Attractor Dynamics in Feedforward Neural Networks

We study the probabilistic generative models parameterized by feedforward neural networks. An attractor dynamics for probabilistic inference in these models is derived from a mean field approximation for large, layered sigmoidal networks. Fixed points of the dynamics correspond to solutions of the mean field equations, which relate the statistics of each unit to those of its Markov blanket. We establish global convergence of the dynamics by providing a Lyapunov function and show that the dynamics generate the signals required for unsupervised learning. Our results for feedforward networks provide a counterpart to those of Cohen-Grossberg and Hopfield for symmetric networks. 1 Introduction Attractor neural networks lend a computational purpose to continuous dynamical systems. Celebrated uses of these networks include the storage of associative memories (Amit, 1989), the reconstruction of noisy images (Koch et al, 1986), and the search for shortest paths in the traveling salesman proble..

Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored

A hybrid algorithm for Bayesian network structure learning with application to multi-label learning

We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is based on divide-and-conquer constraint-based subroutines to learn the local structure around a target variable. We conduct two series of experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning. First, we use eight well-known Bayesian network benchmarks with various data sizes to assess the quality of the learned structure returned by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in terms of goodness of fit to new data and quality of the network structure with respect to the true dependence structure of the data. Second, we investigate H2PC's ability to solve the multi-label learning problem. We provide theoretical results to characterize and identify graphically the so-called minimal label powersets that appear as irreducible factors in the joint distribution under the faithfulness condition. The multi-label learning problem is then decomposed into a series of multi-class classification problems, where each multi-class variable encodes a label powerset. H2PC is shown to compare favorably to MMHC in terms of global classification accuracy over ten multi-label data sets covering different application domains. Overall, our experiments support the conclusions that local structural learning with H2PC in the form of local neighborhood induction is a theoretically well-motivated and empirically effective learning framework that is well suited to multi-label learning. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.Comment: arXiv admin note: text overlap with arXiv:1101.5184 by other author

Influence diagrams : a new approach to modelling games

Game theory seeks to describe the interaction of two or more actors with distinct objectives. This is achieved using a mathematical model known as a game. Virtually all game theory relies on either the extensive form or the normal form to represent the games being studied. By drawing on the previously unrelated fields of game theory and graphical modelling, and by taking a new approach to the way in which a game is modelled, an alternative to the extensive and normal forms is developed: the belief influence diagram (BID). Starting from the basic definition of a game and using a new form of conditional belief called a prospective function, it is shown how the decision influence diagram can be adapted to model games. The advantages of the BID over the extensive and normal forms are explored, particularly its ability to model some of the qualitative aspects of games and to model games of greater complexity. By using BIDs in the modelling of games, fresh insight can be gained into certain features of the game, such as what sources of information an actor in the game should take account of. New concepts of sufficiency and parsimony are defined which relate to the BID. It is shown how these concepts, when combined with different forms of rationality, can lead to a variety of methods for simplifying a BID, and hence simplifying the game which it represents. It is shown that such simplifications arc invariant with respect to the order in which the simplifying steps are carried out. A schematic version of the BID is used to model finite repeated games and to develop concepts of learning and local sufficiency. It is shown how BIDs can be used to facilitate an induction proof in a finite repeated game and to model a highly complex competitive market. This last example is used to illustrate how BIDs can be helpful in evaluating some qualitative aspects of a model

Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

Automatic Segmentation of Cells of Different Types in Fluorescence Microscopy Images

Recognition of different cell compartments, types of cells, and their interactions is a critical aspect of quantitative cell biology. This provides a valuable insight for understanding cellular and subcellular interactions and mechanisms of biological processes, such as cancer cell dissemination, organ development and wound healing. Quantitative analysis of cell images is also the mainstay of numerous clinical diagnostic and grading procedures, for example in cancer, immunological, infectious, heart and lung disease. Computer automation of cellular biological samples quantification requires segmenting different cellular and sub-cellular structures in microscopy images. However, automating this problem has proven to be non-trivial, and requires solving multi-class image segmentation tasks that are challenging owing to the high similarity of objects from different classes and irregularly shaped structures. This thesis focuses on the development and application of probabilistic graphical models to multi-class cell segmentation. Graphical models can improve the segmentation accuracy by their ability to exploit prior knowledge and model inter-class dependencies. Directed acyclic graphs, such as trees have been widely used to model top-down statistical dependencies as a prior for improved image segmentation. However, using trees, a few inter-class constraints can be captured. To overcome this limitation, polytree graphical models are proposed in this thesis that capture label proximity relations more naturally compared to tree-based approaches. Polytrees can effectively impose the prior knowledge on the inclusion of different classes by capturing both same-level and across-level dependencies. A novel recursive mechanism based on two-pass message passing is developed to efficiently calculate closed form posteriors of graph nodes on polytrees. Furthermore, since an accurate and sufficiently large ground truth is not always available for training segmentation algorithms, a weakly supervised framework is developed to employ polytrees for multi-class segmentation that reduces the need for training with the aid of modeling the prior knowledge during segmentation. Generating a hierarchical graph for the superpixels in the image, labels of nodes are inferred through a novel efficient message-passing algorithm and the model parameters are optimized with Expectation Maximization (EM). Results of evaluation on the segmentation of simulated data and multiple publicly available fluorescence microscopy datasets indicate the outperformance of the proposed method compared to state-of-the-art. The proposed method has also been assessed in predicting the possible segmentation error and has been shown to outperform trees. This can pave the way to calculate uncertainty measures on the resulting segmentation and guide subsequent segmentation refinement, which can be useful in the development of an interactive segmentation framework

Graphical models and message-passing algorithms for network-constrained decision problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. [201]-210).Inference problems, typically posed as the computation of summarizing statistics (e.g., marginals, modes, means, likelihoods), arise in a variety of scientific fields and engineering applications. Probabilistic graphical models provide a scalable framework for developing efficient inference methods, such as message-passing algorithms that exploit the conditional independencies encoded by the given graph. Conceptually, this framework extends naturally to a distributed network setting: by associating to each node and edge in the graph a distinct sensor and communication link, respectively, the iterative message-passing algorithms are equivalent to a sequence of purely-local computations and nearest-neighbor communications. Practically, modern sensor networks can also involve distributed resource constraints beyond those satisfied by existing message-passing algorithms, including e.g., a fixed small number of iterations, the presence of low-rate or unreliable links, or a communication topology that differs from the probabilistic graph. The principal focus of this thesis is to augment the optimization problems from which existing message-passing algorithms are derived, explicitly taking into account that there may be decision-driven processing objectives as well as constraints or costs on available network resources. The resulting problems continue to be NP-hard, in general, but under certain conditions become amenable to an established team-theoretic relaxation technique by which a new class of efficient message-passing algorithms can be derived. From the academic perspective, this thesis marks the intersection of two lines of active research, namely approximate inference methods for graphical models and decentralized Bayesian methods for multi-sensor detection.(cont)The respective primary contributions are new message-passing algorithms for (i) "online" measurement processing in which global decision performance degrades gracefully as network constraints become arbitrarily severe and for (ii) "offline" strategy optimization that remain tractable in a larger class of detection objectives and network constraints than previously considered. From the engineering perspective, the analysis and results of this thesis both expose fundamental issues in distributed sensor systems and advance the development of so-called "self-organizing fusion-layer" protocols compatible with emerging concepts in ad-hoc wireless networking.by O. Patrick Kreidl.Ph.D