Towards dynamic term size computation via program transformation

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of applications related to program optimization such as, for example, recursion elimination and granularity analysis. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predefined) predicates which traverse the terms involved. We propose a technique based on program transformation which has the potential of performing this computation much more efficiently. The technique is based on finding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows finding minimal transformations under certain criteria. We also discuss the advantages and present some applications of our technique.

A technique for dynamic term size computation via program transformation

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of applications related to program optimization such as, for example, granularity analysis and selection among different algorithms or control rules whose performance may be dependent on such size. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predefined) predicates which traverse the terms involved. We propose a technique based on program transformation which has the potential of performing this computation much more efficiently. The technique is based on finding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows finding minimal transformations under certain criteria. We also discuss the advantages and applications of our technique and present some performance results.

Dynamic term size computation in logic programs via program transformation

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of applications related to program optimization such as, for example, recursion elimination and granularity analysis. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predefined) predicates which traverse the terms involved. We propose a technique based on program transformation which has the potential of performing this computation much more efficiently. The technique is based on finding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows finding minimal transformations under certain criteria. We also discuss the advantages and present some applications of our technique.

Bayesian scene analysis for multi-camera 3D tracking and camera positioning

Los sistemas de seguimiento mono-cámara han demostrado su notable capacidad para el análisis de trajectorias de objectos móviles y para monitorización de escenas de interés; sin embargo, tanto su robustez como sus posibilidades en cuanto a comprensión semántica de la escena están fuertemente limitadas por su naturaleza local y monocular, lo que los hace insuficientes para aplicaciones realistas de videovigilancia. El objetivo de esta tesis es la extensión de las posibilidades de los sistemas de seguimiento de objetos móviles para lograr un mayor grado de robustez y comprensión de la escena. La extensión propuesta se divide en dos direcciones separadas. La primera puede considerarse local, ya que está orientada a la mejora y enriquecimiento de las posiciones estimadas para los objetos móviles observados directamente por las cámaras del sistema; dicha extensión se logra mediante el desarrollo de un sistema multi-cámara de seguimiento 3D, capaz de proporcionar consistentemente las posiciones 3D de múltiples objetos a partir de las observaciones capturadas por un conjunto de sensores calibrados y con campos de visión solapados. La segunda extensión puede considerarse global, dado que su objetivo consiste en proporcionar un contexto global para relacionar las observaciones locales realizadas por una cámara con una escena de mucho mayor tamaño; para ello se propone un sistema automático de localización de cámaras basado en las trayectorias observadas de varios objetos móviles y en un mapa esquemático de la escena global monitorizada. Ambas líneas de investigación se tratan utilizando, como marco común, técnicas de estimación bayesiana: esta elección está justificada por la versatilidad y flexibilidad proporcionada por dicho marco estadístico, que permite la combinación natural de múltiples fuentes de información sobre los parámetros a estimar, así como un tratamiento riguroso de la incertidumbre asociada a las mismas mediante la inclusión de modelos de observación específicamente diseñados. Además, el marco seleccionado abre grandes posibilidades operacionales, puesto que permite la creación de diferentes métodos numéricos adaptados a las necesidades y características específicas de distintos problemas tratados. El sistema de seguimiento 3D con múltiples cámaras propuesto está específicamente diseñado para permitir descripciones esquemáticas de las medidas realizadas individualmente por cada una de las cámaras del sistema: esta elección de diseño, por tanto, no asume ningún algoritmo específico de detección o seguimiento 2D en ninguno de los sensores de la red, y hace que el sistema propuesto sea aplicable a redes reales de vigilancia con capacidades limitadas tanto en términos de procesamiento como de transmision. La combinación robusta de las observaciones capturadas individualmente por las cámaras, ruidosas, incompletas y probablemente contaminadas por falsas detecciones, se basa en un metodo de asociación bayesiana basado en geometría y color: los