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Spreadsheet workbook contents are simple programs. Because of this, probabilistic programming techniques can be used to perform Bayesian inversion of spreadsheet computations. What is more, existing execution engines in spreadsheet applications such as Microsoft Excel can be made to do this using only built-in functionality. We demonstrate this by developing a native Excel implementation of both a particle Markov Chain Monte Carlo variant and black-box variational inference for spreadsheet probabilistic programming. The resulting engine performs probabilistically coherent inference over spreadsheet computations, notably including spreadsheets that include user-defined black-box functions. Spreadsheet engines that choose to integrate the functionality we describe in this paper will give their users the ability to both easily develop probabilistic models and maintain them over time by including actuals via a simple user-interface mechanism. For spreadsheet end-users this would mean having access to efficient and probabilistically coherent probabilistic modeling and inference for use in all kinds of decision making under uncertainty.

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.

This work seeks to understand the connections between learning and decision making under uncertainty. Specifically, we ask that question: when we are going to use learned models within the loop of a larger decision making process, how should we alter the learning procedure or somehow tune the learning to the specific needs of the actual decision making task? To answer this question, we developed a theory of task based model learning, learning models tuned not (just) for predictive accuracy, but to optimize the closed loop performance of a decision making procedure (specifically, those based on stochastic optimization) that uses these models as an intermediate step. Training such models requires that we differentiate through an optimization problem, for which we developed the theory and implementations. On several tasks, we show that such learning substantially outperforms traditional learning processes, where the learning and decision making stages are separate.

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages to facilitate their modeling. Most of the existing probabilistic languages, however, focus only on discrete distributions, and there has been little effort to develop probabilistic languages whose expressive power is beyond discrete distributions. This dissertation presents a probabilistic language, called PTP (ProbabilisTic Programming), which supports all kinds of probability distributions. The key idea behind PTP is to use sampling functions, i.e., mappings from the unit interval (0.0, 1.0] to probability domains, to specify probability distributions. By using sampling functions as its mathematical basis, PTP provides a unified representation scheme for probability distributions, without drawing a syntactic or semantic distinction between different kinds of probability distributions. Independently of PTP, we develop a linguistic framework to account for computational effects in general. [The framework] extends a monadic language by applying the possible world interpretation of modal logic. A characteristic feature of [the framework] is the distinction between stateful computational effects, called world effects, and contextual computational effects, called control effects. PTP arises as an instance of [the framework] with a language construct for probabilistic choices. We use a sound and complete translator of PTP to embed it in Objective CAML. The use of PTP is demonstrated with three applications in robotics: robot localization, people tracking, and robotic mapping. Thus PTP serves as another example of high-level language applied to a problem domain where imperative languages have been traditionally dominant.

We study machine learning formulations of inductive program synthesis; that is, given input-output examples, synthesize source code that maps inputs to corresponding outputs. Our key contribution is TerpreT, a domain-specific language for expressing program synthesis problems. A TerpreT model is composed of a specification of a program representation and an interpreter that describes how programs map inputs to outputs. The inference task is to observe a set of input-output examples and infer the underlying program. From a TerpreT model we automatically perform inference using four different back-ends: gradient descent (thus each TerpreT model can be seen as defining a differentiable interpreter), linear program (LP) relaxations for graphical models, discrete satisfiability solving, and the Sketch program synthesis system. TerpreT has two main benefits. First, it enables rapid exploration of a range of domains, program representations, and interpreter models. Second, it separates the model specification from the inference algorithm, allowing proper comparisons between different approaches to inference. We illustrate the value of TerpreT by developing several interpreter models and performing an extensive empirical comparison between alternative inference algorithms on a variety of program models. To our knowledge, this is the first work to compare gradient-based search over program space to traditional search-based alternatives. Our key empirical finding is that constraint solvers dominate the gradient descent and LP-based formulations. This is a workshop summary of a longer report at arXiv:1608.04428

