. Our method works by matching distributions between training and testing sets in feature space. Experimental results demonstrate that our method works well in practice.

15064608

Large-Margin Gaussian Mixture Modeling for Automatic Speech Recognition

Discriminative training for acoustic models has been widely studied to improve the performance of automatic speech recognition systems. To enhance the generalization ability of discriminatively trained models, a large-margin training framework has recently been proposed. This work investigates large-margin training in detail, integrates the training with more flexible classifier structures such as hierarchical classifiers and committee-based classifiers, and compares the performance of the proposed modeling scheme with existing discriminative methods such as minimum classification error (MCE) training. Experiments are performed on a standard phonetic classification task and a large vocabulary speech recognition (LVCSR) task. In the phonetic classification experiments, the proposed modeling scheme yields about 1.5% absolute error reduction over the current state of the art. In the LVCSR experiments on the MIT lecture corpus, the large-margin model has about 6.0% absolute word error rate reduction over the baseline model and about 0.6% absolute error rate reduction over the MCE model. Thesis Supervisor: James R. Glass Title: Principal Research Scientist

9358755

Hyperparameter Learning for Graph Based Semi-supervised Learning Algorithms

Semi-supervised learning algorithms have been successfully applied in many applications with scarce labeled data, by utilizing the unlabeled data. One important category is graph based semi-supervised learning algorithms, for which the performance depends considerably on the quality of the graph, or its hyperparameters. In this paper, we deal with the less explored problem of learning the graphs. We propose a graph learning method for the harmonic energy minimization method; this is done by minimizing the leave-one-out prediction error on labeled data points. We use a gradient based method and designed an efficient algorithm which significantly accelerates the calculation of the gradient by applying the matrix inversion lemma and using careful pre-computation. Experimental results show that the graph learning method is effective in improving the performance of the classification algorithm.

189067213

Attribute-efficient learning of linear threshold functions under unconcentrated distributions

2945707

Adaptor Grammars: A Framework for Specifying Compositional Nonparametric Bayesian Models

This paper introduces adaptor grammars, a class of probabilistic models of language that generalize probabilistic context-free grammars (PCFGs). Adaptor grammars augment the probabilistic rules of PCFGs with "adaptors" that can induce dependencies among successive uses. With a particular choice of adaptor, based on the Pitman-Yor process, nonparametric Bayesian models of language using Dirichlet processes and hierarchical Dirichlet processes can be written as simple grammars. We present a general-purpose inference algorithm for adaptor grammars, making it easy to define and use such models, and illustrate how several existing nonparametric Bayesian models can be expressed within this framework.

14599753

An Oracle Inequality for Clipped Regularized Risk Minimizers

We establish a general oracle inequality for clipped approximate minimizers of regularized empirical risks and apply this inequality to support vector machine (SVM) type algorithms. We then show that for SVMs using Gaussian RBF kernels for classification this oracle inequality leads to learning rates that are faster than the ones established in [9]. Finally, we use our oracle inequality to show that a simple parameter selection approach based on a validation set can yield the same fast learning rates without knowing the noise exponents which were required to be known a-priori in [9].

8723013

AdaBoost is Consistent

The risk, or probability of error, of the classifier produced by the AdaBoost algorithm is investigated. In particular, we consider the stopping strategy to be used in AdaBoost to achieve universal consistency. We show that provided AdaBoost is stopped after nv iterations—for sample size n and v 0.

18338409

Data Integration for Classification Problems Employing Gaussian Process Priors

By adopting Gaussian process priors a fully Bayesian solution to the problem of integrating possibly heterogeneous data sets within a classification setting is presented. Approximate inference schemes employing Variational & Expectation Propagation based methods are developed and rigorously assessed. We demonstrate our approach to integrating multiple data sets on a large scale protein fold prediction problem where we infer the optimal combinations of covariance functions and achieve state-of-the-art performance without resorting to any ad hoc parameter tuning and classifier combination.

15481825

MLLE: Modified Locally Linear Embedding Using Multiple Weights

The locally linear embedding (LLE) is improved by introducing multiple linearly independent local weight vectors for each neighborhood. We characterize the reconstruction weights and show the existence of the linearly independent weight vectors at each neighborhood. The modified locally linear embedding (MLLE) proposed in this paper is much stable. It can retrieve the ideal embedding if MLLE is applied on data points sampled from an isometric manifold. MLLE is also compared with the local tangent space alignment (LTSA). Numerical examples are given that show the improvement and efficiency of MLLE.

1360082

Accelerated Variational Dirichlet Process Mixtures

Dirichlet Process (DP) mixture models are promising candidates for clustering applications where the number of clusters is unknown a priori. Due to computational considerations these models are unfortunately unsuitable for large scale data-mining applications. We propose a class of deterministic accelerated DP mixture models that can routinely handle millions of data-cases. The speedup is achieved by incorporating kd-trees into a variational Bayesian algorithm for DP mixtures in the stick-breaking representation, similar to that of Blei and Jordan (2005). Our algorithm differs in the use of kd-trees and in the way we handle truncation: we only assume that the variational distributions are fixed at their priors after a certain level. Experiments show that speedups relative to the standard variational algorithm can be significant.

7502194

Multi-Task Feature Learning

We present a method for learning a low-dimensional representation which is shared across a set of multiple related tasks. The method builds upon the well-known 1-norm regularization problem using a new regularizer which controls the number of learned features common for all the tasks. We show that this problem is equivalent to a convex optimization problem and develop an iterative algorithm for solving it. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the latter step we learn commonacross-tasks representations and in the former step we learn task-specific functions using these representations. We report experiments on a simulated and a real data set which demonstrate that the proposed method dramatically improves the performance relative to learning each task independently. Our algorithm can also be used, as a special case, to simply select – not learn – a few common features across the tasks.

7721432

Doubly Stochastic Normalization for Spectral Clustering

In this paper we focus on the issue of normalization of the affinity matrix in spectral clustering. We show that the difference between N-cuts and Ratio-cuts is in the error measure being used (relative-entropy versus L1 norm) in finding the closest doubly-stochastic matrix to the input affinity matrix. We then develop a scheme for finding the optimal, under Frobenius norm, doubly-stochastic approximation using Von-Neumann's successive projections lemma. The new normalization scheme is simple and efficient and provides superior clustering performance over many of the standardized tests.

658553

Sample Complexity of Policy Search with Known Dynamics

We consider methods that try to find a good policy for a Markov decision process by choosing one from a given class. The policy is chosen based on its empirical performance in simulations. We are interested in conditions on the complexity of the policy class that ensure the success of such simulation based policy search methods. We show that under bounds on the amount of computation involved in computing policies, transition dynamics and rewards, uniform convergence of empirical estimates to true value functions occurs. Previously, such results were derived by assuming boundedness of pseudodimension and Lipschitz continuity. These assumptions and ours are both stronger than the usual combinatorial complexity measures. We show, via minimax inequalities, that this is essential: boundedness of pseudodimension or fat-shattering dimension alone is not sufficient.

12991446

implicit Online Learning with Kernels

We present two new algorithms for online learning in reproducing kernel Hilbert spaces. Our first algorithm, ILK (implicit online learning with kernels), employs a new, implicit update technique that can be applied to a wide variety of convex loss functions. We then introduce a bounded memory version, SILK (sparse ILK), that maintains a compact representation of the predictor without compromising solution quality, even in non-stationary environments. We prove loss bounds and analyze the convergence rate of both. Experimental evidence shows that our proposed algorithms outperform current methods on synthetic and real data.