resultados de dicha asociación permiten el seguimiento 3D de los objetos de la escena mediante el uso de un filtro de partículas. El sistema de fusión de observaciones propuesto tiene, como principales características, una gran precisión en términos de localización 3D de objetos, y una destacable capacidad de recuperación tras eventuales errores debidos a un número insuficiente de datos de entrada. El sistema automático de localización de cámaras se basa en la observación de múltiples objetos móviles y un mapa esquemático de las áreas transitables del entorno monitorizado para inferir la posición absoluta de dicho sensor. Para este propósito, se propone un novedoso marco bayesiano que combina modelos dinámicos inducidos por el mapa en los objetos móviles presentes en la escena con las trayectorias observadas por la cámara, lo que representa un enfoque nunca utilizado en la literatura existente. El sistema de localización se divide en dos sub-tareas diferenciadas, debido a que cada una de estas tareas requiere del diseño de algoritmos específicos de muestreo para explotar en profundidad las características del marco desarrollado: por un lado, análisis de la ambigüedad del caso específicamente tratado y estimación aproximada de la localización de la cámara, y por otro, refinado de la localización de la cámara. El sistema completo, diseñado y probado para el caso específico de localización de cámaras en entornos de tráfico urbano, podría tener aplicación también en otros entornos y sensores de diferentes modalidades tras ciertas adaptaciones. ABSTRACT Mono-camera tracking systems have proved their capabilities for moving object trajectory analysis and scene monitoring, but their robustness and semantic possibilities are strongly limited by their local and monocular nature and are often insufficient for realistic surveillance applications. This thesis is aimed at extending the possibilities of moving object tracking systems to a higher level of scene understanding. The proposed extension comprises two separate directions. The first one is local, since is aimed at enriching the inferred positions of the moving objects within the area of the monitored scene directly covered by the cameras of the system; this task is achieved through the development of a multi-camera system for robust 3D tracking, able to provide 3D tracking information of multiple simultaneous moving objects from the observations reported by a set of calibrated cameras with semi-overlapping fields of view. The second extension is global, as is aimed at providing local observations performed within the field of view of one camera with a global context relating them to a much larger scene; to this end, an automatic camera positioning system relying only on observed object trajectories and a scene map is designed. The two lines of research in this thesis are addressed using Bayesian estimation as a general unifying framework. Its suitability for these two applications is justified by the flexibility and versatility of that stochastic framework, which allows the combination of multiple sources of information about the parameters to estimate in a natural and elegant way, addressing at the same time the uncertainty associated to those sources through the inclusion of models designed to this end. In addition, it opens multiple possibilities for the creation of different numerical methods for achieving satisfactory and efficient practical solutions to each addressed application. The proposed multi-camera 3D tracking method is specifically designed to work on schematic descriptions of the observations performed by each camera of the system: this choice allows the use of unspecific off-the-shelf 2D detection and/or tracking subsystems running independently at each sensor, and makes the proposal suitable for real surveillance networks with moderate computational and transmission capabilities. The robust combination of such noisy, incomplete and possibly unreliable schematic descriptors relies on a Bayesian association method, based on geometry and color, whose results allow the tracking of the targets in the scene with a particle filter. The main features exhibited by the proposal are, first, a remarkable accuracy in terms of target 3D positioning, and second, a great recovery ability after tracking losses due to insufficient input data. The proposed system for visual-based camera self-positioning uses the observations of moving objects and a schematic map of the passable areas of the environment to infer the absolute sensor position. To this end, a new Bayesian framework combining trajectory observations and map-induced dynamic models for moving objects is designed, which represents an approach to camera positioning never addressed before in the literature. This task is divided into two different sub-tasks, setting ambiguity analysis and approximate position estimation, on the one hand, and position refining, on the other, since they require the design of specific sampling algorithms to correctly exploit the discriminative features of the developed framework. This system, designed for camera positioning and demonstrated in urban traffic environments, can also be applied to different environments and sensors of other modalities after certain required adaptations.

