Bayesian Polytrees With Learned Deep Features for Multi-Class Cell Segmentation.

The recognition of different cell compartments, the types of cells, and their interactions is a critical aspect of quantitative cell biology. 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. To alleviate this, graphical models are useful due to their ability to make use of prior knowledge and model inter-class dependences. Directed acyclic graphs, such as trees, have been widely used to model top-down statistical dependences as a prior for improved image segmentation. However, using trees, a few inter-class constraints can be captured. To overcome this limitation, we propose polytree graphical models that capture label proximity relations more naturally compared to tree-based approaches. A novel recursive mechanism based on two-pass message passing was developed to efficiently calculate closed-form posteriors of graph nodes on polytrees. The algorithm is evaluated on simulated data and on two publicly available fluorescence microscopy datasets, outperforming directed trees and three state-of-the-art convolutional neural networks, namely, SegNet, DeepLab, and PSPNet. Polytrees are shown to outperform directed trees in predicting segmentation error by highlighting areas in the segmented image that do not comply with prior knowledge. This paves the way to uncertainty measures on the resulting segmentation and guide subsequent segmentation refinement

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

A cortical model of object perception based on Bayesian networks and belief propagation.

Evidence suggests that high-level feedback plays an important role in visual perception by shaping the response in lower cortical levels (Sillito et al. 2006, Angelucci and Bullier 2003, Bullier 2001, Harrison et al. 2007). A notable example of this is reflected by the retinotopic activation of V1 and V2 neurons in response to illusory contours, such as Kanizsa figures, which has been reported in numerous studies (Maertens et al. 2008, Seghier and Vuilleumier 2006, Halgren et al. 2003, Lee 2003, Lee and Nguyen 2001). The illusory contour activity emerges first in lateral occipital cortex (LOC), then in V2 and finally in V1, strongly suggesting that the response is driven by feedback connections. Generative models and Bayesian belief propagation have been suggested to provide a theoretical framework that can account for feedback connectivity, explain psychophysical and physiological results, and map well onto the hierarchical distributed cortical connectivity (Friston and Kiebel 2009, Dayan et al. 1995, Knill and Richards 1996, Geisler and Kersten 2002, Yuille and Kersten 2006, Deneve 2008a, George and Hawkins 2009, Lee and Mumford 2003, Rao 2006, Litvak and Ullman 2009, Steimer et al. 2009). The present study explores the role of feedback in object perception, taking as a starting point the HMAX model, a biologically inspired hierarchical model of object recognition (Riesenhuber and Poggio 1999, Serre et al. 2007b), and extending it to include feedback connectivity. A Bayesian network that captures the structure and properties of the HMAX model is developed, replacing the classical deterministic view with a probabilistic interpretation. The proposed model approximates the selectivity and invariance operations of the HMAX model using the belief propagation algorithm. Hence, the model not only achieves successful feedforward recognition invariant to position and size, but is also able to reproduce modulatory effects of higher-level feedback, such as illusory contour completion, attention and mental imagery. Overall, the model provides a biophysiologically plausible interpretation, based on state-of-theart probabilistic approaches and supported by current experimental evidence, of the interaction between top-down global feedback and bottom-up local evidence in the context of hierarchical object perception

Influence modelling and learning between dynamic bayesian networks using score-based structure learning