Static alias analysis of different type of programming languages has been drawing researcher attention. However most of the results of existing techniques for alias analysis are not precise enough compared to needs of modern compilers. Probabilistic versions of these results, in which result elements are associated with occurrence probabilities, are required in optimizations techniques of modern compilers. This paper presents a new probabilistic approach for alias analysis of parallel programs. The treated parallelism model is that of SPMD where in SPMD, a program is executed using a fixed number of program threads running on distributed machines on different data. The analyzed programs are assumed to be in the static single assignment (SSA) form which is a program representation form facilitating program analysis. The proposed technique has the form of simply-strictured system of inference rules. This enables using the system in applications like Proof-Carrying Code (PPC) which is a general technique for proving the safety characteristics of modern programs.

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution is to adapt the classic operational semantics of lambda-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distribution-based semantics. To move closer to inference techniques, we also define the sampling-based semantics of a term as a function from a trace of random samples to a value. We show that the distribution induced by integrating over all traces equals the distribution-based semantics. Our second contribution is to formalize the implementation technique of trace Markov chain Monte Carlo (MCMC) for our calculus and to show its correctness. A key step is defining sufficient conditions for the distribution induced by trace MCMC to converge to the distribution-based semantics. To the best of our knowledge, this is the first rigorous correctness proof for trace MCMC for a higher-order functional language.

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution is to adapt the classic operational semantics of lambda-calculus to a continuous setting via creating a measure space on terms and defining step-indexed approximations. We prove equivalence of big-step and small-step formulations of this distribution-based semantics. To move closer to inference techniques, we also define the sampling-based semantics of a term as a function from a trace of random samples to a value. We show that the distribution induced by integrating over all traces equals the distribution-based semantics. Our second contribution is to formalize the implementation technique of trace Markov chain Monte Carlo (MCMC) for our calculus and to show its correctness. A key step is defining sufficient conditions for the distribution induced by trace MCMC to converge to the distribution-based semantics. To the best of our knowledge, this is the first rigorous correctness proof for trace MCMC for a higher-order functional language.

Forward inference techniques such as sequential Monte Carlo and particle Markov chain Monte Carlo for probabilistic programming can be implemented in any programming language by creative use of standardized operating system functionality including processes, forking, mutexes, and shared memory. Exploiting this we have defined, developed, and tested a probabilistic programming language intermediate representation language we call probabilistic C, which itself can be compiled to machine code by standard compilers and linked to operating system libraries yielding an efficient, scalable, portable probabilistic programming compilation target. This opens up a new hardware and systems research path for optimizing probabilistic programming systems.

This Final Report summarizes the research conducted in the course of DARPA PPAML program, which was focused on enabling the use of discriminative solvers to solve discriminative tasks specified in probabilistic programs. The research produced two complementary methods of constructive discriminative solvers: model-driven and data-driven ones: research frameworks and software implementations) in both generative and discriminative areas: Generative models: a novel framework for most accurate computation of key statistical elements of model-driven problems (such as conditional probability, regression, etc.) Discriminative models: a novel framework for capturing domain knowledge in the form of features and kernels for standard data-driven problems (solved in LUPI approaches). These achievements are described in in this report and in 9 papers published in the course of DARPA PPAML program.

Generative Models are the Swiss Army Knife for the Decision Scientist. Generative models allow the simulation of scenarios based on different business hypotheses (Bayesian priors). With Probabilistic Programming, decision makers can simulate the impact of business drivers in times of great uncertainty. Furthermore, Probabilistic Programming Languages provide all the inference tools necessary to identify the assumptions that have most likely generated an outcome. Inference is a statistical tool that enables optimal decision-making based on models that explicitly quantify uncertainty. Generative models of key optimization parameters are necessary input to Robust Optimization and Stochastic Programming problems. Python provides all the tools to successfully integrate Probabilitistic Programs with Robust and Stochastic Optimization and therefore cope with high uncertainty in optimization. Please see our speaker release agreement for details: https://ep2020.europython.eu/events/speaker-release-agreement/

