Uniformly reweighted belief propagation for distributed Bayesian hypothesis testing

Belief propagation (BP) is a technique for distributed inference in wireless networks and is often used even when the underlying graphical model contains cycles. In this paper, we propose a uniformly reweighted BP scheme that reduces the impact of cycles by weighting messages by a constant ?edge appearance probability? rho ? 1. We apply this algorithm to distributed binary hypothesis testing problems (e.g., distributed detection) in wireless networks with Markov random field models. We demonstrate that in the considered setting the proposed method outperforms standard BP, while maintaining similar complexity. We then show that the optimal ? can be approximated as a simple function of the average node degree, and can hence be computed in a distributed fashion through a consensus algorithm.

Brain tissue segmentation on Diffusion Weighted Magnetic Resonance data

Introduction Diffusion weighted Imaging (DWI) techniques are able to measure, in vivo and non-invasively, the diffusivity of water molecules inside the human brain. DWI has been applied on cerebral ischemia, brain maturation, epilepsy, multiple sclerosis, etc. [1]. Nowadays, there is a very high availability of these images. DWI allows the identification of brain tissues, so its accurate segmentation is a common initial step for the referred applications. Materials and Methods We present a validation study on automated segmentation of DWI based on the Gaussian mixture and hidden Markov random field models. This methodology is widely solved with iterative conditional modes algorithm, but some studies suggest [2] that graph-cuts (GC) algorithms improve the results when initialization is not close to the final solution. We implemented a segmentation tool integrating ITK with a GC algorithm [3], and a validation software using fuzzy overlap measures [4]. Results Segmentation accuracy of each tool is tested against a gold-standard segmentation obtained from a T1 MPRAGE magnetic resonance image of the same subject, registered to the DWI space. The proposed software shows meaningful improvements by using the GC energy minimization approach on DTI and DSI (Diffusion Spectrum Imaging) data. Conclusions The brain tissues segmentation on DWI is a fundamental step on many applications. Accuracy and robustness improvements are achieved with the proposed software, with high impact on the application’s final result.

A mean field model of ligand-protein interactions: implications for the structural assessment of human immunodeficiency virus type 1 protease complexes and receptor-specific binding.

We propose a general mean field model of ligand-protein interactions to determine the thermodynamic equilibrium of a system at finite temperature. The method is employed in structural assessments of two human immuno-deficiency virus type 1 protease complexes where the gross effects of protein flexibility are incorporated by utilizing a data base of crystal structures. Analysis of the energy spectra for these complexes has revealed that structural and thermo-dynamic aspects of molecular recognition can be rationalized on the basis of the extent of frustration in the binding energy landscape. In particular, the relationship between receptor-specific binding of these ligands to human immunodeficiency virus type 1 protease and a minimal frustration principle is analyzed.

Random field models and priors on wind

This report seeks to make concrete some of the ideas we have been discussing about sensible priors for winds over the ocean. In particular, random field models are reviewed, as are permissible covariance functions. The criteria which these covariance functions must satisfy in order that vorticity and divergence exist and are continuous are defined. The use of Helmholtz theorem is discussed, and possible choices for the covariances are suggested.

Flexible Gaussian process wind field models

This technical report builds on previous reports to derive the likelihood and its derivatives for a Gaussian Process with a modified Bessel function based covariance function. The full derivation is shown. The likelihood (with gradient information) can be used in maximum likelihood procedures (i.e. gradient based optimisation) and in Hybrid Monte Carlo sampling (i.e. within a Bayesian framework).