Bayesian scene analysis for multi-camera 3D tracking and camera positioning

Los sistemas de seguimiento mono-cámara han demostrado su notable capacidad para el análisis de trajectorias de objectos móviles y para monitorización de escenas de interés; sin embargo, tanto su robustez como sus posibilidades en cuanto a comprensión semántica de la escena están fuertemente limitadas por su naturaleza local y monocular, lo que los hace insuficientes para aplicaciones realistas de videovigilancia. El objetivo de esta tesis es la extensión de las posibilidades de los sistemas de seguimiento de objetos móviles para lograr un mayor grado de robustez y comprensión de la escena. La extensión propuesta se divide en dos direcciones separadas. La primera puede considerarse local, ya que está orientada a la mejora y enriquecimiento de las posiciones estimadas para los objetos móviles observados directamente por las cámaras del sistema; dicha extensión se logra mediante el desarrollo de un sistema multi-cámara de seguimiento 3D, capaz de proporcionar consistentemente las posiciones 3D de múltiples objetos a partir de las observaciones capturadas por un conjunto de sensores calibrados y con campos de visión solapados. La segunda extensión puede considerarse global, dado que su objetivo consiste en proporcionar un contexto global para relacionar las observaciones locales realizadas por una cámara con una escena de mucho mayor tamaño; para ello se propone un sistema automático de localización de cámaras basado en las trayectorias observadas de varios objetos móviles y en un mapa esquemático de la escena global monitorizada. Ambas líneas de investigación se tratan utilizando, como marco común, técnicas de estimación bayesiana: esta elección está justificada por la versatilidad y flexibilidad proporcionada por dicho marco estadístico, que permite la combinación natural de múltiples fuentes de información sobre los parámetros a estimar, así como un tratamiento riguroso de la incertidumbre asociada a las mismas mediante la inclusión de modelos de observación específicamente diseñados. Además, el marco seleccionado abre grandes posibilidades operacionales, puesto que permite la creación de diferentes métodos numéricos adaptados a las necesidades y características específicas de distintos problemas tratados. El sistema de seguimiento 3D con múltiples cámaras propuesto está específicamente diseñado para permitir descripciones esquemáticas de las medidas realizadas individualmente por cada una de las cámaras del sistema: esta elección de diseño, por tanto, no asume ningún algoritmo específico de detección o seguimiento 2D en ninguno de los sensores de la red, y hace que el sistema propuesto sea aplicable a redes reales de vigilancia con capacidades limitadas tanto en términos de procesamiento como de transmision. La combinación robusta de las observaciones capturadas individualmente por las cámaras, ruidosas, incompletas y probablemente contaminadas por falsas detecciones, se basa en un metodo de asociación bayesiana basado en geometría y color: los resultados de dicha asociación permiten el seguimiento 3D de los objetos de la escena mediante el uso de un filtro de partículas. El sistema de fusión de observaciones propuesto tiene, como principales características, una gran precisión en términos de localización 3D de objetos, y una destacable capacidad de recuperación tras eventuales errores debidos a un número insuficiente de datos de entrada. El sistema automático de localización de cámaras se basa en la observación de múltiples objetos móviles y un mapa esquemático de las áreas transitables del entorno monitorizado para inferir la posición absoluta de dicho sensor. Para este propósito, se propone un novedoso marco bayesiano que combina modelos dinámicos inducidos por el mapa en los objetos móviles presentes en la escena con las trayectorias observadas por la cámara, lo que representa un enfoque nunca utilizado en la literatura existente. El sistema de localización se divide en dos sub-tareas diferenciadas, debido a que cada una de estas tareas requiere del diseño de algoritmos específicos de muestreo para explotar en profundidad las características del marco desarrollado: por un lado, análisis de la ambigüedad del caso específicamente tratado y estimación aproximada de la localización de la cámara, y por otro, refinado de la localización de la cámara. El sistema completo, diseñado y probado para el caso específico de localización de cámaras en entornos de tráfico urbano, podría tener aplicación también en otros entornos y sensores de diferentes modalidades tras ciertas adaptaciones. ABSTRACT Mono-camera tracking systems have proved their capabilities for moving object trajectory analysis and scene monitoring, but their robustness and semantic possibilities are strongly limited by their local and monocular nature and are often insufficient for realistic surveillance applications. This thesis is aimed at extending the possibilities of moving object tracking systems to a higher level of scene understanding. The proposed extension comprises two separate directions. The first one is local, since is aimed at enriching the inferred positions of the moving objects within the area of the monitored scene directly covered by the cameras of the system; this task is achieved through the development of a multi-camera system for robust 3D tracking, able to provide 3D tracking information of multiple simultaneous moving objects from the observations reported by a set of calibrated cameras with semi-overlapping fields of view. The second extension is global, as is aimed at providing local observations performed within the field of view of one camera with a global context relating them to a much larger scene; to this end, an automatic camera positioning system relying only on observed object trajectories and a scene map is designed. The two lines of research in this thesis are addressed using Bayesian estimation as a general unifying framework. Its suitability for these two applications is justified by the flexibility and versatility of that stochastic framework, which allows the combination of multiple sources of information about the parameters to estimate in a natural and elegant way, addressing at the same time the uncertainty associated to those sources through the inclusion of models designed to this end. In addition, it opens multiple possibilities for the creation of different numerical methods for achieving satisfactory and efficient practical solutions to each addressed application. The proposed multi-camera 3D tracking method is specifically designed to work on schematic descriptions of the observations performed by each camera of the system: this choice allows the use of unspecific off-the-shelf 2D detection and/or tracking subsystems running independently at each sensor, and makes the proposal suitable for real surveillance networks with moderate computational and transmission capabilities. The robust combination of such noisy, incomplete and possibly unreliable schematic descriptors relies on a Bayesian association method, based on geometry and color, whose results allow the tracking of the targets in the scene with a particle filter. The main features exhibited by the proposal are, first, a remarkable accuracy in terms of target 3D positioning, and second, a great recovery ability after tracking losses due to insufficient input data. The proposed system for visual-based camera self-positioning uses the observations of moving objects and a schematic map of the passable areas of the environment to infer the absolute sensor position. To this end, a new Bayesian framework combining trajectory observations and map-induced dynamic models for moving objects is designed, which represents an approach to camera positioning never addressed before in the literature. This task is divided into two different sub-tasks, setting ambiguity analysis and approximate position estimation, on the one hand, and position refining, on the other, since they require the design of specific sampling algorithms to correctly exploit the discriminative features of the developed framework. This system, designed for camera positioning and demonstrated in urban traffic environments, can also be applied to different environments and sensors of other modalities after certain required adaptations.

