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

Learning Topologies of Acyclic Networks with Tree Structures

Network topology identification is known as the process of revealing the interconnections of a network where each node is representative of an atomic entity in a complex system. This procedure is an important topic in the study of dynamic networks since it has broad applications spanning different scientific fields. Furthermore, the study of tree structured networks is deemed significant since a large amount of scientific work is devoted to them and the techniques targeting trees can often be further extended to study more general structures. This dissertation considers the problem of learning the unknown structure of a network when the underlying topology is a directed tree, namely, it does not contain any cycles.The first result of this dissertation is an algorithm that consistently learns a tree structure when only a subset of the nodes is observed, given that the unobserved nodes satisfy certain degree conditions. This method makes use of an additive metric and statistics of the observed data only up to the second order. As it is shown, an additive metric can always be defined for networks with special dynamics, for example when the dynamics is linear. However, in the case of generic networks, additive metrics cannot always be defined. Thus, we derive a second result that solves the same problem, but requires the statistics of the observed data up to the third order, as well as stronger degree conditions for the unobserved nodes. Moreover, for both cases, it is shown that the same degree conditions are also necessary for a consistent reconstruction, achieving the fundamental limitations. The third result of this dissertation provides a technique to approximate a complex network via a simpler one when the assumption of linearity is exploited. The goal of this approximation is to highlight the most significant connections which could potentially reveal more information about the network. In order to show the reliability of this method, we consider high frequency financial data and show how well the businesses are clustered together according to their sector

