Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

Learning Latent Tree Graphical Models

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset

A tomographic ocean sound speed profile from a long veritcal acoustic array

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 1992An average sound speed profile over a 1000 km section of the northeast Pacific ocean is obtained using Ocean Acoustic Tomography, from data acquired during the 1987 SVLA experiment on a long (900 m) 120 hydrophone vertical acoustic array. In particular, we pulse compress the received signal with a phase-only matched filter. The signal, centered at 80Hz, is phase-modulated by a maximal length sequence. A fast m-sequence cross-correlation algorithm based on the Hadamard transform is used. In addition, wide band Doppler correction and coherent averaging of repetitions of the signal are performed. The tomographic inversion is initialized from a range averaged climatological profile. Multipaths are identified from ray theory. The identified arrivals are inverted for a range-independent sound speed profile change estimate. Estimates of source and array position error are also obtained. For the limited data set used, the sound speed change estimate is found to be insignificant, and a significant instrument position estimate is obtained

Navigation of brain networks

Understanding the mechanisms of neural communication in large-scale brain networks remains a major goal in neuroscience. We investigated whether navigation is a parsimonious routing model for connectomics. Navigating a network involves progressing to the next node that is closest in distance to a desired destination. We developed a measure to quantify navigation efficiency and found that connectomes in a range of mammalian species (human, mouse and macaque) can be successfully navigated with near-optimal efficiency (>80% of optimal efficiency for typical connection densities). Rewiring network topology or repositioning network nodes resulted in 45%-60% reductions in navigation performance. Specifically, we found that brain networks cannot be progressively rewired (randomized or clusterized) to result in topologies with significantly improved navigation performance. Navigation was also found to: i) promote a resource-efficient distribution of the information traffic load, potentially relieving communication bottlenecks; and, ii) explain significant variation in functional connectivity. Unlike prevalently studied communication strategies in connectomics, navigation does not mandate biologically unrealistic assumptions about global knowledge of network topology. We conclude that the wiring and spatial embedding of brain networks is conducive to effective decentralized communication. Graph-theoretic studies of the connectome should consider measures of network efficiency and centrality that are consistent with decentralized models of neural communication

MAPPING THE OCEAN SOUND SPEED AT THE ALOHA CABLED OBSERVATORY USING RELIABLE ACOUSTIC PATH TOMOGRAPHY

M.S.M.S. Thesis. University of Hawaiʻi at Mānoa 201

Doctor of Philosophy

dissertationAccurate interpretation of seismic travel times and amplitudes in both the exploration and global scales is complicated by the band-limited nature of seismic data. We present a stochastic method, Viterbi sparse spike detection (VSSD), to reduce a seismic waveform into a most probable constituent spike train. Model waveforms are constructed from a set of candidate spike trains convolved with a source wavelet estimate. For each model waveform, a profile hidden Markov model (HMM) is constructed to represent the waveform as a stochastic generative model with a linear topology corresponding to a sequence of samples. The Viterbi algorithm is employed to simultaneously find the optimal nonlinear alignment between a model waveform and the seismic data, and to assign a score to each candidate spike train. The most probable travel times and amplitudes are inferred from the alignments of the highest scoring models. Our analyses show that the method can resolve closely spaced arrivals below traditional resolution limits and that travel time estimates are robust in the presence of random noise and source wavelet errors. We applied the VSSD method to constrain the elastic properties of a ultralow- velocity zone (ULVZ) at the core-mantle boundary beneath the Coral Sea. We analyzed vertical component short period ScP waveforms for 16 earthquakes occurring in the Tonga-Fiji trench recorded at the Alice Springs Array (ASAR) in central Australia. These waveforms show strong pre and postcursory seismic arrivals consistent with ULVZ layering. We used the VSSD method to measure differential travel-times and amplitudes of the post-cursor arrival ScSP and the precursor arrival SPcP relative to ScP. We compare our measurements to a database of approximately 340,000 synthetic seismograms finding that these data are best fit by a ULVZ model with an S-wave velocity reduction of 24%, a P-wave velocity reduction of 23%, a thickness of 8.5 km, and a density increase of 6%. We simultaneously constrain both P- and S-wave velocity reductions as a 1:1 ratio inside this ULVZ. This 1:1 ratio is not consistent with a partial melt origin to ULVZs. Rather, we demonstrate that a compositional origin is more likely