A Ph.D. thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science May 2018Although partially observable stochastic processes are ubiquitous in many fields of science, little work has been devoted to discovering and analysing the means by which several such processes may interact to influence each other. In this thesis we extend probabilistic structure learning between random variables to the context of temporal models which represent partially observable stochastic processes. Learning an influence structure and distribution between processes can be useful for density estimation and knowledge discovery. A common approach to structure learning, in observable data, is score-based structure learning, where we search for the most suitable structure by using a scoring metric to value structural configurations relative to the data. Most popular structure scores are variations on the likelihood score which calculates the probability of the data given a potential structure. In observable data, the decomposability of the likelihood score, which is the ability to represent the score as a sum of family scores, allows for efficient learning procedures and significant computational saving. However, in incomplete data (either by latent variables or missing samples), the likelihood score is not decomposable and we have to perform inference to evaluate it. This forces us to use non-linear optimisation techniques to optimise the likelihood function. Furthermore, local changes to the network can affect other parts of the network, which makes learning with incomplete data all the more difficult. We define two general types of influence scenarios: direct influence and delayed influence which can be used to define influence around richly structured spaces; consisting of multiple processes that are interrelated in various ways. We will see that although it is possible to capture both types of influence in a single complex model by using a setting of the parameters, complex representations run into fragmentation issues. This is handled by extending the language of dynamic Bayesian networks to allow us to construct single compact models that capture the properties of a system’s dynamics, and produce influence distributions dynamically. The novelty and intuition of our approach is to learn the optimal influence structure in layers. We firstly learn a set of independent temporal models, and thereafter, optimise a structure score over possible structural configurations between these temporal models. Since the search for the optimal structure is done using complete data we can take advantage of efficient learning procedures from the structure learning literature. We provide the following contributions: we (a) introduce the notion of influence between temporal models; (b) extend traditional structure scores for random variables to structure scores for temporal models; (c) provide a complete algorithm to recover the influence structure between temporal models; (d) provide a notion of structural assembles to relate temporal models for types of influence; and finally, (e) provide empirical evidence for the effectiveness of our method with respect to generative ground-truth distributions. The presented results emphasise the trade-off between likelihood of an influence structure to the ground-truth and the computational complexity to express it. Depending on the availability of samples we might choose different learning methods to express influence relations between processes. On one hand, when given too few samples, we may choose to learn a sparse structure using tree-based structure learning or even using no influence structure at all. On the other hand, when given an abundant number of samples, we can use penalty-based procedures that achieve rich meaningful representations using local search techniques. Once we consider high-level representations of dynamic influence between temporal models, we open the door to very rich and expressive representations which emphasise the importance of knowledge discovery and density estimation in the temporal setting.MT 201

Learning Functional Prepositions

In first language acquisition, what does it mean for a grammatical category to have been acquired, and what are the mechanisms by which children learn functional categories in general? In the context of prepositions (Ps), if the lexical/functional divide cuts through the P category, as has been suggested in the theoretical literature, then constructivist accounts of language acquisition would predict that children develop adult-like competence with the more abstract units, functional Ps, at a slower rate compared to their acquisition of lexical Ps. Nativists instead assume that the features of functional P are made available by Universal Grammar (UG), and are mapped as quickly, if not faster, than the semantic features of their lexical counterparts. Conversely, if Ps are either all lexical or all functional, on both accounts of acquisition we should observe few differences in learning. Three empirical studies of the development of P were conducted via computer analysis of the English and Spanish sub-corpora of the CHILDES database. Study 1 analyzed errors in child usage of Ps, finding almost no errors in commission in either language, but that the English learners lag in their production of functional Ps relative to lexical Ps. That no such delay was found in the Spanish data suggests that the English pattern is not universal. Studies 2 and 3 applied novel measures of phrasal (P head + nominal complement) productivity to the data. Study 2 examined prepositional phrases (PPs) whose head-complement pairs appeared in both child and adult speech, while Study 3 considered PPs produced by children that never occurred in adult speech. In both studies the productivity of Ps for English children developed faster than that of lexical Ps. In Spanish there were few differences, suggesting that children had already mastered both orders of Ps early in acquisition. These empirical results suggest that at least in English P is indeed a split category, and that children acquire the syntax of the functional subset very quickly, committing almost no errors. The UG position is thus supported. Next, the dissertation investigates a \u27soft nativist\u27 acquisition strategy that composes the distributional analysis of input, minimal a priori knowledge of the possible co-occurrence of morphosyntactic features associated with functional elements, and linguistic knowledge that is presumably acquired via the experience of pragmatic, communicative situations. The output of the analysis consists in a mapping of morphemes to the feature bundles of nominative pronouns for English and Spanish, plus specific claims about the sort of knowledge required from experience. The acquisition model is then extended to adpositions, to examine what, if anything, distributional analysis can tell us about the functional sequences of PPs. The results confirm the theoretical position according to which spatiotemporal Ps are lexical in character, rooting their own extended projections, and that functional Ps express an aspectual sequence in the functional superstructure of the PP

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Proceedings of the 11th international Conference on Cognitive Modeling : ICCM 2012

The International Conference on Cognitive Modeling (ICCM) is the premier conference for research on computational models and computation-based theories of human behavior. ICCM is a forum for presenting, discussing, and evaluating the complete spectrum of cognitive modeling approaches, including connectionism, symbolic modeling, dynamical systems, Bayesian modeling, and cognitive architectures. ICCM includes basic and applied research, across a wide variety of domains, ranging from low-level perception and attention to higher-level problem-solving and learning. Online-Version published by Universitätsverlag der TU Berlin (www.univerlag.tu-berlin.de