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Probabilistic Models for Scalable Knowledge Graph Construction

In the past decade, systems that extract information from millions of Internet documents have become commonplace. Knowledge graphs -- structured knowledge bases that describe entities, their attributes and the relationships between them -- are a powerful tool for understanding and organizing this vast amount of information. However, a significant obstacle to knowledge graph construction is the unreliability of the extracted information, due to noise and ambiguity in the underlying data or errors made by the extraction system and the complexity of reasoning about the dependencies between these noisy extractions. My dissertation addresses these challenges by exploiting the interdependencies between facts to improve the quality of the knowledge graph in a scalable framework. I introduce a new approach called knowledge graph identification (KGI), which resolves the entities, attributes and relationships in the knowledge graph by incorporating uncertain extractions from multiple sources, entity co-references, and ontological constraints. I define a probability distribution over possible knowledge graphs and infer the most probable knowledge graph using a combination of probabilistic and logical reasoning. Such probabilistic models are frequently dismissed due to scalability concerns, but my implementation of KGI maintains tractable performance on large problems through the use of hinge-loss Markov random fields, which have a convex inference objective. This allows the inference of large knowledge graphs using 4M facts and 20M ground constraints in 2 hours. To further scale the solution, I develop a distributed approach to the KGI problem which runs in parallel across multiple machines, reducing inference time by 90%. Finally, I extend my model to the streaming setting, where a knowledge graph is continuously updated by incorporating newly extracted facts. I devise a general approach for approximately updating inference in convex probabilistic models, and quantify the approximation error by defining and bounding inference regret for online models. Together, my work retains the attractive features of probabilistic models while providing the scalability necessary for large-scale knowledge graph construction. These models have been applied on a number of real-world knowledge graph projects, including the NELL project at Carnegie Mellon and the Google Knowledge Graph.

Competition and fixation of cohorts of adaptive mutations under Fisher geometrical model

One of the simplest models of adaptation to a new environment is Fisher's Geometric Model (FGM), in which populations move on a multidimensional landscape defined by the traits under selection. The predictions of this model have been found to be consistent with current observations of patterns of fitness increase in experimentally evolved populations. Recent studies investigated the dynamics of allele frequency change along adaptation of microbes to simple laboratory conditions and unveiled a dramatic pattern of competition between cohorts of mutations, i.e., multiple mutations simultaneously segregating and ultimately reaching fixation. Here, using simulations, we study the dynamics of phenotypic and genetic change as asexual populations under clonal interference climb a Fisherian landscape, and ask about the conditions under which FGM can display the simultaneous increase and fixation of multiple mutations-mutation cohorts-along the adaptive walk. We find that FGM under clonal interference, and with varying levels of pleiotropy, can reproduce the experimentally observed competition between different cohorts of mutations, some of which have a high probability of fixation along the adaptive walk. Overall, our results show that the surprising dynamics of mutation cohorts recently observed during experimental adaptation of microbial populations can be expected under one of the oldest and simplest theoretical models of adaptation-FGM.

Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model

We predict macroscopic fracture related material parameters of fully exfoliated clay/epoxy nano- composites based on their fine scale features. Fracture is modeled by a phase field approach which is implemented as user subroutines UEL and UMAT in the commercial finite element software Abaqus. The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter. Two different constitutive models for the matrix and the clay platelets are used; the nonlinear coupled system con- sisting of the equilibrium equation and a diffusion-type equation governing the phase field evolution are solved via a NewtoneRaphson approach. In order to predict the tensile strength and fracture toughness of the clay/epoxy composites we evaluated the J integral for different specimens with varying cracks. The effect of different geometry and material parameters, such as the clay weight ratio (wt.%) and the aspect ratio of clay platelets are studied.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Fusion of Multi-Atlas Segmentations with Spatial Distribution Modeling

In recent years, multi-atlas fusion methods have gainedsignificant attention in medical image segmentation. Inthis paper, we propose a general Markov Random Field(MRF) based framework that can perform edge-preservingsmoothing of the labels at the time of fusing the labelsitself. More specifically, we formulate the label fusionproblem with MRF-based neighborhood priors, as an energyminimization problem containing a unary data term and apairwise smoothness term. We present how the existingfusion methods like majority voting, global weightedvoting and local weighted voting methods can be reframedto profit from the proposed framework, for generatingmore accurate segmentations as well as more contiguoussegmentations by getting rid of holes and islands. Theproposed framework is evaluated for segmenting lymphnodes in 3D head and neck CT images. A comparison ofvarious fusion algorithms is also presented.