Thomas Wiecki - Probabilistic Programming in Python [EuroPython 2014] [24 July 2014] Probabilistic Programming allows flexible specification of statistical models to gain insight from data. The high interpretability and ease by which different sources can be combined has huge value for Data Science. PyMC3 features next generation sampling algorithms, an intuitive model specification syntax, and just-in-time compilation for speed, to allow estimation of large-scale probabilistic models. ----- Probabilistic Programming allows flexible specification of statistical models to gain insight from data. Estimation of best fitting parameter values, as well as uncertainty in these estimations, can be automated by sampling algorithms like Markov chain Monte Carlo (MCMC). The high interpretability and flexibility of this approach has lead to a huge paradigm shift in scientific fields ranging from Cognitive Science to Data Science and Quantitative Finance. PyMC3 is a new Python module that features next generation sampling algorithms and an intuitive model specification syntax. The whole code base is written in pure Python and Just-in-time compiled via Theano for speed. In this talk I will provide an intuitive introduction to Bayesian statistics and how probabilistic models can be specified and estimated using PyMC3.

Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute interesting probabilities of various large, real-world problems. When the structure of model is given, constructing a probabilistic program is rather straightforward. Thus, main focus have been to learn the best model parameters and compute marginal probabilities. In this paper, we provide a new perspective to build expressive probabilistic program from continue time series data when the structure of model is not given. The intuition behind of our method is to find a descriptive covariance structure of time series data in nonparametric Gaussian process regression. We report that such descriptive covariance structure efficiently derives a probabilistic programming description accurately.

Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or summarize statistically. However, in many real-world applications, these simulations need to be inverted to match the observed data. This typically requires the custom design, derivation and implementation of sophisticated inversion algorithms. Here we give a framework for inverting a broad class of complex software simulators via probabilistic programming and automatic inference, using under 20 lines of probabilistic code. Our approach is based on a formulation of inversion as approximate inference in a simple sequential probabilistic model. We implement four inference strategies, including Metropolis-Hastings, a sequentialized Metropolis-Hastings scheme, and a particle Markov chain Monte Carlo scheme, requiring 4 or fewer lines of probabilistic code each. We demonstrate our framework by applying it to invert a real geological software simulator from the oil and gas industry.

We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic programming and deep learning methods. We call what we do "compilation of inference" because our method transforms a denotational specification of an inference problem in the form of a probabilistic program written in a universal programming language into a trained neural network denoted in a neural network specification language. When at test time this neural network is fed observational data and executed, it performs approximate inference in the original model specified by the probabilistic program. Our training objective and learning procedure are designed to allow the trained neural network to be used as a proposal distribution in a sequential importance sampling inference engine. We illustrate our method on mixture models and Captcha solving and show significant speedups in the efficiency of inference.

Is it possible to make statistical inference broadly accessible to non-statisticians without sacrificing mathematical rigor or inference quality? This paper describes BayesDB, a probabilistic programming platform that aims to enable users to query the probable implications of their data as directly as SQL databases enable them to query the data itself. This paper focuses on four aspects of BayesDB: (i) BQL, an SQL-like query language for Bayesian data analysis, that answers queries by averaging over an implicit space of probabilistic models; (ii) techniques for implementing BQL using a broad class of multivariate probabilistic models; (iii) a semi-parametric Bayesian model-builder that auomatically builds ensembles of factorial mixture models to serve as baselines; and (iv) MML, a "meta-modeling" language for imposing qualitative constraints on the model-builder and combining baseline models with custom algorithmic and statistical models that can be implemented in external software. BayesDB is illustrated using three applications: cleaning and exploring a public database of Earth satellites; assessing the evidence for temporal dependence between macroeconomic indicators; and analyzing a salary survey.

