Doctor of Philosophy

dissertationTemporal reasoning denotes the modeling of causal relationships between different variables across different instances of time, and the prediction of future events or the explanation of past events. Temporal reasoning helps in modeling and understanding interactions between human pathophysiological processes, and in predicting future outcomes such as response to treatment or complications. Dynamic Bayesian Networks (DBN) support modeling changes in patients' condition over time due to both diseases and treatments, using probabilistic relationships between different clinical variables, both within and across different points in time. We describe temporal reasoning and representation in general and DBN in particular, with special attention to DBN parameter learning and inference. We also describe temporal data preparation (aggregation, consolidation, and abstraction) techniques that are applicable to medical data that were used in our research. We describe and evaluate various data discretization methods that are applicable to medical data. Projeny, an opensource probabilistic temporal reasoning toolkit developed as part of this research, is also described. We apply these methods, techniques, and algorithms to two disease processes modeled as Dynamic Bayesian Networks. The first test case is hyperglycemia due to severe illness in patients treated in the Intensive Care Unit (ICU). We model the patients' serum glucose and insulin drip rates using Dynamic Bayesian Networks, and recommend insulin drip rates to maintain the patients' serum glucose within a normal range. The model's safety and efficacy are proven by comparing it to the current gold standard. The second test case is the early prediction of sepsis in the emergency department. Sepsis is an acute life threatening condition that requires timely diagnosis and treatment. We present various DBN models and data preparation techniques that detect sepsis with very high accuracy within two hours after the patients' admission to the emergency department. We also discuss factors affecting the computational tractability of the models and appropriate optimization techniques. In this dissertation, we present a guide to temporal reasoning, evaluation of various data preparation, discretization, learning and inference methods, proofs using two test cases using real clinical data, an open-source toolkit, and recommend methods and techniques for temporal reasoning in medicine

Prospects for Declarative Mathematical Modeling of Complex Biological Systems

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them

Efficient planning under uncertainty with macro-actions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 163-168).Planning in large, partially observable domains is challenging, especially when good performance requires considering situations far in the future. Existing planners typically construct a policy by performing fully conditional planning, where each future action is conditioned on a set of possible observations that could be obtained at every timestep. Unfortunately, fully-conditional planning can be computationally expensive, and state-of-the-art solvers are either limited in the size of problems that can be solved, or can only plan out to a limited horizon. We propose that for a large class of real-world, planning under uncertainty problems, it is necessary to perform far-lookahead decision-making, but unnecessary to construct policies that condition all actions on observations obtained at the previous timestep. Instead, these problems can be solved by performing semi conditional planning, where the constructed policy only conditions actions on observations at certain key points. Between these key points, the policy assumes that a macro-action - a temporally-extended, fixed length, open-loop action sequence, comprising a series of primitive actions, is executed. These macro-actions are evaluated within a forward-search framework, which only considers beliefs that are reachable from the agent's current belief under different actions and observations; a belief summarizes an agent's past history of actions and observations. Together, semi-conditional planning in a forward search manner restricts the policy space in exchange for conditional planning out to a longer-horizon. Two technical challenges have to be overcome in order to perform semi-conditional planning efficiently - how the macro-actions can be automatically generated, as well as how to efficiently incorporate the macro action into the forward search framework. We propose an algorithm which automatically constructs the macro-actions that are evaluated within a forward search planning framework, iteratively refining the macro actions as more computation time is made available for planning. In addition, we show that for a subset of problem domains, it is possible to analytically compute the distribution over posterior beliefs that result from a single macro-action. This ability to directly compute a distribution over posterior beliefs enables us to enjoy computational savings when performing macro-action forward search. Performance and computational analysis for the algorithms proposed in this thesis are presented, as well as simulation experiments that demonstrate superior performance relative to existing state-of-the-art solvers on large planning under uncertainty domains. We also demonstrate our planning under uncertainty algorithms on target-tracking applications for an actual autonomous helicopter, highlighting the practical potential for planning in real-world, long-horizon, partially observable domains.by Ruijie He.Ph.D