2447517

Modeling General and Specific Aspects of Documents with a Probabilistic Topic Model

Techniques such as probabilistic topic models and latent-semantic indexing have been shown to be broadly useful at automatically extracting the topical or semantic content of documents, or more generally for dimension-reduction of sparse count data. These types of models and algorithms can be viewed as generating an abstraction from the words in a document to a lower-dimensional latent variable representation that captures what the document is generally about beyond the specific words it contains. In this paper we propose a new probabilistic model that tempers this approach by representing each document as a combination of (a) a background distribution over common words, (b) a mixture distribution over general topics, and (c) a distribution over words that are treated as being specific to that document. We illustrate how this model can be used for information retrieval by matching documents both at a general topic level and at a specific word level, providing an advantage over techniques that only match documents at a general level (such as topic models or latent-sematic indexing) or that only match documents at the specific word level (such as TF-IDF).

6937053

A Hidden Markov Dirichlet Process Model for Genetic Recombination in Open Ancestral Space

We present a new statistical framework called hidden Markov Dirichlet process (HMDP) to jointly model the genetic recombinations among possibly infinite number of founders and the coalescence-with-mutation events in the resulting genealogies. The HMDP posits that a haplotype of genetic markers is generated by a sequence of recombination events that select an ancestor for each locus from an unbounded set of founders according to a 1st-order Markov transition process. Conjoining this process with a mutation model, our method accommodates both between-lineage recombination and withinlineage sequence variations, and leads to a compact and natural interpretation of the population structure and inheritance process. An efficient sampling algorithm based on a two-level nested Pólya urn scheme was also developed.

239378

Branch and Bound for Semi-Supervised Support Vector Machines

Semi-supervised SVMs (S3VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimization problem is non-convex. To examine the full potential of S3VMs modulo local minima problems in current implementations, we apply branch and bound techniques for obtaining exact, globally optimal solutions. Empirical evidence suggests that the globally optimal solution can return excellent generalization performance in situations where other implementations fail completely. While our current implementation is only applicable to small datasets, we discuss variants that can potentially lead to practically useful algorithms.

1989800

Optimal Single-Class Classification Strategies

We consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the target distribution is completely known to the learner and the learner's goal is to construct a classifier capable of guaranteeing a given tolerance for the false-positive error while minimizing the false negative error. We identify both "hard" and "soft" optimal classification strategies for different types of games and demonstrate that soft classification can provide a significant advantage. Our optimal strategies and bounds provide worst-case lower bounds for standard, finite-sample SCC and also motivate new approaches to solving SCC.

2256865

Stochastic Relational Models for Discriminative Link Prediction

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental results are achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.

851882

A Collapsed Variational Bayesian Inference Algorithm for Latent Dirichlet Allocation

Latent Dirichlet allocation (LDA) is a Bayesian network that has recently gained much popularity in applications ranging from document modeling to computer vision. Due to the large scale nature of these applications, current inference procedures like variational Bayes and Gibbs sampling have been found lacking. In this paper we propose the collapsed variational Bayesian inference algorithm for LDA, and show that it is computationally efficient, easy to implement and significantly more accurate than standard variational Bayesian inference for LDA.

1301729

An Approach to Bounded Rationality

A central question in game theory and artificial intelligence is how a rational agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by formulating a simple model of a game with additional costs (computational or otherwise) for each strategy. First we connect this to zero-sum games, proving a counter-intuitive generalization of the classic min-max theorem to zero-sum games with the addition of strategy costs. We then show that potential games with strategy costs remain potential games. Both zero-sum and potential games with strategy costs maintain a very appealing property: simple learning dynamics converge to equilibrium.

9653949

Learnability and the doubling dimension

Given a set F of classifiers and a probability distribution over their domain, one can define a metric by taking the distance between a pair of classifiers to be the probability that they classify a random item differently. We prove bounds on the sample complexity of PAC learning in terms of the doubling dimension of this metric. These bounds imply known bounds on the sample complexity of learning halfspaces with respect to the uniform distribution that are optimal up to a constant factor. We prove a bound that holds for any algorithm that outputs a classifier with zero error whenever this is possible; this bound is in terms of the maximum of the doubling dimension and the VC-dimension of F, and strengthens the best known bound in terms of the VC-dimension alone. We show that there is no bound on the doubling dimension in terms of the VC-dimension of F (in contrast with the metric dimension).

1446998

Learning to Model Spatial Dependency: Semi-Supervised Discriminative Random Fields

We present a novel, semi-supervised approach to training discriminative random fields (DRFs) that efficiently exploits labeled and unlabeled training data to achieve improved accuracy in a variety of image processing tasks. We formulate DRF training as a form of MAP estimation that combines conditional loglikelihood on labeled data, given a data-dependent prior, with a conditional entropy regularizer defined on unlabeled data. Although the training objective is no longer concave, we develop an efficient local optimization procedure that produces classifiers that are more accurate than ones based on standard supervised DRF training. We then apply our semi-supervised approach to train DRFs to segment both synthetic and real data sets, and demonstrate significant improvements over supervised DRFs in each case.

f636374404685ff7734df09a9756791b6946f010

Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (2001)

This is the Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, which was held in Seattle, WA, August 2-5 2001

257735f453f89c2d12d977df351badaf93df3de1

Probabilistic Discovery of Overlapping Cellular Processes and Their Regulation

In this paper, we explore modeling overlapping biological processes. We discuss a probabilistic model of overlapping biological processes, gene membership in those processes, and an addition to that model that identifies regulatory mechanisms controlling process activation. A key feature of our approach is that we allow genes to participate in multiple processes, thus providing a more biologically plausible model for the process of gene regulation. We present algorithms to learn each model automatically from data, using only genomewide measurements of gene expression as input. We compare our results to those obtained by other approaches and show that significant benefits can be gained by modeling both the organization of genes into overlapping cellular processes and the regulatory programs of these processes. Moreover, our method successfully grouped genes known to function together, recovered many regulatory relationships that are known in the literature, and suggested novel hypotheses regarding the regulatory role of previously uncharacterized proteins.

2b889738d7be550c40775ed2fe5a7aa7294ca07c

Word-Sense Disambiguation for Machine Translation

In word sense disambiguation, a system attempts to determine the sense of a word from contextual features. Major barriers to building a high-performing word sense disambiguation system include the difficulty of labeling data for this task and of predicting fine-grained sense distinctions. These issues stem partly from the fact that the task is being treated in isolation from possible uses of automatically disambiguated data. In this paper, we consider the related task of word translation, where we wish to determine the correct translation of a word from context. We can use parallel language corpora as a large supply of partially labeled data for this task. We present algorithms for solving the word translation problem and demonstrate a significant improvement over a baseline system. We then show that the word-translation system can be used to improve performance on a simplified machine-translation task and can effectively and accurately prune the set of candidate translations for a word.

3cd4a9cdb14b3add799115519e8c617491d675ed

From signatures to models: understanding cancer using microarrays

Genomics has the potential to revolutionize the diagnosis and management of cancer by offering an unprecedented comprehensive view of the molecular underpinnings of pathology. Computational analysis is essential to transform the masses of generated data into a mechanistic understanding of disease. Here we review current research aimed at uncovering the modular organization and function of transcriptional networks and responses in cancer. We first describe how methods that analyze biological processes in terms of higher-level modules can identify robust signatures of disease mechanisms. We then discuss methods that aim to identify the regulatory mechanisms underlying these modules and processes. Finally, we show how comparative analysis, combining human data with model organisms, can lead to more robust findings. We conclude by discussing the challenges of generalizing these methods from cells to tissues and the opportunities they offer to improve cancer diagnosis and management.