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are i.i.d. Gaussian variables, we compute the distribution of the convergence rate to the attracting fixed point. Using the framework of Random Matrix Theory, we derive a simple expression for this distribution in the asymptotic limit of large problem size. In this limit, we find that the distribution of the convergence rate is a scaling function, namely it is a function of one variable that is a combination of three parameters: the number of variables, the number of constraints and the convergence rate, rather than a function of these parameters separately. We also estimate numerically the distribution of computation times, namely the time required to reach a vicinity of the attracting fixed point, and find that it is also a scaling function. Using the problem size dependence of the distribution functions, we derive high probability bounds on the convergence rates and on the computation times.

We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate inference algorithm which returns hard lower and upper bounds on the exact probability. We experimentally show that this method outperforms state-of-the-art approximate inference.

We propose Edward, a Turing-complete probabilistic programming language. Edward defines two compositional representations---random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the same model using a variety of composable inference methods, ranging from point estimation to variational inference to MCMC. In addition, Edward can reuse the modeling representation as part of inference, facilitating the design of rich variational models and generative adversarial networks. For efficiency, Edward is integrated into TensorFlow, providing significant speedups over existing probabilistic systems. For example, we show on a benchmark logistic regression task that Edward is at least 35x faster than Stan and 6x faster than PyMC3. Further, Edward incurs no runtime overhead: it is as fast as handwritten TensorFlow.

We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and for learning of such weights from data (parameter estimation). Weighted formulas are given a semantics in terms of soft and hard constraints which determine a probability distribution over answer sets. In contrast to related approaches, we approach inference by optionally utilizing so-called streamlining XOR constraints, in order to reduce the number of computed answer sets. Our approach is prototypically implemented. Examples illustrate the introduced concepts and point at issues and topics for future research.

Databases are widespread, yet extracting relevant data can be difficult. Without substantial domain knowledge, multivariate search queries often return sparse or uninformative results. This paper introduces an approach for searching structured data based on probabilistic programming and nonparametric Bayes. Users specify queries in a probabilistic language that combines standard SQL database search operators with an information theoretic ranking function called predictive relevance. Predictive relevance can be calculated by a fast sparse matrix algorithm based on posterior samples from CrossCat, a nonparametric Bayesian model for high-dimensional, heterogeneously-typed data tables. The result is a flexible search technique that applies to a broad class of information retrieval problems, which we integrate into BayesDB, a probabilistic programming platform for probabilistic data analysis. This paper demonstrates applications to databases of US colleges, global macroeconomic indicators of public health, and classic cars. We found that human evaluators often prefer the results from probabilistic search to results from a standard baseline.

The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.

Probabilistic programming (PP) allows flexible specification of Bayesian statistical models in code. PyMC3 is a new, open-source PP framework with an intutive and readable, yet powerful, syntax that is close to the natural syntax statisticians use to describe models. It features next-generation Markov chain Monte Carlo (MCMC) sampling algorithms such as the No-U-Turn Sampler (NUTS; Hoffman, 2014), a self-tuning variant of Hamiltonian Monte Carlo (HMC; Duane, 1987). Probabilistic programming in Python confers a number of advantages including multi-platform compatibility, an expressive yet clean and readable syntax, easy integration with other scientific libraries, and extensibility via C, C++, Fortran or Cython. These features make it relatively straightforward to write and use custom statistical distributions, samplers and transformation functions, as required by Bayesian analysis.

Machine learning the ability of computers to understand data, manage results and infer insights from uncertain information is the force behind many recent revolutions in computing. Email spam filters, smartphone personal assistants and self-driving vehicles are all based on research advances in machine learning. Unfortunately, even as the demand for these capabilities is accelerating, every new application requires a Herculean effort. Teams of hard-to-find experts must build expensive, custom tools that are often painfully slow and can perform unpredictably against large, complex data sets. This project developed new algorithms for statistical inference in continuous-time probabilistic models. This report first reviews background on continuous-time models and then covers each of the research projects and their deliverables. The full details are covered in the technical papers, included as appendices.

Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP) methods were proposed to overcome this issue through a probability model that captures the structure of the fit individuals and use it to sample new individuals. This work proposes the use of LGP with a Stochastic Context-Free Grammar (SCFG), that has a probability distribution that is updated according to selected individuals. We proposed a method for adapting the grammar into the linear representation of LGP. Tests performed with the proposed probabilistic method, and with two hybrid approaches, on several symbolic regression benchmark problems show that the results are statistically better than the obtained by the traditional LGP.

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP$^2$ for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous non-asymptotic results for LDPC codes, and in particular exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a generalized matching. An interesting by-product of our analysis is to establish the existence of ``probabilistic expansion'' in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst-case setting.

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly structured distributions that arise in probabilistic programs. We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms.

We investigate the semantic intricacies of conditioning, a main feature in probabilistic programming. We provide a weakest (liberal) pre-condition (w(l)p) semantics for the elementary probabilistic programming language pGCL extended with conditioning. We prove that quantitative weakest (liberal) pre-conditions coincide with conditional (liberal) expected rewards in Markov chains and show that semantically conditioning is a truly conservative extension. We present two program transformations which entirely eliminate conditioning from any program and prove their correctness using the w(l)p-semantics. Finally, we show how the w(l)p-semantics can be used to determine conditional probabilities in a parametric anonymity protocol and show that an inductive w(l)p-semantics for conditioning in non-deterministic probabilistic programs cannot exist.

The bibliography is intended to summarize the available literature on 'Two-Stage Linear Programming Under Uncertainty' for the period January, 1964 through August, 1969. Each of the 47 entries presents a summary of the principal thoughts of the article reviewed, headed by a complete bibliographic reference based upon the most up-to-date information available. Alternate sources are quoted as a part of each entry. All entries are cross indexed by author and title relative to the primary chronological order sequence.

Constructing lineages of malware is an important cyber-defense task. Performing this task is difficult, however, due to the amount of malware data and obfuscation techniques by the authors. In this work, we formulate the lineage task as a probabilistic model, and use a novel probabilistic programming solution to jointly infer the lineage and creation times of families of malware.

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow identifying which forces and mechanisms are responsible for the appearance of given structural properties. In spite of this interest, several problems remain open, one of the most important being the design of robust mechanisms for finding the optimal parameters of a generative model, given a set of real networks. In this contribution, we address this problem by means of Probabilistic Constraint Programming. By using as an example the reconstruction of networks representing brain dynamics, we show how this approach is superior to other solutions, in that it allows a better characterisation of the parameters space, while requiring a significantly lower computational cost.

We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL*). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations.

The distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog. When a program contains functions symbols, the distribution semantics is well-defined only if the set of explanations for a query is finite and so is each explanation. Well-definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper we identify a larger class of programs for which the semantics is well-defined together with an efficient procedure for computing the probability of queries. Since LPADs offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE, PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

Probabilistic programming languages allow a modeler to build probabilistic models using complex data structures with all the power of a programming language. We present CTPPL, an expressive probabilistic programming language for dynamic processes that models processes using continuous time. Time is a first class element in our language the amount of time taken by a subprocess can be specified using the full power of the language. We show through examples that CTPPL can easily represent existing continuous time frameworks and makes it easy to represent new ones. We present semantics for CTPPL in terms of a probability measure over trajectories. We present a particle filtering algorithm for the language that works for a large and useful class of CTPPL programs.