Probabilistic Inference in Piecewise Graphical Models

In many applications of probabilistic inference the models contain piecewise densities that are differentiable except at partition boundaries. For instance, (1) some models may intrinsically have finite support, being constrained to some regions; (2) arbitrary density functions may be approximated by mixtures of piecewise functions such as piecewise polynomials or piecewise exponentials; (3) distributions derived from other distributions (via random variable transformations) may be highly piecewise; (4) in applications of Bayesian inference such as Bayesian discrete classification and preference learning, the likelihood functions may be piecewise; (5) context-specific conditional probability density functions (tree-CPDs) are intrinsically piecewise; (6) influence diagrams (generalizations of Bayesian networks in which along with probabilistic inference, decision making problems are modeled) are in many applications piecewise; (7) in probabilistic programming, conditional statements lead to piecewise models. As we will show, exact inference on piecewise models is not often scalable (if applicable) and the performance of the existing approximate inference techniques on such models is usually quite poor. This thesis fills this gap by presenting scalable and accurate algorithms for inference in piecewise probabilistic graphical models. Our first contribution is to present a variation of Gibbs sampling algorithm that achieves an exponential sampling speedup on a large class of models (including Bayesian models with piecewise likelihood functions). As a second contribution, we show that for a large range of models, the time-consuming Gibbs sampling computations that are traditionally carried out per sample, can be computed symbolically, once and prior to the sampling process. Among many potential applications, the resulting symbolic Gibbs sampler can be used for fully automated reasoning in the presence of deterministic constraints among random variables. As a third contribution, we are motivated by the behavior of Hamiltonian dynamics in optics —in particular, the reflection and refraction of light on the refractive surfaces— to present a new Hamiltonian Monte Carlo method that demonstrates a significantly improved performance on piecewise models. Hopefully, the present work represents a step towards scalable and accurate inference in an important class of probabilistic models that has largely been overlooked in the literature

Learning Bayesian network equivalence classes using ant colony optimisation

Bayesian networks have become an indispensable tool in the modelling of uncertain knowledge. Conceptually, they consist of two parts: a directed acyclic graph called the structure, and conditional probability distributions attached to each node known as the parameters. As a result of their expressiveness, understandability and rigorous mathematical basis, Bayesian networks have become one of the first methods investigated, when faced with an uncertain problem domain. However, a recurring problem persists in specifying a Bayesian network. Both the structure and parameters can be difficult for experts to conceive, especially if their knowledge is tacit.To counteract these problems, research has been ongoing, on learning both the structure and parameters of Bayesian networks from data. Whilst there are simple methods for learning the parameters, learning the structure has proved harder. Part ofthis stems from the NP-hardness of the problem and the super-exponential space of possible structures. To help solve this task, this thesis seeks to employ a relatively new technique, that has had much success in tackling NP-hard problems. This technique is called ant colony optimisation. Ant colony optimisation is a metaheuristic based on the behaviour of ants acting together in a colony. It uses the stochastic activity of artificial ants to find good solutions to combinatorial optimisation problems. In the current work, this method is applied to the problem of searching through the space of equivalence classes of Bayesian networks, in order to find a good match against a set of data. The system uses operators that evaluate potential modifications to a current state. Each of the modifications is scored and the results used to inform the search. In order to facilitate these steps, other techniques are also devised, to speed up the learning process. The techniques includeThe techniques are tested by sampling data from gold standard networks and learning structures from this sampled data. These structures are analysed using various goodnessof-fit measures to see how well the algorithms perform. The measures include structural similarity metrics and Bayesian scoring metrics. The results are compared in depth against systems that also use ant colony optimisation and other methods, including evolutionary programming and greedy heuristics. Also, comparisons are made to well known state-of-the-art algorithms and a study performed on a real-life data set. The results show favourable performance compared to the other methods and on modelling the real-life data