410150ab22ffaa054c913b14675938027928a470

Learning Module Networks

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.

55a5e1a4e0068a4f2a8a8bdfbd777c249110ccfe

Discriminative learning of Markov random fields for segmentation of 3D scan data

We address the problem of segmenting 3D scan data into objects or object classes. Our segmentation framework is based on a subclass of Markov random fields (MRFs) which support efficient graph-cut inference. The MRF models incorporate a large set of diverse features and enforce the preference that adjacent scan points have the same classification label. We use a recently proposed maximum-margin framework to discriminatively train the model from a set of labeled scans; as a result we automatically learn the relative importance of the features for the segmentation task. Performing graph-cut inference in the trained MRF can then be used to segment new scenes very efficiently. We test our approach on three large-scale datasets produced by different kinds of 3D sensors, showing its applicability to both outdoor and indoor environments containing diverse objects.

57df77ab2fd98dd6a77f2724159c9257f249843c

Learning Statistical Patterns in Relational Data Using Probabilistic Relational Models

Abstract : This report describes techniques for learning probabilistic models of relational data, and using these models to interpret new relational data. This effort focused on developing undirected probabilistic models for representing and learning graph patterns, learning patterns involving links between objects, learning discriminative models for classification in relational data, developing and labeling two real-world relational data sets - one involving web data and the other a social network - and evaluating the performance of our methods on these data sets, and dealing with distributions that are non-uniform, in that different contexts (time periods, organizations) have statistically different properties. The technology developed under this effort was transitioned and is being used under the Perceptive Assistant Program (PAL) at DARPA.

591b6d0dcc177b72446701bf638b99151cf44bf3

Expectation Propagation for Continuous Time Bayesian Networks

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. As shown previously, exact inference in CTBNs is intractable. We address the problem of approximate inference, allowing for general queries conditioned on evidence over continuous time intervals and at discrete time points. We show how CTBNs can be parameterized within the exponential family, and use that insight to develop a message passing scheme in cluster graphs and allows us to apply expectation propagation to CTBNs. The clusters in our cluster graph do not contain distributions over the cluster variables at individual time points, but distributions over trajectories of the variables throughout a duration. Thus, unlike discrete time temporal models such as dynamic Bayesian networks, we can adapt the time granularity at which we reason for different variables and in different conditions.

5dc9f57a15091524210a84a59c415c6ab4e19c60

SCAPE: shape completion and animation of people

We introduce the SCAPE method (Shape Completion and Animation for PEople)---a data-driven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and non-rigid deformations. We learn a pose deformation model that derives the non-rigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion --- generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a high-quality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan and a marker motion capture sequence of the person.

8cf0f098ff08dd2e5d9efec56bab35f40ab5a0b7

Transfer learning by constructing informative priors

Many applications of supervised learning require good generalization from limited labeled data. In the Bayesian setting, we can use an informative prior to try to achieve this goal by encoding useful domain knowledge. We present an algorithm that constructs such an informative prior for a given discrete supervised learning task. The algorithm uses other “similar” learning problems to discover properties of optimal classifiers, expressed in terms of covariance estimates for pairs of feature parameters. A semidefinite program is then used to combine these estimates and learn a good prior for the current learning task. We apply our methods to binary text classification, and demonstrate a 20 to 40% error reduction over a commonly used prior.

8d56b2a75aa5624660b60787e1f38ee2c70d493a

Learning structured prediction models: a large margin approach

We consider large margin estimation in a broad range of prediction models where inference involves solving combinatorial optimization problems, for example, weighted graph-cuts or matchings. Our goal is to learn parameters such that inference using the model reproduces correct answers on the training data. Our method relies on the expressive power of convex optimization problems to compactly capture inference or solution optimality in structured prediction models. Directly embedding this structure within the learning formulation produces concise convex problems for efficient estimation of very complex and diverse models. We describe experimental results on a matching task, disulfide connectivity prediction, showing significant improvements over state-of-the-art methods.

aadcd0f6fa3f80567f2c93f98d4172a9d339daff

Learning Factor Graphs in Polynomial Time & Sample Complexity

We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time and polynomial number of samples, assuming that the data is generated by a network in this class. This result covers both parameter estimation for a known network structure and structure learning. It implies as a corollary that we can learn factor graphs for both Bayesian networks and Markov networks of bounded degree, in polynomial time and sample complexity. Unlike maximum likelihood estimation, our method does not require inference in the underlying network, and so applies to networks where inference is intractable. We also show that the error of our learned model degrades gracefully when the generating distribution is not a member of the target class of networks.

ab7fbb84ce7a1bcd2cd967291566c31aba9d62aa

Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning the parameters and structure of a CTBN from partially observed data. We show how to apply expectation maximization (EM) and structural expectation maximization (SEM) to CTBNs. The availability of the EM algorithm allows us to extend the representation of CTBNs to allow a much richer class of transition durations distributions, known as phase distributions. This class is a highly expressive semi-parametric representation, which can approximate any duration distribution arbitrarily closely. This extension to the CTBN framework addresses one of the main limitations of both CTBNs and DBNs — the restriction to exponentially / geometrically distributed duration. We present experimental results on a real data set of people's life spans, showing that our algorithm learns reasonable models — structure and parameters — from partially observed data, and, with the use of phase distributions, achieves better performance than DBNs.

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SCAPE: shape completion and animation of people

We introduce the SCAPE method (Shape Completion and Animation for PEople)---a data-driven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and non-rigid deformations. We learn a pose deformation model that derives the non-rigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion --- generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a high-quality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan and a marker motion capture sequence of the person.

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Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks

One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill-climbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easy-to-implement method for addressing this task. Our approach is based on the well-known fact that the best network (of bounded in-degree) consistent with a given node ordering can be found very efficiently. We therefore propose a search not over the space of structures, but over the space of orderings, selecting for each ordering the best network consistent with it. This search space is much smaller, makes more global search steps, has a lower branching factor, and avoids costly acyclicity checks. We present results for this algorithm on both synthetic and real data sets, evaluating both the score of the network found and in the running time. We show that ordering-based search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement.

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Probabilistic Entity-Relationship Models, PRMs, and Plate Models

We introduce a graphical language for re- lational data called the probabilistic entity- relationship (PER) model. The model is an extension of the entity-relationship model, a common model for the abstract repre- sentation of database structure. We con- centrate on the directed version of this model—the directed acyclic probabilistic entity-relationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. dinary graphical models (e.g., directed-acyclic graphs and undirected graphs) are to flat data. In this paper, we introduce a new graphical model for relational data—the probabilistic entity-relationship (PER) model. This model class is more expressive than either PRMs or plate models. We concentrate on a particular type of PER model—the directed acyclic probabilistic entity-relationship (DAPER) model—in which all probabilistic arcs are directed. It is this ver- sion of PER model that is most similar to the plate model and PRM. We define new versions of the plate model and PRM such their expressiveness is equivalent to the DAPER model, and then (in the expanded tech report, Heckerman, Meek, and Koller, 2004) compare the new and old definitions. Consequently, we both demonstrate the similarity among the original lan- guages as well as enhance their abilities to express con- ditional independence in relational data. Our hope is that this demonstration of similarity will foster greater communication and collaboration among statisticians who mostly use plate models and computer scientists who mostly use PRMs. We in fact began this work with an effort to unify traditional PRMs and plate models. In the process, we discovered that it was important to make both entities and relationships (concepts discussed in de- tail in the next section) first class objects in the lan- guage. We in turn discovered an existing language that does this—the entity-relationship (ER) model—a commonly used model for the abstract representation of database structure. We then extended this language to handle probabilistic relationships, creating the PER model. We should emphasize that the languages we discuss are neither meant to serve as a database schema nor meant to be built on top of one. In practice, database schemas are built up over a long period of time as the needs of the database consumers change. Conse-

