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

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

Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations

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

Metabolic Network Alignments and their Applications

The accumulation of high-throughput genomic and proteomic data allows for the reconstruction of the increasingly large and complex metabolic networks. In order to analyze the accumulated data and reconstructed networks, it is critical to identify network patterns and evolutionary relations between metabolic networks. But even finding similar networks becomes computationally challenging. The dissertation addresses these challenges with discrete optimization and the corresponding algorithmic techniques. Based on the property of the gene duplication and function sharing in biological network,we have formulated the network alignment problem which asks the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. We have proposed the first polynomial time algorithm for aligning an acyclic metabolic pattern pathway with an arbitrary metabolic network. We also have proposed a polynomial-time algorithm for patterns with small treewidth and implemented it for series-parallel patterns which are commonly found among metabolic networks. We have developed the metabolic network alignment tool for free public use. We have performed pairwise mapping of all pathways among five organisms and found a set of statistically significant pathway similarities. We also have applied the network alignment to identifying inconsistency, inferring missing enzymes, and finding potential candidates

Context Aware Drivers' Behaviour Detection System for VANET

Wireless communications and mobile computing have led to the enhancement of, and improvement in, intelligent transportation systems (ITS) that focus on road safety applications. As a promising technology and a core component of ITS, Vehicle Ad hoc Networks (VANET) have emerged as an application of Mobile Ad hoc Networks (MANET), which use Dedicated Short Range Communication (DSRC) to allow vehicles in close proximity to communicate with one another, or to communicate with roadside equipment. These types of communication open up a wide range of potential safety and non-safety applications, with the aim of providing an intelligent driving environment that will offer road users more pleasant journeys. VANET safety applications are considered to represent a vital step towards improving road safety and enhancing traffic efficiency, as a consequence of their capacity to share information about the road between moving vehicles. This results in decreasing numbers of accidents and increasing the opportunity to save people's lives. Many researchers from different disciplines have focused their research on the development of vehicle safety applications. Designing an accurate and efficient driver behaviour detection system that can detect the abnormal behaviours exhibited by drivers (i.e. drunkenness and fatigue) and alert them may have an impact on the prevention of road accidents. Moreover, using Context-aware systems in vehicles can improve the driving by collecting and analysing contextual information about the driving environment, hence, increasing the awareness of the driver while driving his/her car. In this thesis, we propose a novel driver behaviour detection system in VANET by utilising a context-aware system approach. The system is comprehensive, non-intrusive and is able to detect four styles of driving behaviour: drunkenness, fatigue, reckless and normal behaviour. The behaviour of the driver in this study is considered to be uncertain context and is defined as a dynamic interaction between the driver, the vehicle and the environment; meaning it is affected by many factors and develops over the time. Therefore, we have introduced a novel Dynamic Bayesian Network (DBN) framework to perform reasoning about uncertainty and to deduce the behaviour of drivers by combining information regarding the above mentioned factors. A novel On Board Unit (OBU) architecture for detecting the behaviour of the driver has been introduced. The architecture has been built based on the concept of context-awareness; it is divided into three phases that represent the three main subsystems of context-aware system; sensing, reasoning and acting subsystems. The proposed architecture explains how the system components interact in order to detect abnormal behaviour that is being exhibited by driver; this is done to alert the driver and prevent accidents from occurring. The implementation of the proposed system has been carried out using GeNIe version 2.0 software to construct the DBN model. The DBN model has been evaluated using synthetic data in order to demonstrate the detection accuracy of the proposed model under uncertainty, and the importance of including a large amount of contextual information within the detection process

Belief Propagation and Revision in Networks with Loops

Local belief propagation rules of the sort proposed by Pearl(1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay the foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive ananalytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP estimate obtained by belief revisionat convergence is guaranteed to give the globally optimal sequence of states. The result is independent of the length of the cycle and the size of the statespace. For networks with multiple loops, we introduce the concept of a "balanced network" and show simulati