Estimation of Distribution Algorithms and Minimum Relative Entropy

In the field of optimization using probabilistic models of the search space, this thesis identifies and elaborates several advancements in which the principles of maximum entropy and minimum relative entropy from information theory are used to estimate a probability distribution. The probability distribution within the search space is represented by a graphical model (factorization, Bayesian network or junction tree). An estimation of distribution algorithm (EDA) is an evolutionary optimization algorithm which uses a graphical model to sample a population within the search space and then estimates a new graphical model from the selected individuals of the population. - So far, the Factorized Distribution Algorithm (FDA) builds a factorization or Bayesian network from a given additive structure of the objective function to be optimized using a greedy algorithm which only considers a subset of the variable dependencies. Important connections can be lost by this method. This thesis presents a heuristic subfunction merge algorithm which is able to consider all dependencies between the variables (as long as the marginal distributions of the model do not become too large). On a 2-D grid structure, this algorithm builds a pentavariate factorization which allows to solve the deceptive grid benchmark problem with a much smaller population size than the conventional factorization. Especially for small population sizes, calculating large marginal distributions from smaller ones using Maximum Entropy and iterative proportional fitting leads to a further improvement. - The second topic is the generalization of graphical models to loopy structures. Using the Bethe-Kikuchi approximation, the loopy graphical model (region graph) can learn the Boltzmann distribution of an objective function by a generalized belief propagation algorithm (GBP). It minimizes the free energy, a notion adopted from statistical physics which is equivalent to the relative entropy to the Boltzmann distribution. Previous attempts to combine the Kikuchi approximation with EDA have relied on an expensive Gibbs sampling procedure for generating a population from this loopy probabilistic model. In this thesis a combination with a factorization is presented which allows more efficient sampling. The free energy is generalized to incorporate the inverse temperature ß. The factorization building algorithm mentioned above can be employed here, too. The dynamics of GBP is investigated, and the method is applied on Ising spin glass ground state search. Small instances (7 x 7) are solved without difficulty. Larger instances (10 x 10 and 15 x 15) do not converge to the true optimum with large ß, but sampling from the factorization can find the optimum with about 1000-10000 sampling attempts, depending on the instance. If GBP does not converge, it can be replaced by a concave-convex procedure which guarantees convergence. - Third, if no probabilistic structure is given for the objective function, a Bayesian network can be learned to capture the dependencies in the population. The relative entropy between the population-induced distribution and the Bayesian network distribution is equivalent to the log-likelihood of the model. The log-likelihood has been generalized to the BIC/MDL score which reduces overfitting by punishing complicated structure of the Bayesian network. A previous information theoretic analysis of BIC/MDL in the context of EDA is continued, and empiric evidence is given that the method is able to learn the correct structure of an objective function, given a sufficiently large population. - Finally, a way to reduce the search space of EDA is presented by combining it with a local search heuristics. The Kernighan Lin hillclimber, known originally for the traveling salesman problem and graph bipartitioning, is generalized to arbitrary binary problems. It can be applied in a stand-alone manner, as an iterative 1+1 search algorithm, or combined with EDA. On the MAXSAT problem it performs in a similar scale to the specialized SAT solver Walksat. An analysis of the Kernighan Lin local optima indicates that the combination with an EDA is favorable. The thesis shows how evolutionary optimization can be improved using interdisciplinary results from information theory, statistics, probability calculus and statistical physics. The principles of information theory for estimating probability distributions are applicable in many areas. EDAs are a good application because an improved estimation affects directly the optimization success.Estimation of Distribution Algorithms und Minimierung der relativen Entropie Im Bereich der Optimierung mit probabilistischen Modellen des Suchraums werden einige Fortschritte identifiziert und herausgearbeitet, in denen die Prinzipien der maximalen Entropie und der minimalen relativen Entropie aus der Informationstheorie verwendet werden, um eine Wahrscheinlichkeitsverteilung zu schätzen. Die Wahrscheinlichkeitsverteilung im Suchraum wird durch ein graphisches Modell beschrieben (Faktorisierung, Bayessches Netz oder Verbindungsbaum). Ein Estimation of Distribution Algorithm (EDA) ist ein evolutionärer Optimierungsalgorithmus, der mit Hilfe eines graphischen Modells eine Population im Suchraum erzeugt und dann anhand der selektierten Individuen dieser Population ein neues graphisches Modell erzeugt. - Bislang baut der Factorized Distribution Algorithm (FDA) eine Faktorisierung oder ein Bayessches Netz aus einer gegebenen additiven Struktur der Zielfunktion durch einen Greedy-Algorithmus, der nur einen Teil der Verbindungen zwischen den Variablen berücksichtigt. Wichtige verbindungen können durch diese Methode verloren gehen. Diese Arbeit stellt einen heuristischen Subfunktionenverschmelzungsalgorithmus vor, der in der Lage ist, alle Abhängigkeiten zwischen den Variablen zu berücksichtigen (wofern die Randverteilungen des Modells nicht zu groß werden). Auf einem 2D-Gitter erzeugt dieser Algorithmus eine pentavariate Faktorisierung, die es ermöglicht, das Deceptive-Grid-Testproblem mit viel kleinerer Populationsgröße zu lösen als mit der konventionellen Faktorisierung. Insbesondere für kleine Populationsgrößen kann das Ergebnis noch verbessert werden, wenn große Randverteilungen aus kleineren vermittels des Prinzips der maximalen Entropie und des Iterative Proportional Fitting- Algorithmus berechnet werden. - Das zweite Thema ist die Verallgemeinerung graphischer Modelle zu zirkulären Strukturen. Mit der Bethe-Kikuchi-Approximation kann das zirkuläre graphische Modell (der Regionen-Graph) die Boltzmannverteilung einer Zielfunktion durch einen generalisierten Belief Propagation-Algorithmus (GBP) lernen. Er minimiert die freie Energie, eine Größe aus der statistischen Physik, die äquivalent zur relativen Entropie zur Boltzmannverteilung ist. Frühere Versuche, die Kikuchi-Approximation mit EDA zu verbinden, benutzen einen aufwendigen Gibbs-Sampling-Algorithmus, um eine Population aus dem zirkulären Wahrscheinlichkeitsmodell zu erzeugen. In dieser Arbeit wird eine Verbindung mit Faktorisierungen vorgestellt, die effizienteres Sampling erlaubt. Die freie Energie wird um die inverse Temperatur ß erweitert. Der oben erwähnte Algorithmus zur Erzeugung einer Faktorisierung kann auch hier angewendet werden. Die Dynamik von GBP wird untersucht und auf Ising-Modelle angewendet. Kleine Probleme (7 x 7) werden ohne Schwierigkeit gelöst. Größere Probleme (10 x 10 und 15 x 15) konvergieren mit großem ß nicht mehr zum wahren Optimum, aber durch Sampling von der Faktorisierung kann das Optimum bei einer Samplegröße von 1000 bis 10000, je nach Probleminstanz, gefunden werden. Wenn GBP nicht konvergiert, kann es durch eine Konkav-Konvex-Prozedur ersetzt werden, die Konvergenz garantiert. - Drittens kann, wenn für die Zielfunktion keine Struktur gegeben ist, ein Bayessches Netz gelernt werden, um die Abhängigkeiten in der Population zu erfassen. Die relative Entropie zwischen der Populationsverteilung und der Verteilung durch das Bayessche Netz ist äquivalent zur Log-Likelihood des Modells. Diese wurde erweitert zum BIC/MDL-Kriterium, das Überanpassung lindert, indem komplizierte Strukturen bestraft werden. Eine vorangegangene informationstheoretische Analyse von BIC/MDL im EDA-Bereich wird erweitert, und empirisch wird belegt, daß die Methode die korrekte Struktur einer Zielfunktion bei genügend großer Population lernen kann. - Schließlich wird vorgestellt, wie durch eine lokale Suchheuristik der Suchraum von EDA reduziert werden kann. Der Kernighan-Lin-Hillclimber, der ursprünglich für das Problem des Handlungsreisenden und Graphen-Bipartitionierung konzipiert ist, wird für beliebige binäre Probleme erweitert. Er kann allein angewandt werden, als iteratives 1+1-Suchverfahren, oder in Kombination mit EDA. Er löst das MAXSAT-Problem in ähnlicher Größenordnung wie der spezialisierte Hillclimber Walksat. Eine Analyse der lokalen Optima von Kernighan-Lin zeigt, daß die Kombination mit EDA vorteilhaft ist. Die Arbeit zeigt, wie evolutionäre Optimierung verbessert werden kann, indem interdisziplinäre Ergebnisse aus Informationstheorie, Statistik, Wahrscheinlichkeitsrechnung und statistischer Physik eingebracht werden. Die Prinzipien der Informationstheorie zur Schätzung von Wahrscheinlichkeitsverteilungen lassen sich in vielen Bereichen anwenden. EDAs sind eine gute Anwendung, denn eine verbesserte Schätzung beeinflußt direkt den Optimierungserfolg

How long, O Bayesian network, will I sample thee? A program analysis perspective on expected sampling times

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference is often infeasible for large BNs, popular approximate inference methods rely on sampling. We study the problem of determining the expected time to obtain a single valid sample from a BN. To this end, we translate the BN together with observations into a probabilistic program. We provide proof rules that yield the exact expected runtime of this program in a fully automated fashion. We implemented our approach and successfully analyzed various real-world BNs taken from the Bayesian network repository

Learning Extended Tree Augmented Naive Structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds ’ algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments show that we obtain models with better prediction accuracy than Naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka

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