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Rich Probabilistic Models For Genomic Data

Genomic datasets, spanning many organisms and data types, are rapidly being produced, creating new opportunities for understanding the molecular mechanisms underlying human disease, and for studying complex biological processes on a global scale. Transforming these immense amounts of data into biological information is a challenging task. In this thesis, we address this challenge by presenting a statistical modeling language, based on Bayesian networks, for representing heterogeneous biological entities and modeling the mechanism by which they interact. We use statistical learning approaches in order to learn the details of these models (structure and parameters) automatically from raw genomic data. The biological insights are then derived directly from the learned model. We describe three applications of this framework to the study of gene regulation: (1) Understanding the process by which DNA patterns (motifs) in the control regions of genes play a role in controlling their activity. Using only DNA sequence and gene expression data as input, these models recovered many of the known motifs in yeast and several known motif combinations in human. (2) Finding regulatory modules and their actual regulator genes directly from gene expression data. Some of the predictions from this analysis were tested successfully in the wet-lab, suggesting regulatory roles for three previously uncharacterized proteins. (3) Combining gene expression profiles from several organisms for a more robust prediction of gene function and regulatory pathways, and for studying the degree to which regulatory relationships have been conserved across evolution.

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Max-Margin Parsing

We present a novel discriminative approach to parsing inspired by the large-margin criterion underlying support vector machines. Our formulation uses a factorization analogous to the standard dynamic programs for parsing. In particular, it allows one to efficiently learn a model which discriminates among the entire space of parse trees, as opposed to reranking the top few candidates. Our models can condition on arbitrary features of input sentences, thus incorporating an important kind of lexical information without the added algorithmic complexity of modeling headedness. We provide an efficient algorithm for learning such models and show experimental evidence of the model’s improved performance over a natural baseline model and a lexicalized probabilistic context-free grammar.

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Simultaneous Localization and Mapping with Sparse Extended Information Filters

In this paper we describe a scalable algorithm for the simultaneous mapping and localization (SLAM) problem. SLAM is the problem of acquiring a map of a static environment with a mobile robot. The vast majority of SLAM algorithms are based on the extended Kalman filter (EKF). In this paper we advocate an algorithm that relies on the dual of the EKF, the extended information filter (EIF). We show that when represented in the information form, map posteriors are dominated by a small number of links that tie together nearby features in the map. This insight is developed into a sparse variant of the EIF, called the sparse extended information filter (SEIF). SEIFs represent maps by graphical networks of features that are locally interconnected, where links represent relative information between pairs of nearby features, as well as information about the robot’s pose relative to the map. We show that all essential update equations in SEIFs can be executed in constant time, irrespective of the size of the map. We also provide empirical results obtained for a benchmark data set collected in an outdoor environment, and using a multi-robot mapping simulation.

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Probabilistic Models for Relational Data

We introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entity-relationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of this model—the directed acyclic probabilistic entity-relationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. In addition to describing the new language, we discuss important facets of modeling relational data, including the use of restricted relationships, self relationships, and probabilistic relationships. Many examples are provided.

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Understanding tuberculosis epidemiology using structured statistical models

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The Correlated Correspondence Algorithm for Unsupervised Registration of Nonrigid Surfaces

We present an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not need markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. The algorithm registers two meshes by optimizing a joint probabilistic model over all point-to-point correspondences between them. This model enforces preservation of local mesh geometry, as well as more global constraints that capture the preservation of geodesic distance between corresponding point pairs. The algorithm applies even when one of the meshes is an incomplete range scan; thus, it can be used to automatically fill in the remaining surfaces for this partial scan, even if those surfaces were previously only seen in a different configuration. We evaluate the algorithm on several real-world datasets, where we demonstrate good results in the presence of significant movement of articulated parts and non-rigid surface deformation. Finally, we show that the output of the algorithm can be used for compelling computer graphics tasks such as interpolation between two scans of a non-rigid object and automatic recovery of articulated object models.

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Detecting and modeling doors with mobile robots

We describe a probabilistic framework for detection and modeling of doors from sensor data acquired in corridor environments with mobile robots. The framework captures shape, color, and motion properties of door and wall objects. The probabilistic model is optimized with a version of the expectation maximization algorithm, which segments the environment into door and wall objects and learns their properties. The framework allows the robot to generalize the properties of detected object instances to new object instances. We demonstrate the algorithm on real-world data acquired by a Pioneer robot equipped with a laser range finder and an omni-directional camera. Our results show that our algorithm reliably segments the environment into walls and doors, finding both doors that move and doors that do not move. We show that our approach achieves better results than models that only capture behavior, or only capture appearance.

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Identifying Protein-Protein Interaction Sites on a Genome-Wide Scale

Protein interactions typically arise from a physical interaction of one or more small sites on the surface of the two proteins. Identifying these sites is very important for drug and protein design. In this paper, we propose a computational method based on probabilistic relational model that attempts to address this task using high-throughput protein interaction data and a set of short sequence motifs. We learn the model using the EM algorithm, with a branch-and-bound algorithm as an approximate inference for the E-step. Our method searches for motifs whose presence in a pair of interacting proteins can explain their observed interaction. It also tries to determine which motif pairs have high affinity, and can therefore lead to an interaction. We show that our method is more accurate than others at predicting new protein-protein interactions. More importantly, by examining solved structures of protein complexes, we find that 2/3 of the predicted active motifs correspond to actual interaction sites.

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Learning associative Markov networks

Markov networks are extensively used to model complex sequential, spatial, and relational interactions in fields as diverse as image processing, natural language analysis, and bioinformatics. However, inference and learning in general Markov networks is intractable. In this paper, we focus on learning a large subclass of such models (called associative Markov networks) that are tractable or closely approximable. This subclass contains networks of discrete variables with K labels each and clique potentials that favor the same labels for all variables in the clique. Such networks capture the "guilt by association" pattern of reasoning present in many domains, in which connected ("associated") variables tend to have the same label. Our approach exploits a linear programming relaxation for the task of finding the best joint assignment in such networks, which provides an approximate quadratic program (QP) for the problem of learning a margin-maximizing Markov network. We show that for associative Markov network over binary-valued variables, this approximate QP is guaranteed to return an optimal parameterization for Markov networks of arbitrary topology. For the nonbinary case, optimality is not guaranteed, but the relaxation produces good solutions in practice. Experimental results with hypertext and newswire classification show significant advantages over standard approaches.

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Recovering Articulated Object Models from 3D Range Data

We address the problem of unsupervised learning of complex articulated object models from 3D range data. We describe an algorithm whose input is a set of meshes corresponding to different configurations of an articulated object. The algorithm automatically recovers a decomposition of the object into approximately rigid parts, the location of the parts in the different object instances, and the articulated object skeleton linking the parts. Our algorithm first registers all the meshes using an unsupervised non-rigid technique described in a companion paper. It then segments the meshes using a graphical model that captures the spatial contiguity of parts. The segmentation is done using the EM algorithm, iterating between finding a decomposition of the object into rigid parts, and finding the location of the parts in the object instances. Although the graphical model is densely connected, the object decomposition step can be performed optimally and efficiently, allowing us to identify a large number of object parts while avoiding local maxima. We demonstrate the algorithm on real world datasets, recovering a 15-part articulated model of a human puppet from just 7 different puppet configurations, as well as a 4 part model of a flexing arm where significant non-rigid deformation was present.

