262 research outputs found

    Deterministic stream-sampling for probabilistic programming: semantics and verification

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    Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving that they generate samples from the correct distribution - is crucial to the use of probabilistic programming languages for statistical modelling and inference. However, the typical denotational semantics of probabilistic programs is incompatible with deterministic notions of sampling. This is problematic, considering that most statistical inference is performed using pseudorandom number generators.We present a higher-order probabilistic programming language centred on the notion of samplers and sampler operations. We give this language an operational and denotational semantics in terms of continuous maps between topological spaces. Our language also supports discontinuous operations, such as comparisons between reals, by using the type system to track discontinuities. This feature might be of independent interest, for example in the context of differentiable programming.Using this language, we develop tools for the formal verification of sampler correctness. We present an equational calculus to reason about equivalence of samplers, and a sound calculus to prove semantic correctness of samplers, i.e. that a sampler correctly targets a given measure by construction

    The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

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    We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results

    Managing distributed situation awareness in a team of agents

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    The research presented in this thesis investigates the best ways to manage Distributed Situation Awareness (DSA) for a team of agents tasked to conduct search activity with limited resources (battery life, memory use, computational power, etc.). In the first part of the thesis, an algorithm to coordinate agents (e.g., UAVs) is developed. This is based on Delaunay triangulation with the aim of supporting efficient, adaptable, scalable, and predictable search. Results from simulation and physical experiments with UAVs show good performance in terms of resources utilisation, adaptability, scalability, and predictability of the developed method in comparison with the existing fixed-pattern, pseudorandom, and hybrid methods. The second aspect of the thesis employs Bayesian Belief Networks (BBNs) to define and manage DSA based on the information obtained from the agents' search activity. Algorithms and methods were developed to describe how agents update the BBN to model the system’s DSA, predict plausible future states of the agents’ search area, handle uncertainties, manage agents’ beliefs (based on sensor differences), monitor agents’ interactions, and maintains adaptable BBN for DSA management using structural learning. The evaluation uses environment situation information obtained from agents’ sensors during search activity, and the results proved superior performance over well-known alternative methods in terms of situation prediction accuracy, uncertainty handling, and adaptability. Therefore, the thesis’s main contributions are (i) the development of a simple search planning algorithm that combines the strength of fixed-pattern and pseudorandom methods with resources utilisation, scalability, adaptability, and predictability features; (ii) a formal model of DSA using BBN that can be updated and learnt during the mission; (iii) investigation of the relationship between agents search coordination and DSA management

    Deterministic stream-sampling for probabilistic programming: semantics and verification

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    Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving that they generate samples from the correct distribution - is crucial to the use of probabilistic programming languages for statistical modelling and inference. However, the typical denotational semantics of probabilistic programs is incompatible with deterministic notions of sampling. This is problematic, considering that most statistical inference is performed using pseudorandom number generators. We present a higher-order probabilistic programming language centred on the notion of samplers and sampler operations. We give this language an operational and denotational semantics in terms of continuous maps between topological spaces. Our language also supports discontinuous operations, such as comparisons between reals, by using the type system to track discontinuities. This feature might be of independent interest, for example in the context of differentiable programming. Using this language, we develop tools for the formal verification of sampler correctness. We present an equational calculus to reason about equivalence of samplers, and a sound calculus to prove semantic correctness of samplers, i.e. that a sampler correctly targets a given measure by construction.Comment: Extended version of LiCS 2023 pape

    Vielfalt und Integration - diversitĂĄ ed integrazione - diversitĂ© et intĂ©gration: Sprache(n) in sozialen und digitalen RĂ€umen: Eine Festschrift fĂŒr Elisabeth Burr

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    Diese Festschrift fĂŒr Elisabeth Burr stellt Vielfalt und Integration in der Sprachwissenschaft und in den Digital Humanities in den Mittelpunkt. Die BeitrĂ€ge berĂŒhren zentrale Fragen im Schaffen Burrs: Wie kann Sprache und ihre Variation in AbhĂ€ngigkeit von sozialen und geographischen Faktoren adĂ€quat beschrieben werden? Wie lassen sich informatische und digitale ZugĂ€nge dafĂŒr nutzen? VerknĂŒpft werden sie mit ihr wichtigen und aktuellen Themen aus Sozio-, Gender- und Korpuslinguistik, Dialektologie und Sprachgeographie sowie den digitalen Geisteswissenschaften. Die Beitragenden sind u. a. Stefania Spina, Thomas Krefeld, Annette Gerstenberg, Lazslo Hinyadi, Carol Chiodo und Lauren Tilton, Manuel Burghardt, Øyvind Eide, JĂŒrgen Hermes, Andreas Witt. Ray Siemens, Arianna Ciula, Alejandro BĂ­a sowie Rob Evans

    Evaluating footwear “in the wild”: Examining wrap and lace trail shoe closures during trail running

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    Trail running participation has grown over the last two decades. As a result, there have been an increasing number of studies examining the sport. Despite these increases, there is a lack of understanding regarding the effects of footwear on trail running biomechanics in ecologically valid conditions. The purpose of our study was to evaluate how a Wrap vs. Lace closure (on the same shoe) impacts running biomechanics on a trail. Thirty subjects ran a trail loop in each shoe while wearing a global positioning system (GPS) watch, heart rate monitor, inertial measurement units (IMUs), and plantar pressure insoles. The Wrap closure reduced peak foot eversion velocity (measured via IMU), which has been associated with fit. The Wrap closure also increased heel contact area, which is also associated with fit. This increase may be associated with the subjective preference for the Wrap. Lastly, runners had a small but significant increase in running speed in the Wrap shoe with no differences in heart rate nor subjective exertion. In total, the Wrap closure fit better than the Lace closure on a variety of terrain. This study demonstrates the feasibility of detecting meaningful biomechanical differences between footwear features in the wild using statistical tools and study design. Evaluating footwear in ecologically valid environments often creates additional variance in the data. This variance should not be treated as noise; instead, it is critical to capture this additional variance and challenges of ecologically valid terrain if we hope to use biomechanics to impact the development of new products

    Statistical learning of random probability measures

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    The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle

    Quantitative Verification and Synthesis of Resilient Networks

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    Curry and Howard Meet Borel

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    We show that an intuitionistic version of counting propositional logic corresponds, in the sense of Curry and Howard, to an expressive type system for the probabilistic eventcalculus, a vehicle calculus in which both call-by-name and call-by-value evaluation of discrete randomized functional programs can be simulated. Remarkably, proofs (respectively, types) do not only guarantee that validity (respectively, termination) holds, but also reveal the underlying probability. We finally show that by endowing the type system with an intersection operator, one obtains a system precisely capturing the probabilistic behavior of-terms
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