Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from limited data is difficult, therefore transfer learning can improve the robustness of learned networks by leveraging data from related tasks. Existing transfer learning algorithms for Bayesian network structure learning give a single maximum a posteriori estimate of network models. Yet, many other models may be equally likely, and so a more informative result is provided by Bayesian structure discovery. Bayesian structure discovery algorithms estimate posterior probabilities of structural features, such as edges. We present transfer learning for Bayesian structure discovery which allows us to explore the shared and unique structural features among related tasks. Efficient computation requires that our transfer learning objective factors into local calculations, which we prove is given by a broad class of transfer biases. Theoretically, we show the efficiency of our approach. Empirically, we show that compared to single task learning, transfer learning is better able to positively identify true edges. We apply the method to whole-brain neuroimaging data.

Network structure learning algorithms have aided network discovery in fields such as bioinformatics, neuroscience, ecology and social science. However, challenges remain in learning informative networks for related sets of tasks because the search space of Bayesian network structures is characterized by large basins of approximately equivalent solutions. Multitask algorithms select a set of networks that are near each other in the search space, rather than a score-equivalent set of networks chosen from independent regions of the space. This selection preference allows a domain expert to see only differences supported by the data. However, the usefulness of these algorithms for scientific datasets is limited because existing algorithms naively assume that all pairs of tasks are equally related. We introduce a framework that relaxes this assumption by incorporating domain knowledge about task-relatedness into the learning objective. Using our framework, we introduce the first multitask Bayesian network algorithm that leverages domain knowledge about the relatedness of tasks. We use our algorithm to explore the effect of task-relatedness on network discovery and show that our algorithm learns networks that are closer to ground truth than naive algorithms and that our algorithm discovers patterns that are interesting.

With the increasing prevalence of richer, more complex data sources, learning with multiple views is becoming more widespread. Multiple kernel learning (MKL) has been developed to address this problem, but in general, the solutions provided by traditional MKL are restricted to a classification objective function. In this work, we develop a novel multiple kernel learning algorithm that is based on a spectral clustering objective function which is able to find an optimal kernel weight vector for the clustering problem. We go on to show how this optimization problem can be cast as a semidefinite program and efficiently solved using off-the-shelf interior point methods.

In many real-world networks, nodes have class labels or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of nodes such that, if we knew their labels, we could accurately predict the labels of all the other nodes. We develop an active learning algorithm for this problem which uses information-theoretic techniques to choose which nodes to explore. We test our algorithm on networks from three different domains: a social network, a network of English words that appear adjacently in a novel, and a marine food web. Our algorithm makes no initial assumptions about how the groups connect, and performs well even when faced with quite general types of network structure. In particular, we do not assume that nodes of the same class are more likely to be connected to each other - only that they connect to the rest of the network in similar ways.

MOTIVATION: Condition-specific networks capture system-wide behavior under varying conditions such as environmental stresses, cell types or tissues. These networks frequently comprise parts that are unique to each condition, and parts that are shared among related conditions. Existing approaches for learning condition-specific networks typically identify either only differences or only similarities across conditions. Most of these approaches first learn networks per condition independently, and then identify similarities and differences in a post-learning step. Such approaches do not exploit the shared information across conditions during network learning. RESULTS: We describe an approach for learning condition-specific networks that identifies the shared and unique subgraphs during network learning simultaneously, rather than as a post-processing step. Our approach learns networks across condition sets, shares data from different conditions and produces high-quality networks that capture biologically meaningful information. On simulated data, our approach outperformed an existing approach that learns networks independently for each condition, especially for small training datasets. On microarray data of hundreds of deletion mutants in two, yeast stationary-phase cell populations, the inferred network structure identified several common and population-specific effects of these deletion mutants and several high-confidence cases of double-deletion pairs, which can be experimentally tested. Our results are consistent with and extend the existing knowledge base of differentiated cell populations in yeast stationary phase. AVAILABILITY AND IMPLEMENTATION: C++ code can be accessed from http://www.broadinstitute.org/~sroy/condspec/ .

Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities (n!). It makes the direct definition of a multinomial distribution over permutation space impractical for all but a very small n. In this work we propose an embedding of all n! permutations for a given n in a surface of a hyper sphere defined in ℝ(n-1). As a result of the embedding, we acquire ability to define continuous distributions over a hyper sphere with all the benefits of directional statistics. We provide polynomial time projections between the continuous hyper sphere representation and the n!-element permutation space. The framework provides a way to use continuous directional probability densities and the methods developed thereof for establishing densities over permutations. As a demonstration of the benefits of the framework we derive an inference procedure for a state-space model over permutations. We demonstrate the approach with simulations on a large number of objects hardly manageable by the state of the art inference methods, and an application to a real flight traffic control dataset.

In many real-world domains, undirected graphical models such as Markov random fields provide a more natural representation of the statistical dependency structure than directed graphical models. Unfortunately, structure learning of undirected graphs using likelihood-based scores remains difficult because of the intractability of computing the partition function. We describe a new Markov random field structure learning algorithm, motivated by canonical parameterization of Abbeel et al. We provide computational improvements on their parameterization by learning per-variable canonical factors, which makes our algorithm suitable for domains with hundreds of nodes. We compare our algorithm against several algorithms for learning undirected and directed models on simulated and real datasets from biology. Our algorithm frequently outperforms existing algorithms, producing higher-quality structures, suggesting that enforcing consistency during structure learning is beneficial for learning undirected graphs.

The dual formulation of the support vector machine (SVM) objective function is an instance of a nonnegative quadratic programming problem. We reformulate the SVM objective function as a matrix factorization problem which establishes a connection with the regularized nonnegative matrix factorization (NMF) problem. This allows us to derive a novel multiplicative algorithm for solving hard and soft margin SVM. The algorithm follows as a natural extension of the updates for NMF and semi-NMF. No additional parameter setting, such as choosing learning rate, is required. Exploiting the connection between SVM and NMF formulation, we show how NMF algorithms can be applied to the SVM problem. Multiplicative updates that we derive for SVM problem also represent novel updates for semi-NMF. Further this unified view yields algorithmic insights in both directions: we demonstrate that the Kernel Adatron algorithm for solving SVMs can be adapted to NMF problems. Experiments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic convergence of the updates and establish tight bounds. We test them on several datasets using various kernels and report equivalent classification performance to that of a standard SVM.

The cell defense mechanism of RNA interference has applications in gene function analysis and promising potentials in human disease therapy. To effectively silence a target gene, it is desirable to select appropriate initiator siRNA molecules having satisfactory silencing capabilities. Computational prediction for silencing efficacy of siRNAs can assist this screening process before using them in biological experiments. String kernel functions, which operate directly on the string objects representing siRNAs and target mRNAs, have been applied to support vector regression for the prediction and improved accuracy over numerical kernels in multidimensional vector spaces constructed from descriptors of siRNA design rules. To fully utilize information provided by string and numerical data, we propose to unify the two in a kernel feature space by devising a multiple kernel regression framework where a linear combination of the kernels is used. We formulate the multiple kernel learning into a quadratically constrained quadratic programming (QCQP) problem, which although yields global optimal solution, is computationally demanding and requires a commercial solver package. We further propose three heuristics based on the principle of kernel-target alignment and predictive accuracy. Empirical results demonstrate that multiple kernel regression can improve accuracy, decrease model complexity by reducing the number of support vectors, and speed up computational performance dramatically. In addition, multiple kernel regression evaluates the importance of constituent kernels, which for the siRNA efficacy prediction problem, compares the relative significance of the design rules. Finally, we give insights into the multiple kernel regression mechanism and point out possible extensions.

Many interesting problems, including Bayesian network structure-search, can be cast in terms of finding the optimum value of a function over the space of graphs. However, this function is often expensive to compute exactly. We here present a method derived from the study of reproducing-kernel Hilbert spaces which takes advantage of the regular structure of the space of all graphs on a fixed number of nodes to obtain approximations to the desired function quickly and with reasonable accuracy. We then test this method on both a small testing set and a real-world Bayesian network; the results suggest that not only is this method reasonably accurate, but that the BDe score itself varies quadratically over the space of all graphs.