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A module map showing conditional activity of expression modules in cancer

DNA microarrays are widely used to study changes in gene expression in tumors, but such studies are typically system-specific and do not address the commonalities and variations between different types of tumor. Here we present an integrated analysis of 1,975 published microarrays spanning 22 tumor types. We describe expression profiles in different tumors in terms of the behavior of modules, sets of genes that act in concert to carry out a specific function. Using a simple unified analysis, we extract modules and characterize gene-expression profiles in tumors as a combination of activated and deactivated modules. Activation of some modules is specific to particular types of tumor; for example, a growth-inhibitory module is specifically repressed in acute lymphoblastic leukemias and may underlie the deregulated proliferation in these cancers. Other modules are shared across a diverse set of clinical conditions, suggestive of common tumor progression mechanisms. For example, the bone osteoblastic module spans a variety of tumor types and includes both secreted growth factors and their receptors. Our findings suggest that there is a single mechanism for both primary tumor proliferation and metastasis to bone. Our analysis presents multiple research directions for diagnostic, prognostic and therapeutic studies.

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Adaptive Probabilistic Networks with Hidden Variables

Probabilistic networks (also known as Bayesian belief networks) allow a compact description of complex stochastic relationships among several random variables. They are used widely for uncertain reasoning in artificial intelligence. In this paper, we investigate the problem of learning probabilistic networks with known structure and hidden variables. This is an important problem, because structure is much easier to elicit from experts than numbers, and the world is rarely fully observable. We present a gradient-based algorithm and show that the gradient can be computed locally, using information that is available as a byproduct of standard inference algorithms for probabilistic networks. Our experimental results demonstrate that using prior knowledge about the structure, even with hidden variables, can significantly improve the learning rate of probabilistic networks. We extend the method to networks in which the conditional probability tables are described using a small number of parameters. Examples include noisy-OR nodes and dynamic probabilistic networks. We show how this additional structure can be exploited by our algorithm to speed up the learning even further. We also outline an extension to hybrid networks, in which some of the nodes take on values in a continuous domain.

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Multi-Agent Planning in Complex Uncertain Environments

Many tasks require a team of agents to act together in a coordinated way in a complex, uncertain environment. Examples include search and rescue, control of a complex system such as a factory, or robot soccer. Such tasks involve many agents, and huge numbers of states and possible actions. Factored Markov decision processes (MDPs) provide a formal foundation for modeling such complex systems naturally and compactly. We propose a framework for multi-agent coordination and planning in factored MDPs based on the use of a factored value function — an approximate decomposition of the team value function as a sum of value functions of small subteams of agents. We show that factored value functions naturally give rise to an optimal distributed algorithm for joint action selection, whose communication structure naturally mirrors the interactions between the subteams. We present an efficient linear-programming-based algorithm for computing a factored value function for a factored MDP. We show how the use of factored value functions can form the basis for interdomain plan generalization, where we “learn” from plans constructed for some set of problems, and can provide good solutions to other unseen problems of the same type without any need for planning. We describe the application of this approach to the task of multi-agent planning in a strategic computer war game, and the application by Kok et al. for multi-agent coordination in their world-champion RoboSoccer team. Acknowledgements. Joint work with Carlos Guestrin, Ronald Parr, Chris Gearhart, Neal Kanodia, and Shobha Venkataraman.

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Sfp1 is a stress- and nutrient-sensitive regulator of ribosomal protein gene expression.

Yeast cells modulate their protein synthesis capacity in response to physiological needs through the transcriptional control of ribosomal protein (RP) genes. Here we demonstrate that the transcription factor Sfp1, previously shown to play a role in the control of cell size, regulates RP gene expression in response to nutrients and stress. Under optimal growth conditions, Sfp1 is localized to the nucleus, bound to the promoters of RP genes, and helps promote RP gene expression. In response to inhibition of target of rapamycin (TOR) signaling, stress, or changes in nutrient availability, Sfp1 is released from RP gene promoters and leaves the nucleus, and RP gene transcription is down-regulated. Additionally, cells lacking Sfp1 fail to appropriately modulate RP gene expression in response to environmental cues. We conclude that Sfp1 integrates information from nutrient- and stress-responsive signaling pathways to help control RP gene expression.

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Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.

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Constructing Small Sample Spaces for De � Randomization of Algorithms

The subject of this paper is nding small sample spaces for joint distributions of n Bernoulli random variables where the probabilities of some events are prescribed The problem of recognizing whether the prescribed probabilities are consistent is NP hard It is shown however that if the probabilities are consistent then there exists a sample space that supports them whose cardinality does not exceed the number of events with prescribed probabilities It is also shown that if the probabilities are consistent with a joint distribution of n independent Bernoulli variables then a small sample space can be constructed in polynomial time This last result is useful for converting randomized algorithms into deterministic ones We demonstrate this technique by an application to the problem of nding large independent sets in sparse hypergraphs

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Probabilistic discovery of overlapping cellular processes and their regulation

Many of the functions carried out by a living cell are regulated at the transcriptional level, to ensure that genes are expressed when they are needed. Thus, to understand biological processes, it is thus necessary to understand the cell's transcriptional network. In this paper, we propose a novel probabilistic model of gene regulation for the task of identifying overlapping biological processes and the regulatory mechanism controlling their activation. A key feature of our approach is that we allow genes to participate in multiple processes, thus providing a more biologically plausible model for the process of gene regulation. We present an algorithm to learn this model automatically from data, using only genome-wide measurements of gene expression as input. We compare our results to those obtained by other approaches, and show significant benefits can be gained by modeling both the organization of genes into overlapping cellular processes and the regulatory programs of these processes. Moreover, our method successfully grouped genes known to function together, recovered many regulatory relationships that are known in the literature, and suggested novel hypotheses regarding the regulatory role of previously uncharacterized proteins.

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FastSLAM: An Efficient Solution to the Simultaneous Localization And Mapping Problem with Unknown Data

This article provides a comprehensive description of FastSLAM, a new family of algorithms for the simultaneous localization and mapping problem, which specifically address hard data association problems. The algorithm uses a particle filter for sampling robot paths, and extended Kalman filters for representing maps acquired by the vehicle. This article presents two variants of this algorithm, the original algorithm along with a more recent variant that provides improved performance in certain operating regimes. In addition to a mathematical derivation of the new algorithm, we present a proof of convergence and experimental results on its performance on real-world data.

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Discovering molecular pathways from protein interaction and gene expression data

In this paper, we describe an approach for identifying 'pathways' from gene expression and protein interaction data. Our approach is based on the assumption that many pathways exhibit two properties: their genes exhibit a similar gene expression profile, and the protein products of the genes often interact. Our approach is based on a unified probabilistic model, which is learned from the data using the EM algorithm. We present results on two Saccharomyces cerevisiae gene expression data sets, combined with a binary protein interaction data set. Our results show that our approach is much more successful than other approaches at discovering both coherent functional groups and entire protein complexes.

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Generalizing Plans to New Environments in Relational MDPs

A longstanding goal in planning research is the ability to generalize plans developed for some set of environments to a new but similar environment, with minimal or no replanning. Such generalization can both reduce planning time and allow us to tackle larger domains than the ones tractable for direct planning. In this paper, we present an approach to the generalization problem based on a new framework of relational Markov Decision Processes (RMDPs). An RMDP can model a set of similar environments by representing objects as instances of different classes. In order to generalize plans to multiple environments, we define an approximate value function specified in terms of classes of objects and, in a multiagent setting, by classes of agents. This class-based approximate value function is optimized relative to a sampled subset of environments, and computed using an efficient linear programming method. We prove that a polynomial number of sampled environments suffices to achieve performance close to the performance achievable when optimizing over the entire space. Our experimental results show that our method generalizes plans successfully to new, significantly larger, environments, with minimal loss of performance relative to environment-specific planning. We demonstrate our approach on a real strategic computer war game.