Une nouvelle méthode d'inversion pour les problèmes de synthèse de Fourier en imagerie

- La plupart des méthodes classiques d'inversion en synthèse de Fourier sont basées sur l'interpolation et la Transformée de Fourier (TF) inverse rapide. Mais, lorsque les données ne remplissent pas d'une manière uniforme le domaine de Fourier, ce qui est le cas dans grand nombre d'applications en imagerie, ou lorsque la phase du signal n'est pas accessible, comme en interférométrie non cohérente, ces méthodes ne fournissent pas de résultats satisfaisants. La méthode proposée est une méthode de régularisation basée sur l'estimation bayésienne. Une modélisation appropriée de l'image permet de remédier, d'une manière simple, au manque d'information lié aux données et de fournir des résultats satisfaisants. Notre objectif ici est de fournir une méthode utilisable en pratique en faisant un compromis entre complexité de mise en oeuvre et performances. La méthode proposée est testée sur des données expérimentales en imagerie microonde

MRI Data Processing Acceleration on GPU

Tato bakalářská práce byla vypracována v průběhu studijního pobytu na Universita della Svizzera italiana ve Švýcarsku. Identifikace trajektorií neuronových vláken uvnitř lidského mozku má velký význam v mnoha lékařských aplikacích, jako neurologická diagnostika, neuro-navigace, léčba epilepsie, chirurgické operace a tak dále. Za použití dat z MRI, metod postavených na Markovských řetězích a Monte Carlu mohou být možné trajektorie vypočítany a ty nejpravděpodobnější zobrazeny. Tyto informace o trajektoriích mohou sloužit jako vstup pro pokročilé metody lékařské diagnotiky a léčby. Vzhledem k obrovskému množství dat a velkého počtu iterací toto může být časově náročný proces. Za účely, jako jsou statistická analýza a/nebo porovnávání několika datových sad a/nebo pacientů, požadavky na výpočetní čas jsou enormní. Rychlejší diagnóza může také přinést nasazení léčby dříve. Nyní existuje jen velmi málo implementací softwaru pro neurální traktografii. Implementací softwaru pro pravděpodobnostní neurální traktografii je ještě méně. Nynější implementace, provádějící všechny operace postupně na CPU, jsou značně pomalé. Účelem této práce je poskytnout efektivní implementaci, která vvyužíva GPU. Za účelem implementace na GPU, je poskytnuto porovnaní technologíí CUDA a OpenCL.This BSc Thesis was performed during a study stay at the Universita della Svizzera italiana, Swiss. The identification of trajectories of neuron fibres within the human brain is of great importance in many medical applications as the neural diagnostics, neuronavigation, treatment of epilepsy, surgical removal of tumors and etc. By using diffusion MRI-data as input, and by employing Monte-Carlo like methods, possible trajectories are generated and the most likely ones can be visualized. These can serve as input for advanced medical diagnosis and treatments. Due to the huge amount of data to be analyzed and many iterations, this is a time consuming process. For the purposes such as statistical analysis and comparsion over several datasets or several patients, computational time requirements are enourmous. Faster diagnosis can improve routine throughput and provide earlier treatment of illness. At this time, there exists only a very few implementations of neural tractography sof tware. For probabilistic neural tractography is the list of software even thiner. Today's implementations using standard serial CPU execution suffer from high time consumption. The goal is to provide an efficient implementation which makes use of GPGPUs and exploits parallelism in the method. For the GPU implementation, a comparsion of CUDA and OpenCL technologies will be provided, using the more suitable one.