Topological Mapping and Navigation in Real-World Environments

We introduce the Hierarchical Hybrid Spatial Semantic Hierarchy (H2SSH), a hybrid topological-metric map representation. The H2SSH provides a more scalable representation of both small and large structures in the world than existing topological map representations, providing natural descriptions of a hallway lined with offices as well as a cluster of buildings on a college campus. By considering the affordances in the environment, we identify a division of space into three distinct classes: path segments afford travel between places at their ends, decision points present a choice amongst incident path segments, and destinations typically exist at the start and end of routes. Constructing an H2SSH map of the environment requires understanding both its local and global structure. We present a place detection and classification algorithm to create a semantic map representation that parses the free space in the local environment into a set of discrete areas representing features like corridors, intersections, and offices. Using these areas, we introduce a new probabilistic topological simultaneous localization and mapping algorithm based on lazy evaluation to estimate a probability distribution over possible topological maps of the global environment. After construction, an H2SSH map provides the necessary representations for navigation through large-scale environments. The local semantic map provides a high-fidelity metric map suitable for motion planning in dynamic environments, while the global topological map is a graph-like map that allows for route planning using simple graph search algorithms. For navigation, we have integrated the H2SSH with Model Predictive Equilibrium Point Control (MPEPC) to provide safe and efficient motion planning for our robotic wheelchair, Vulcan. However, navigation in human environments entails more than safety and efficiency, as human behavior is further influenced by complex cultural and social norms. We show how social norms for moving along corridors and through intersections can be learned by observing how pedestrians around the robot behave. We then integrate these learned norms with MPEPC to create a socially-aware navigation algorithm, SA-MPEPC. Through real-world experiments, we show how SA-MPEPC improves not only Vulcan’s adherence to social norms, but the adherence of pedestrians interacting with Vulcan as well.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144014/1/collinej_1.pd

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning

Learning cognitive maps: Finding useful structure in an uncertain world

In this chapter we will describe the central mechanisms that influence how people learn about large-scale space. We will focus particularly on how these mechanisms enable people to effectively cope with both the uncertainty inherent in a constantly changing world and also with the high information content of natural environments. The major lessons are that humans get by with a less is more approach to building structure, and that they are able to quickly adapt to environmental changes thanks to a range of general purpose mechanisms. By looking at abstract principles, instead of concrete implementation details, it is shown that the study of human learning can provide valuable lessons for robotics. Finally, these issues are discussed in the context of an implementation on a mobile robot. © 2007 Springer-Verlag Berlin Heidelberg

Context Exploitation in Data Fusion

Complex and dynamic environments constitute a challenge for existing tracking algorithms. For this reason, modern solutions are trying to utilize any available information which could help to constrain, improve or explain the measurements. So called Context Information (CI) is understood as information that surrounds an element of interest, whose knowledge may help understanding the (estimated) situation and also in reacting to that situation. However, context discovery and exploitation are still largely unexplored research topics. Until now, the context has been extensively exploited as a parameter in system and measurement models which led to the development of numerous approaches for the linear or non-linear constrained estimation and target tracking. More specifically, the spatial or static context is the most common source of the ambient information, i.e. features, utilized for recursive enhancement of the state variables either in the prediction or the measurement update of the filters. In the case of multiple model estimators, context can not only be related to the state but also to a certain mode of the filter. Common practice for multiple model scenarios is to represent states and context as a joint distribution of Gaussian mixtures. These approaches are commonly referred as the join tracking and classification. Alternatively, the usefulness of context was also demonstrated in aiding the measurement data association. Process of formulating a hypothesis, which assigns a particular measurement to the track, is traditionally governed by the empirical knowledge of the noise characteristics of sensors and operating environment, i.e. probability of detection, false alarm, clutter noise, which can be further enhanced by conditioning on context. We believe that interactions between the environment and the object could be classified into actions, activities and intents, and formed into structured graphs with contextual links translated into arcs. By learning the environment model we will be able to make prediction on the target\u2019s future actions based on its past observation. Probability of target future action could be utilized in the fusion process to adjust tracker confidence on measurements. By incorporating contextual knowledge of the environment, in the form of a likelihood function, in the filter measurement update step, we have been able to reduce uncertainties of the tracking solution and improve the consistency of the track. The promising results demonstrate that the fusion of CI brings a significant performance improvement in comparison to the regular tracking approaches