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Max-Margin Markov Networks

In typical classification tasks, we seek a function which assigns a label to a single object. Kernel-based approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ability to use high-dimensional feature spaces, and from their strong theoretical guarantees. However, many real-world tasks involve sequential, spatial, or structured data, where multiple labels must be assigned. Existing kernel-based methods ignore structure in the problem, assigning labels independently to each object, losing much useful information. Conversely, probabilistic graphical models, such as Markov networks, can represent correlations between labels, by exploiting problem structure, but cannot handle high-dimensional feature spaces, and lack strong theoretical generalization guarantees. In this paper, we present a new framework that combines the advantages of both approaches: Maximum margin Markov (M3) networks incorporate both kernels, which efficiently deal with high-dimensional features, and the ability to capture correlations in structured data. We present an efficient algorithm for learning M3 networks based on a compact quadratic program formulation. We provide a new theoretical bound for generalization in structured domains. Experiments on the task of handwritten character recognition and collective hypertext classification demonstrate very significant gains over previous approaches.

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Learning on the Test Data: Leveraging Unseen Features

This paper addresses the problem of classification in situations where the data distribution is not homogeneous: Data instances might come from different locations or times, and therefore are sampled from related but different distributions. In particular, features may appear in some parts of the data that are rarely or never seen in others. In most situations with nonhomogeneous data, the training data is not representative of the distribution under which the classifier must operate. We propose a method, based on probabilistic graphical models, for utilizing unseen features during classification. Our method introduces, for each such unseen feature, a continuous hidden variable describing its influence on the class -- whether it tends to be associated with some label. We then use probabilistic inference over the test data to infer a distribution over the value of this hidden variable. Intuitively, we "learn" the role of this unseen feature from the test set, generalizing from those instances whose label we are fairly sure about. Our overall probabilistic model is learned from the training data. In particular, we also learn models for characterizing the role of unseen features; these models use "meta-features" of those features, such as words in the neighborhood of an unseen feature, to infer its role. We present results for this framework on the task of classifying news articles and web pages, showing significant improvements over models that do not use unseen features.

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Efficient Solution Algorithms for Factored MDPs

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and context-specific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomial-sized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on max-norm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 1040 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing state-of-the-art approach, showing, in some problems, exponential gains in computation time.

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Link Prediction in Relational Data

Many real-world domains are relational in nature, consisting of a set of objects related to each other in complex ways. This paper focuses on predicting the existence and the type of links between entities in such domains. We apply the relational Markov network framework of Taskar et al. to define a joint probabilistic model over the entire link graph — entity attributes and links. The application of the RMN algorithm to this task requires the definition of probabilistic patterns over subgraph structures. We apply this method to two new relational datasets, one involving university webpages, and the other a social network. We show that the collective classification approach of RMNs, and the introduction of subgraph patterns over link labels, provide significant improvements in accuracy over flat classification, which attempts to predict each link in isolation.

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Planning under uncertainty in complex structured environments

Many real-world tasks require multiple decision makers (agents) to coordinate their actions in order to achieve common long-term goals. Examples include: manufacturing systems, where managers of a factory coordinate to maximize profit; rescue robots that, after an earthquake, must safely find victims as fast as possible; or sensor networks, where multiple sensors collaborate to perform a large-scale sensing task under strict power constraints. All of these tasks require the solution of complex long-term multiagent planning problems in uncertain dynamic environments. Factored Markov decision processes (MDPs) allow us to represent complex uncertain dynamic systems very compactly by exploiting problem-specific structure. Specifically, the state of the system is described by a set of variables that evolve stochastically over time using a representation, called dynamic Bayesian network, that often allows for an exponential reduction in representation complexity. However, the complexity of exact solution algorithms for such MDPs grows exponentially in the number of variables, and in the number of agents. This thesis builds a formal framework and approximate planning algorithms that exploit structure in factored MDPs to solve problems with many trillions of states and actions very efficiently. The main contributions of this thesis include: Factored linear programs: A novel LP decomposition technique, using ideas from inference in Bayesian networks, that can exploit problem structure to reduce exponentially-large LPs to polynomially-sized ones that are provably equivalent. Factored approximate planning: A suite of algorithms, building on our factored LP decomposition technique, that exploit structure in factored MDPs to obtain exponential reductions in planning time. Distributed coordination: An efficient distributed multiagent decision making algorithm, where the coordination structure arises naturally from the factored representation of the system dynamics. Generalization in relational MDPs: A framework for obtaining general solutions from a small set of environments, allowing agents to act in new environments without replanning. Empirical evaluation: A detailed evaluation on a variety of large-scale tasks, including multiagent coordination in a real strategic computer game, demonstrating that our formal framework yields effective plans, complex agent coordination, and successful generalization in some of the largest planning problems in the literature.

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A Gene-Coexpression Network for Global Discovery of Conserved Genetic Modules

To elucidate gene function on a global scale, we identified pairs of genes that are coexpressed over 3182 DNA microarrays from humans, flies, worms, and yeast. We found 22,163 such coexpression relationships, each of which has been conserved across evolution. This conservation implies that the coexpression of these gene pairs confers a selective advantage and therefore that these genes are functionally related. Manyof these relationships provide strong evidence for the involvement of new genes in core biological functions such as the cell cycle, secretion, and protein expression. We experimentallyconfirmed the predictions implied bysome of these links and identified cell proliferation functions for several genes. By assembling these links into a gene-coexpression network, we found several components that were animal-specific as well as interrelationships between newly evolved and ancient modules.

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A Continuation Method for Nash Equilibria in Structured Games

Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact algorithms for computing Nash equilibria in structured game representations, including both graphical games and multi-agent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normal-form and extensive-form games due to Govindan and Wilson; they follow a trajectory through a space of perturbed games and their equilibria, exploiting game structure through fast computation of the Jacobian of the payoff function. They are theoretically guaranteed to find at least one equilibrium of the game, and may find more. Our approach provides the first efficient algorithm for computing exact equilibria in graphical games with arbitrary topology, and the first algorithm to exploit fine-grained structural properties of MAIDs. Experimental results are presented demonstrating the effectiveness of the algorithms and comparing them to predecessors. The running time of the graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. The algorithm for MAIDs can effectively solve games that are much larger than those solvable by previous methods.

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Label and Link Prediction in Relational Data

Many real-world domains are relational in nature, consisting of a set of entities linked to each other in complex ways. Two important tasks in such data are predicting entity labels and links between entities. We present a flexible framework that builds on (conditional) Markov networks and successfully addresses both tasks by capturing complex dependencies in the data. These models can compactly represent probabilistic patterns over subgraph structures and use them to predict labels and links effectively. We show how to train these models, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities and links. We evaluate our framework on several relational datasets, including university webpages and social networks. Our approach achieves significantly better performance than flat classification, which attempts to predict each label and link in isolation.

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Module Networks : Discovering Regulatory Modules and their Condition Specific Regulators from Gene Expression Data

Modules and their Condition Specific Regulators from Gene Expression Data Eran Segal , Michael Shapira, Aviv Regev, Dana Pe’er David Botstein, Daphne Koller , Nir Friedman Much of a cell's activity is organized as a network of interacting modules: sets of genes co-regulated to respond to different conditions. We present a probabilistic method for discovering regulatory modules from gene expression data. Our procedure identifies modules of co-regulated genes, their regulators, and the conditions under which regulation occurs, generating testable hypotheses in the form "regulator 'X' regulates module 'Y' under conditions 'W'". We applied the method to a Saccharomyces cerevisiae expression dataset, demonstrating its ability to identify functionally coherent modules and their correct regulators. We present microarray experiments supporting three novel predictions, suggesting regulatory roles for previously uncharacterized proteins.