UNLABELLED: We have developed a new software system, REgulatory Network generator with COmbinatorial control (RENCO), for automatic generation of differential equations describing pre-transcriptional combinatorics in artificial regulatory networks. RENCO has the following benefits: (a) it explicitly models protein-protein interactions among transcription factors, (b) it captures combinatorial control of transcription factors on target genes and (c) it produces output in Systems Biology Markup Language (SBML) format, which allows these equations to be directly imported into existing simulators. Explicit modeling of the protein interactions allows RENCO to incorporate greater mechanistic detail of the transcription machinery compared to existing models and can provide a better assessment of algorithms for regulatory network inference. AVAILABILITY: RENCO is a C++ command line program, available at http://sourceforge.net/projects/renco/

String kernels directly model sequence similarities without the necessity of extracting numerical features in a vector space. Since they better capture complex traits in the sequences, string kernels often achieve better prediction performance. RNA interference is a cell defense mechanism with many biological and therapeutical applications, where strings can be used to represent target messenger RNAs and initiating short RNAs and string kernels can be applied for training and prediction. While most existing string kernels are developed for general purpose sequences and have been applied to text and protein classifications, the RNA string kernel is particularly designed to model mismatches, GU wobbles, and bulges of RNA biology and has been applied to RNAi off-target evaluation. We adapt the RNA string kernel to compute the similarity of siRNA sequences and use it in support vector regression to predict siRNA silencing efficacy. We evaluate the performance of the RNA kernel against the spectrum kernel, the string subsequence kernel of arbitrary mismatch, the randomized string kernel, and numerical kernels computed from numerical features extracted according to siRNA design rules. We also give insights into computational performance and common properties and differences of the RNA kernel as compared to other kernels. Empirical results on biological data sets demonstrate that the RNA string kernel performed favorably than most existing string kernels and achieved significant improvements over kernels computed from numerical descriptors extracted according to structural and thermodynamic rules. Meanwhile, the string kernels achieved favorable results relative to other methods in related work. Furthermore, the RNA string kernel is simple to implement and fast to compute.

In this paper, we give the first constant-factor approximation algorithm for the rooted Orienteering problem, as well as a new problem that we call the Discounted-Reward traveling salesman problem (TSP), motivated by robot navigation. In both problems, we are given a graph with lengths on edges and rewards on nodes, and a start node s. In the Orienteering problem, the goal is to find a path starting at s that maximizes the reward collected, subject to a hard limit on the total length of the path. In the Discounted-Reward TSP, instead of a length limit we are given a discount factor $\gamma$, and the goal is to maximize the total discounted reward collected, where the reward for a node reached at time t is discounted by $\gamma^t$. This problem is motivated by an approximation to a planning problem in the Markov decision process (MDP) framework under the commonly employed infinite horizon discounted reward optimality criterion. The approximation arises from a need to deal with exponentially large state spaces that emerge when trying to model one-time events and nonrepeatable rewards (such as for package deliveries). We also consider tree and multiple-path variants of these problems and provide approximations for those as well. Although the unrooted Orienteering problem, where there is no fixed start node s, has been known to be approximable using algorithms for related problems such as k-TSP (in which the amount of reward to be collected is fixed and the total length is approximately minimized), ours is the first to approximate the rooted question, solving an open problem in [E. M. Arkin, J. S. B. Mitchell, and G. Narasimhan, Proceedings of the $14$th ACM Symposium on Computational Geometry, 1998, pp. 307–316] and [B. Awerbuch, Y. Azar, A. Blum, and S. Vempala, SIAM J. Comput., 28 (1998), pp. 254–262]. We complement our approximation result for Orienteering by showing that the problem is APX-hard.

In many domains, a Bayesian network's topological structure is not known a priori and must be inferred from data. This requires a scoring function to measure how well a proposed network topology describes a set of data. Many commonly used scores such as BD, BDE, BDEU, etc., are not well suited for class discrimination. Instead, scores such as the class-conditional likelihood (CCL) should be employed. Unfortunately, CCL does not decompose and its application to large domains is not feasible. We introduce a decomposable score, approximate conditional likelihood (ACL) that is capable of identifying class discriminative structures. We show that dynamic Bayesian networks (DBNs) trained with ACL have classification efficacies competitive to those trained with CCL on a set of simulated data experiments. We also show that ACL-trained DBNs outperform BDE-trained DBNs, Gaussian naive Bayes networks and support vector machines within a neuroscience domain too large for CCL.

