Learning the structure of probabilistic graphical models with an extended cascading Indian buffet process

Abstract In this paper, we present an extension of the cascading Indian buffet process (CIBP) intended to learning arbitrary directed acyclic graph structures as opposed to the CIBP, which is limited to purely layered structures. The extended cascading Indian buffet process (eCIBP) essentially consists in adding an extra sampling step to the CIBP to generate connections between non-consecutive layers. In the context of graphical model structure learning, the proposed approach allows learning structures having an unbounded number of hidden random variables and automatically selecting the model complexity. We evaluated the extended process on multivariate density estimation and structure identification tasks by measuring the structure complexity and predictive performance. The results suggest the extension leads to extracting simpler graphs without scarifying predictive precision

Multiagent planning with Bayesian nonparametric asymptotics

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 95-105).Autonomous multiagent systems are beginning to see use in complex, changing environments that cannot be completely specified a priori. In order to be adaptive to these environments and avoid the fragility associated with making too many a priori assumptions, autonomous systems must incorporate some form of learning. However, learning techniques themselves often require structural assumptions to be made about the environment in which a system acts. Bayesian nonparametrics, on the other hand, possess structural flexibility beyond the capabilities of past parametric techniques commonly used in planning systems. This extra flexibility comes at the cost of increased computational cost, which has prevented the widespread use of Bayesian nonparametrics in realtime autonomous planning systems. This thesis provides a suite of algorithms for tractable, realtime, multiagent planning under uncertainty using Bayesian nonparametrics. The first contribution is a multiagent task allocation framework for tasks specified as Markov decision processes. This framework extends past work in multiagent allocation under uncertainty by allowing exact distribution propagation instead of sampling, and provides an analytic solution time/quality tradeoff for system designers. The second contribution is the Dynamic Means algorithm, a novel clustering method based upon Bayesian nonparametrics for realtime, lifelong learning on batch-sequential data containing temporally evolving clusters. The relationship with previous clustering models yields a modelling scheme that is as fast as typical classical clustering approaches while possessing the flexibility and representational power of Bayesian nonparametrics. The final contribution is Simultaneous Clustering on Representation Expansion (SCORE), which is a tractable model-based reinforcement learning algorithm for multimodel planning problems, and serves as a link between the aforementioned task allocation framework and the Dynamic Means algorithmby Trevor D. J. Campbell.S.M

Composable Probabilistic Inference with Blaise

Probabilistic inference provides a unified, systematic framework for specifying and solving these problems. Recent work has demonstrated the great value of probabilistic models defined over complex, structured domains. However, our ability to imagine probabilistic models has far outstripped our ability to programmatically manipulate them and to effectively implement inference, limiting the complexity of the problems that we can solve in practice.This thesis presents Blaise, a novel framework for composable probabilistic modeling and inference, designed to address these limitations. Blaise has three components: * The Blaise State-Density-Kernel (SDK) graphical modeling language that generalizes factor graphs by: (1) explicitly representing inference algorithms (and their locality) using a new type of graph node, (2) representing hierarchical composition and repeated substructures in the state space, the interest distribution, and the inference procedure, and (3) permitting the structure of the model to change during algorithm execution. * A suite of SDK graph transformations that may be used to extend a model (e.g. to construct a mixture model from a model of a mixture component), or to make inference more effective (e.g. by automatically constructing a parallel tempered version of an algorithm or by exploiting conjugacy in a model). * The Blaise Virtual Machine, a runtime environment that can efficiently execute the stochastic automata represented by Blaise SDK graphs. Blaise encourages the construction of sophisticated models by composing simpler models, allowing the designer to implement and verify small portions of the model and inference method, and to reuse model components from one task to another. Blaise decouples the implementation of the inference algorithm from the specification of the interest distribution, even in cases (such as Gibbs sampling) where the shape of the interest distribution guides the inference. This gives modelers the freedom to explore alternate models without slow, error-prone reimplementation. The compositional nature of Blaise enables novel reinterpretations of advanced Monte Carlo inference techniques (such as parallel tempering) as simple transformations of Blaise SDK graphs.In this thesis, I describe each of the components of the Blaise modeling framework, as well as validating the Blaise framework by highlighting a variety of contemporary sophisticated models that have been developed by the Blaise user community. I also present several surprising findings stemming from the Blaise modeling framework, including that an Infinite Relational Model can be built using exactly the same inference methods as a simple mixture model, that constructing a parallel tempered inference algorithm should be a point-and-click/one-line-of-code operation, and that Markov chain Monte Carlo for probabilistic models with complicated long-distance dependencies, such as a stochastic version of Scheme, can be managed using standard Blaise mechanisms