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Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data

Much of a cell's activity is organized as a network of interacting modules: sets of genes coregulated to respond to different conditions. We present a probabilistic method for identifying regulatory modules from gene expression data. Our procedure identifies modules of coregulated genes, their regulators and the conditions under which regulation occurs, generating testable hypotheses in the form 'regulator X regulates module Y under conditions W'. We applied the method to a Saccharomyces cerevisiae expression data set, showing its ability to identify functionally coherent modules and their correct regulators. We present microarray experiments supporting three novel predictions, suggesting regulatory roles for previously uncharacterized proteins.

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Conserved Genetic Modules 5 / 29 / 2003 1 A gene co-expression network for global discovery of conserved genetic modules in H . sapiens , D . melanogaster , C . elegans , and S . cerevisiae

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Learning Continuous Time Bayesian Networks

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning parameters and structure of a CTBN from fully observed data. We define a conjugate prior for CTBNs, and show how it can be used both for Bayesian parameter estimation and as the basis of a Bayesian score for structure learning. Because acyclicity is not a constraint in CTBNs, we can show that the structure learning problem is significantly easier, both in theory and in practice, than structure learning for dynamic Bayesian networks (DBNs). Furthermore, as CTBNs can tailor the parameters and dependency structure to the different time granularities of the evolution of different variables, they can provide a better fit to continuous-time processes than DBNs with a fixed time granularity.

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FastSLAM 2.0: An Improved Particle Filtering Algorithm for Simultaneous Localization and Mapping that Provably Converges

Proceedings of IJCAI 2003 In [15], Montemerlo et al. proposed an algorithm called FastSLAM as an efficient and robust solution to the simultaneous localization and mapping problem. This paper describes a modified version of FastSLAM which overcomes important deficiencies of the original algorithm. We prove convergence of this new algorithm for linear SLAM problems and provide real-world experimental results that illustrate an order of magnitude improvement in accuracy over the original FastSLAM algorithm.

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Decomposing Gene Expression into Cellular Processes

We propose a probabilistic model for cellular processes, and an algorithm for discovering them from gene expression data. A process is associated with a set of genes that participate in it; unlike clustering techniques, our model allows genes to participate in multiple processes. Each process may be active to a different degree in each experiment. The expression measurement for gene g in array a is a sum, over all processes in which g participates, of the activity levels of these processes in array a. We describe an iterative procedure, based on the EM algorithm, for decomposing the expression matrix into a given number of processes. We present results on Yeast gene expression data, which indicate that our approach identifies real biological processes.

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Statistical learning from relational data

Much of the data in the world is relational in nature, involving multiple objects, related to each other in a variety of ways. Examples include both structured databases such as customer transaction data, semi-structured data such as hyperlinked pages on the world-wide web or networks of interacting genes, and unstructured data such as text. In this talk, I will describe a statistical framework for learning from relational data. The approach is based on probabilistic models, which have been applied with great success to a variety of machine learning tasks. Generally, this framework has been applied to data represented as fixed-length attribute-value vectors, or to sequence data. I will describe the language of probabilistic relational models (PRMs), which extend probabilistic graphical models with the expressive power of object-relational languages. PRMs model the uncertainty over the attributes of objects in the domain as well as uncertainty over the existence of relations between objects. I will present techniques for automatically learning PRMs directly from a relational data set, and applications of these techniques to various tasks, such as: collective classification of an entire set of related entities; clustering a set of linked entities into coherent groups; and even predicting the existence of links between entities. The talk will demonstrate the applicability of the techniques on several domains, such as web data and biological data. We discuss some recent trends and events, e.g., the dot com meltdown, and some ways for the field to respond to the challenges, and the opportunities.

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Genome-wide discovery of transcriptional modules from DNA sequence and gene expression

In this paper, we describe an approach for understanding transcriptional regulation from both gene expression and promoter sequence data. We aim to identify transcriptional modules--sets of genes that are co-regulated in a set of experiments, through a common motif profile. Using the EM algorithm, our approach refines both the module assignment and the motif profile so as to best explain the expression data as a function of transcriptional motifs. It also dynamically adds and deletes motifs, as required to provide a genome-wide explanation of the expression data. We evaluate the method on two Saccharomyces cerevisiae gene expression data sets, showing that our approach is better than a standard one at recovering known motifs and at generating biologically coherent modules. We also combine our results with binding localization data to obtain regulatory relationships with known transcription factors, and show that many of the inferred relationships have support in the literature.

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Probabilistic hierarchical clustering for biological data

Biological data, such as gene expression profiles or protein sequences, is often organized in a hierarchy of classes, where the instances assigned to "nearby" classes in the tree are similar. Most approaches for constructing a hierarchy use simple local operations, that are very sensitive to noise or variation in the data. In this paper, we describe probabilistic abstraction hierarchies (PAH) [11], a general probabilistic framework for clustering data into a hierarchy, and show how it can be applied to a wide variety of biological data sets. In a PAH, each class is associated with a probabilistic generative model for the data in the class. The PAH clustering algorithm simultaneously optimizes three things: the assignment of data instances to clusters, the models associated with the clusters, and the structure of the PAH approach is that it utilizes global optimization algorithms for the last two steps, substantially reducing the sensitivity to noise and the propensity to local maxima. We show how to apply this framework to gene expression data, protein sequence data, and HIV protease sequence data. We also show how our framework supports hierarchies involving more than one type of data. We demonstrate that our method extracts useful biological knowledge and is substantially more robust than hierarchical agglomerative clustering.

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Context-specific multiagent coordination and planning with factored MDPs

We present an algorithm for coordinated decision making in cooperative multiagent settings, where the agents' value function canbe represented as a sum of context-specific <i>value rules</i>. The task of finding an optimal joint action in this setting leads to an algorithm where the coordination structure between agents depends on the current state of the system and even on the actual mmaerical values assigned to the value rules. We apply this framework to the task of multiagent planning in dynamic systems, showing how a joint value function of the associated Markov Decision Process can be approximated as a set of value rules using an efficient linear programming algorithm. The agents then apply the coordination graph algorithm at each iteration of the process to decide on the highest-value joint action, potentially leading to a different coordination pattern at each step of the plan.

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From promoter sequence to expression: a probabilistic framework

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.

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Local Algorithms for Finding Equilibria in Structured Games

Consider the problem of a group of agents trying to find a stable strategy profile for a joint interaction. A standard approach is to describe the situation as a single multi-player game and find an equilibrium strategy profile of that game. However, most algorithms for finding equilibria are computationally expensive; they are also centralized, requiring that all relevant payoff information be available to a single agent (or computer) who must determine the entire equilibrium profile. In this paper, we consider the slightly relaxed task of finding an approximate equilibrium. We consider structured game representations, where the interaction between the agents is sparse, an assumption that holds in many real-world situations. We present two algorithms for finding approximate equilibria in these games, one based on a hill-climbing approach and one on constraint satisfaction. We show that these algorithms are inherently local, requiring only limited communication between directly interacting agents. The algorithms can thus be scaled to games involving large numbers of players provided the interaction between the players is not too dense.