While kernel support vector machines are powerful classification algorithms, their computational overhead can be significant, especially for large and high-dimensional data sets. A recent biomedical dataset, for instance, could take as long as 3 weeks to compute its RBF kernel matrix on a modern, single-processor workstation. In this paper, we develop methods for high-performance parallel computation of kernel matrices. There are two key components to a parallel implementation: distribution of the computation across nodes and communication to combine the results. To address the first, we employ a dimension-wise data partition that yields efficient computation and low communication overhead during the initial phase. This partition provides dramatic speedups on large and high-dimensional data, applies to a wide variety of kernel functions, and is an exact computation, producing the same kernel matrix as its sequential implementation. To address communication needs during the second phase, we introduce an approximation specific to the Gaussian RBF kernel that yields sparse partial kernel matrices and, thus, efficient communication. We analyze the approximation error of this method, demonstrating that it falls off exponentially with N, the parameter of the approximation. We also examine the positive definiteness of the approximation with respect to Mercer's condition and show that (a) in the limit of N our approximation becomes positive definite for any data set and (b) for a fixed data set, there exists a finite N yielding a positive definite kernel matrix. We also give a simple iterative method for selecting N to yield a positive definite kernel matrix on any fixed data set. In practice, we find that positive definiteness is achieved on all of the data sets we examine with very small N (2–5). Finally, we test the empirical performance of our two methods on a variety of large, real-world data sets, demonstrating large computational speedups with little or no impact on accuracy.

In this paper, we give the first constant-factor approximation algorithm for the rooted orienteering problem, as well as a new problem that we call the Discounted-Reward TSP, motivated by robot navigation. In both problems, we are given a graph with lengths on edges and prizes (rewards) on nodes, and a start node s. In the orienteering problem, the goal is to find a path that maximizes the reward collected, subject to a hard limit on the total length of the path. In the Discounted-Reward TSP, instead of a length limit we are given a discount factor /spl gamma/, and the goal is to maximize total discounted reward collected, where reward for a node reached at time t is discounted by /spl gamma//sup t/. This is similar to the objective considered in Markov decision processes (MDPs) except we only receive a reward the first time a node is visited. We also consider tree and multiple-path variants of these problems and provide approximations for those as well. Although the unrooted orienteering problem, where there is no fixed start node s, has been known to be approximable using algorithms for related problems such as k-TSP (in which the amount of reward to be collected is fixed and the total length is approximately minimized), ours is the first to approximate the rooted question, solving an open problem based on B. Awerbuch et al. (1999) and E.M. Arkin (1998).

The anomaly-detection problem can be formulated as one of learning to characterize the behaviors of an individual, system, or network in terms of temporal sequences of discrete data. We present an approach on the basis of instance-based learning (IBL) techniques. To cast the anomaly-detection task in an IBL framework, we employ an approach that transforms temporal sequences of discrete, unordered observations into a metric space via a similarity measure that encodes intra-attribute dependencies. Classification boundaries are selected from an a posteriori characterization of valid user behaviors, coupled with a domain heuristic. An empirical evaluation of the approach on user command data demonstrates that we can accurately differentiate the profiled user from alternative users when the available features encode sufficient information. Furthermore, we demonstrate that the system detects anomalous conditions quickly — an important quality for reducing potential damage by a malicious user. We present several techniques for reducing data storage requirements of the user profile, including instance-selection methods and clustering. As empirical evaluation shows that a new greedy clustering algorithm reduces the size of the user model by 70%, with only a small loss in accuracy.

The anom~y detection problem can be formtiated as one of learning to characterize the behaviom of an individud, system, or network in terms of temporal sequences of di~ crete data.We present an approach to this problem based on instance based learning (IBL) techniques.To cast the anom~y detection task in an IBL framework, we employ an approach that transforms temporal sequences of discrete, unordered observations into a metric space via a similarity measure that encodes intra-attribute dependence=.Classification boundaries are selected from an a posterior characterization of the v&d user's behaviors, coupled with a d~ main heuristic.An empirical evrduation of the approach on user command data demonstratees that we can accurately differentiate the profled user from alternative users when the avdable featura encode sticient information.Futherrnore, we demonstrate that the system detects anomalous conditions quickly -an important qufity for reducing potential damage by a mdcious user.We present several techniques for reducing the data storage requirements of the user profle, including instance selection methods and clustering.An empirical evahtation shows that a new greedy clustering dgonthm reduces the size of the user model by 70% with ordy a smd loss in accuracy.A comparison of the greedy clustering technique to clustering with K-centers shows that greedy clustering is preferable in terms of accuracy and computation time for this domain.