Composable probabilistic inference with BLAISE

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 185-190).If we are to understand human-level cognition, we must understand how the mind finds the patterns that underlie the incomplete, noisy, and ambiguous data from our senses and that allow us to generalize our experiences to new situations. A wide variety of commercial applications face similar issues: industries from health services to business intelligence to oil field exploration critically depend on their ability to find patterns in vast amounts of data and use those patterns to make accurate predictions. Probabilistic inference provides a unified, systematic framework for specifying and solving these problems. Recent work has demonstrated the great value of probabilistic models defined over complex, structured domains. However, our ability to imagine probabilistic models has far outstripped our ability to programmatically manipulate them and to effectively implement inference, limiting the complexity of the problems that we can solve in practice. This thesis presents BLAISE, a novel framework for composable probabilistic modeling and inference, designed to address these limitations. BLAISE has three components: * The BLAISE State-Density-Kernel (SDK) graphical modeling language that generalizes factor graphs by: (1) explicitly representing inference algorithms (and their locality) using a new type of graph node, (2) representing hierarchical composition and repeated substructures in the state space, the interest distribution, and the inference procedure, and (3) permitting the structure of the model to change during algorithm execution. * A suite of SDK graph transformations that may be used to extend a model (e.g. to construct a mixture model from a model of a mixture component), or to make inference more effective (e.g. by automatically constructing a parallel tempered version of an algorithm or by exploiting conjugacy in a model).(cont.) * The BLAISE Virtual Machine, a runtime environment that can efficiently execute the stochastic automata represented by BLAISE SDK graphs. BLAISE encourages the construction of sophisticated models by composing simpler models, allowing the designer to implement and verify small portions of the model and inference method, and to reuse mode components from one task to another. BLAISE decouples the implementation of the inference algorithm from the specification of the interest distribution, even in cases (such as Gibbs sampling) where the shape of the interest distribution guides the inference. This gives modelers the freedom to explore alternate models without slow, error-prone reimplementation. The compositional nature of BLAISE enables novel reinterpretations of advanced Monte Carlo inference techniques (such as parallel tempering) as simple transformations of BLAISE SDK graphs. In this thesis, I describe each of the components of the BLAISE modeling framework, as well as validating the BLAISE framework by highlighting a variety of contemporary sophisticated models that have been developed by the BLAISE user community. I also present several surprising findings stemming from the BLAISE modeling framework, including that an Infinite Relational Model can be built using exactly the same inference methods as a simple mixture model, that constructing a parallel tempered inference algorithm should be a point-and-click/one-line-of-code operation, and that Markov chain Monte Carlo for probabilistic models with complicated long-distance dependencies, such as a stochastic version of Scheme, can be managed using standard BLAISE mechanisms.by Keith Allen Bonawitz.Ph.D

Deep learning models of biological visual information processing

Improved computational models of biological vision can shed light on key processes contributing to the high accuracy of the human visual system. Deep learning models, which extract multiple layers of increasingly complex features from data, achieved recent breakthroughs on visual tasks. This thesis proposes such flexible data-driven models of biological vision and also shows how insights regarding biological visual processing can lead to advances within deep learning. To harness the potential of deep learning for modelling the retina and early vision, this work introduces a new dataset and a task simulating an early visual processing function and evaluates deep belief networks (DBNs) and deep neural networks (DNNs) on this input. The models are shown to learn feature detectors similar to retinal ganglion and V1 simple cells and execute early vision tasks. To model high-level visual information processing, this thesis proposes novel deep learning architectures and training methods. Biologically inspired Gaussian receptive field constraints are imposed on restricted Boltzmann machines (RBMs) to improve the fidelity of the data representation to encodings extracted by visual processing neurons. Moreover, concurrently with learning local features, the proposed local receptive field constrained RBMs (LRF-RBMs) automatically discover advantageous non-uniform feature detector placements from data. Following the hierarchical organisation of the visual cortex, novel LRF-DBN and LRF-DNN models are constructed using LRF-RBMs with gradually increasing receptive field sizes to extract consecutive layers of features. On a challenging face dataset, unlike DBNs, LRF-DBNs learn a feature hierarchy exhibiting hierarchical part-based composition. Also, the proposed deep models outperform DBNs and DNNs on face completion and dimensionality reduction, thereby demonstrating the strength of methods inspired by biological visual processing