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FastSLAM: a factored solution to the simultaneous localization and mapping problem

The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filter-based algorithms, for example, require time quadratic in the number of landmarks to incorporate each sensor observation. This paper presents FastSLAM, an algorithm that recursively estimates the full posterior distribution over robot pose and landmark locations, yet scales logarithmically with the number of landmarks in the map. This algorithm is based on an exact factorization of the posterior into a product of conditional landmark distributions and a distribution over robot paths. The algorithm has been run successfully on as many as 50,000 landmarks, environments far beyond the reach of previous approaches. Experimental results demonstrate the advantages and limitations of the FastSLAM algorithm on both simulated and real-world data.

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Simultaneous Mapping and Localization with Sparse Extended Information Filters: Theory and Initial Results

This paper describes a scalable algorithm for the simultaneous mapping and localization (SLAM) problem. SLAM is the problem of determining the location of environmental features with a roving robot. Many of today’s popular techniques are based on extended Kalman filters (EKFs), which require update time quadratic in the number of features in the map. This paper develops the notion of sparse extended information filters (SEIFs), as a new method for solving the SLAM problem. SEIFs exploit structure inherent in the SLAM problem, representing maps through local, Web-like networks of features. By doing so, updates can be performed in constant time, irrespective of the number of features in the map. This paper presents several original constant-time results of SEIFs, and provides simulation results that show the high accuracy of the resulting maps in comparison to the computationally more cumbersome EKF solution.

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SLAM Updates Require Constant Time

This paper describes a scalable algorithm for the simultaneous mapping and localization (SLAM) problem. SLAM is the problem of determining the location of environmental features with a roving robot. Many of today’s popular techniques are based on extended Kalman filters (EKFs), which require update time quadratic in the number of features in the map. This paper develops the notion of sparse extended information filters (SEIFs), as a new method for solving the SLAM problem. SEIFs exploit structure inherent in the SLAM problem, representing maps through local, Web-like networks of features. By doing so, updates can be performed in constant time, irrespective of the number of features in the map. This paper presents several original constant-time results of SEIFs, and provides simulation results that show the high accuracy of the resulting maps in comparison to the computationally more cumbersome EKF solution.

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Uncertainty in artificial intelligence : proceedings of the Eighteenth Conference (2002) : August 1-4, 2002, University of Alberta, Edmonton

Proceedings of the annual Conference on Uncertainty in Artificial Intelligence, available for 1991-present. Since 1985, the Conference on Uncertainty in Artificial Intelligence (UAI) has been the primary international forum for exchanging results on the use of principled uncertain-reasoning methods in intelligent systems. The UAI Proceedings have become a basic reference for researches and practitioners who want to know about both theoretical advances and the latest applied developments in the field.

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Monitoring a Complez Physical System using a Hybrid Dynamic Bayes Net

The Reverse Water Gas Shift system (RWGS) is a complex physical system designed to produce oxygen from the carbon dioxide atmosphere on Mars. If sent to Mars, it would operate without human supervision, thus requiring a reliable automated system for monitoring and control. The RWGS presents many challenges typical of real-world systems, including: noisy and biased sensors, nonlinear behavior, effects that are manifested over different time granularities, and unobservability of many important quantities. In this paper we model the RWGS using a hybrid (discrete/continuous) Dynamic Bayesian Network (DBN), where the state at each time slice contains 33 discrete and 184 continuous variables. We show how the system state can be tracked using probabilistic inference over the model. We discuss how to deal with the various challenges presented by the RWGS, providing a suite of techniques that are likely to be useful in a wide range of applications. In particular, we describe a general framework for dealing with nonlinear behavior using numerical integration techniques, extending the successful Unscented Filter. We also show how to use a fixed-point computation to deal with effects that develop at different time scales, specifically rapid changes occurring during slowly changing processes. We test our model using real data collected from the RWGS, demonstrating the feasibility of hybrid DBNs for monitoring complex real-world physical systems.

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Learning Hierarchical Object Maps of Non-Stationary Environments with Mobile Robots

Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of non-stationary objects found in office-type environments. Our algorithm exploits the fact that many objects found in office environments look alike (e.g., chairs, recycling bins). It does so through a two-level hierarchical representation, which links individual objects with generic shape templates of object classes. We derive an approximate EM algorithm for learning shape parameters at both levels of the hierarchy, using local occupancy grid maps for representing shape. Additionally, we develop a Bayesian model selection algorithm that enables the robot to estimate the total number of objects and object templates in the environment. Experimental results using a real robot equipped with a laser range finder indicate that our approach performs well at learning object-based maps of simple office environments. The approach outperforms a previously developed non-hierarchical algorithm that models objects but lacks class templates.

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Discriminative Probabilistic Models for Relational Data

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov networks and addresses two limitations of the previous approach. First, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. Second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. We show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. We provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies.

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Learning Probabilistic Models of Link Structure

Most real-world data is heterogeneous and richly interconnected. Examples include the Web, hypertext, bibliometric data and social networks. In contrast, most statistical learning methods work with "flat" data representations, forcing us to convert our data into a form that loses much of the link structure. The recently introduced framework of probabilistic relational models (PRMs) embraces the object-relational nature of structured data by capturing probabilistic interactions between attributes of related entities. In this paper, we extend this framework by modeling interactions between the attributes and the link structure itself. An advantage of our approach is a unified generative model for both content and relational structure. We propose two mechanisms for representing a probabilistic distribution over link structures: reference uncertainty and existence uncertainty. We describe the appropriate conditions for using each model and present learning algorithms for each. We present experimental results showing that the learned models can be used to predict link structure and, moreover, the observed link structure can be used to provide better predictions for the attributes in the model.

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Multi-agent algorithms for solving graphical games

Consider the problem of a group of agents trying to find a stable strategy profile for a joint interaction. A standard approach is to describe the situation as a single multiplayer game and find an equilibrium strategy profile of that game. However, most algorithms for finding equilibria are computationally expensive; they are also centralized, requiring that all relevant payoff information be available to a single agent (or computer) who must determine the entire equilibrium profile. In this paper, we exploit two ideas to address these problems. We consider structured game representations, where the interaction between the agents is sparse, an assumption that holds in many real-world situations. We also consider the slightly relaxed task of finding an approximate equilibrium. We present two algorithms for finding approximate equilibria in these games, one based on a hill-climbing approach and one on constraint satisfaction. We show that these algorithms exploit the game structure to achieve faster computation. They are also inherently local, requiring only limited communication between directly interacting agents. They can thus be scaled to games involving large numbers of agents, provided the interaction between the agents is not too dense.

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Acting rationally with incomplete utility information

Rational decision making requires full knowledge of the utility function of the person affected by the decisions. However, the task of acquiring such knowledge is often infeasible due to the size of the outcome space and the complexity of the utility elicitation process. We argue that a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density function over its possible values. We show that we can apply statistical density estimation techniques to learn a probabilistic model of utilities from a database of partially elicited utility functions. The Bayesian learning framework we define for this problem also allows us to discover the number of statistically coherent subpopulations and select a structured utility model for each subpopulation. The factorization of the utilities in the learned model and the generalization obtained from density estimation allow us to provide a compact and robust representation of the utility functions in the population. Such a model can serve as a prior distribution when we encounter a new user whose utility function we need to discover. Any information we obtain in the course of utility elicitation process or by observing the user's behavior can be used to adjust the model to the user by Bayesian conditioning. We present two applications of such customizable utility models. The first, designed for a decision support system, directs the utility elicitation process by choosing questions most relevant for the current user and the current decision problem. The second focuses on non-cooperative situations where a second agent is optimizing its own decisions relative to its uncertainty about the utility of the first.