Bayesian network modeling of the consensus between experts: an application to neuron classification

Neuronal morphology is hugely variable across brain regions and species, and their classification strategies are a matter of intense debate in neuroscience. GABAergic cortical interneurons have been a challenge because it is difficult to find a set of morphological properties which clearly define neuronal types. A group of 48 neuroscience experts around the world were asked to classify a set of 320 cortical GABAergic interneurons according to the main features of their three-dimensional morphological reconstructions. A methodology for building a model which captures the opinions of all the experts was proposed. First, one Bayesian network was learned for each expert, and we proposed an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts was induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts was built. A thorough analysis of the consensus model identified different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types was defined by performing inference in the Bayesian multinet. These findings were used to validate the model and to gain some insights into neuron morphology.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Bayesian estimation of g-and-k distributions using MCMC

In this paper we investigate a Bayesian procedure for the estimation of a flexible generalised distribution, notably the MacGillivray adaptation of the g-and-κ distribution. This distribution, described through its inverse cdf or quantile function, generalises the standard normal through extra parameters which together describe skewness and kurtosis. The standard quantile-based methods for estimating the parameters of generalised distributions are often arbitrary and do not rely on computation of the likelihood. MCMC, however, provides a simulation-based alternative for obtaining the maximum likelihood estimates of parameters of these distributions or for deriving posterior estimates of the parameters through a Bayesian framework. In this paper we adopt the latter approach, The proposed methodology is illustrated through an application in which the parameter of interest is slightly skewed.

Approximate processing of massive continuous quantile queries over high-speed data streams

Quantile computation has many applications including data mining and financial data analysis. It has been shown that an is an element of-approximate summary can be maintained so that, given a quantile query d (phi, is an element of), the data item at rank [phi N] may be approximately obtained within the rank error precision is an element of N over all N data items in a data stream or in a sliding window. However, scalable online processing of massive continuous quantile queries with different phi and is an element of poses a new challenge because the summary is continuously updated with new arrivals of data items. In this paper, first we aim to dramatically reduce the number of distinct query results by grouping a set of different queries into a cluster so that they can be processed virtually as a single query while the precision requirements from users can be retained. Second, we aim to minimize the total query processing costs. Efficient algorithms are developed to minimize the total number of times for reprocessing clusters and to produce the minimum number of clusters, respectively. The techniques are extended to maintain near-optimal clustering when queries are registered and removed in an arbitrary fashion against whole data streams or sliding windows. In addition to theoretical analysis, our performance study indicates that the proposed techniques are indeed scalable with respect to the number of input queries as well as the number of items and the item arrival rate in a data stream.

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

Bayesian invariant measurements of generalisation

The problem of evaluating different learning rules and other statistical estimators is analysed. A new general theory of statistical inference is developed by combining Bayesian decision theory with information geometry. It is coherent and invariant. For each sample a unique ideal estimate exists and is given by an average over the posterior. An optimal estimate within a model is given by a projection of the ideal estimate. The ideal estimate is a sufficient statistic of the posterior, so practical learning rules are functions of the ideal estimator. If the sole purpose of learning is to extract information from the data, the learning rule must also approximate the ideal estimator. This framework is applicable to both Bayesian and non-Bayesian methods, with arbitrary statistical models, and to supervised, unsupervised and reinforcement learning schemes.

On the relationship between Bayesian error bars and the input data density

We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions.

Computation with infinite neural networks

For neural networks with a wide class of weight priors, it can be shown that in the limit of an infinite number of hidden units, the prior over functions tends to a gaussian process. In this article, analytic forms are derived for the covariance function of the gaussian processes corresponding to networks with sigmoidal and gaussian hidden units. This allows predictions to be made efficiently using networks with an infinite number of hidden units and shows, somewhat paradoxically, that it may be easier to carry out Bayesian prediction with infinite networks rather than finite ones.

A Bayesian approach to on-line learning

Online learning is discussed from the viewpoint of Bayesian statistical inference. By replacing the true posterior distribution with a simpler parametric distribution, one can define an online algorithm by a repetition of two steps: An update of the approximate posterior, when a new example arrives, and an optimal projection into the parametric family. Choosing this family to be Gaussian, we show that the algorithm achieves asymptotic efficiency. An application to learning in single layer neural networks is given.

A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.