Lara Kattan https://www.pyohio.org/2019/presentations/116 Let's build up our knowledge of probabilistic programming and Bayesian inference! All you need to start is basic knowledge of linear regression; familiarity with running a model of any type in Python is helpful. By the end of this presentation, you'll know the following: - What probabilistic programming is and why it's necessary for Bayesian inference - What Bayesian inference is, how it's different from classical frequentist inference, and why it's becoming so relevant for applied data science in the real world - How to write your own Bayesian models in the Python library PyMC3, including metrics for judging how well the model is performing - How to go about learning more about the topic of Bayesian inference and how to bring it to your current data science job We'll meet our objectives by answering three questions: 1. What is probabilistic programming? * PP is the idea that we can use computer code to build probability distributions * Theory of the primitives in probabilistic programming and how we can build models out of distributions 2. What is Bayesian inference and why should I add it to my toolbox on top of classical ML models? * Classically, we had simulations, but they run in only one direction: get data input and move it according to assumptions of parameters and get a prediction * Bayesian inference adds another direction: use the data to go back and pick one of many possible parameters as the most likely to have created the data (posterior distributions) * Use Bayes' theorem to find the most likely values of the model parameters 3. What is PyMC3 and how can I start building and interpreting models using it? * **We'll work through actual examples of models using PyMC3, including hierarchical models** * Solving Bayes' theorem in practice requires taking integrals * If we don't want to do integrals by hand, we need to use numerical solution methods * From the package authors: "[PyMC3 is an ]open source probabilistic programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed" The intention is to get hands-on experience building PyMC3 models to demystify probabilistic programming / Bayesian inference for those more well versed in traditional ML, and, most importantly, to understand how these models can be relevant in our daily work as data scientists in business. If you can write a model in sklearn, you can make the leap to Bayesian inference with PyMC3, a user-friendly intro to probabilistic programming (PP) in Python. PP just means building models where the building blocks are probability distributions! And we can use PP to do Bayesian inference easily. Bayesian inference allows us to solve problems that aren't otherwise tractable with classical methods. === https://pyohio.org A FREE annual conference for anyone interested in Python in and around Ohio, the entire Midwest, maybe even the whole world. Produced by NDV: https://youtube.com/channel/UCQ7dFBzZGlBvtU2hCecsBBg?sub_confirmation=1 Sun Jul 28 13:15:00 2019 at Suzanne Scharer

This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

Probabilistic Programming allows flexible specification of statistical models to gain insight from data. Estimation of best fitting parameter values, as well as uncertainty in these estimations, can be automated by sampling algorithms like Markov chain Monte Carlo (MCMC). The high interpretability and flexibility of this approach has lead to a huge paradigm shift in scientific fields ranging from Cognitive Science to Data Science and Quantitative Finance. PyMC3 is a new Python module that features next generation sampling algorithms and an intuitive model specification syntax. The whole code base is written in pure Python and Just-in-time compiled via Theano for speed. In this talk I will provide an intuitive introduction to Bayesian statistics and how probabilistic models can be specified and estimated using PyMC3.

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato's distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. To achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. They involve measure theory, stochastic labelled transition systems, and functor categories, but admit intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties.

We introduce the first, general purpose, slice sampling inference engine for probabilistic programs. This engine is released as part of StocPy, a new Turing-Complete probabilistic programming language, available as a Python library. We present a transdimensional generalisation of slice sampling which is necessary for the inference engine to work on traces with different numbers of random variables. We show that StocPy compares favourably to other PPLs in terms of flexibility and usability, and that slice sampling can outperform previously introduced inference methods. Our experiments include a logistic regression, HMM, and Bayesian Neural Net.

We introduce and demonstrate a new approach to inference in expressive probabilistic programming languages based on particle Markov chain Monte Carlo. Our approach is simple to implement and easy to parallelize. It applies to Turing-complete probabilistic programming languages and supports accurate inference in models that make use of complex control flow, including stochastic recursion. It also includes primitives from Bayesian nonparametric statistics. Our experiments show that this approach can be more efficient than previously introduced single-site Metropolis-Hastings methods.

This is a response to the article 'Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition' (25) in which Professors Hogan, Morris and Thompson (HMT hereafter) recommend abandonment of Chance Constrained Programming (=CCP) in favor of Stochastic Programming with Recourse (=SPR)--which we shall also refer to as 2-stage Linear Programming Under Uncertainty (=LPUU) since this is the main variant of SPR which is relied upon for these conclusions in (25). In the interest of clarity and brevity, we do not pursue all of the topics covered in (25) since, as will become evident, a rather lengthy response is required to chase down even major issues. We also believe that (25) is directed to conceptual rather than practical issues of application and so, also for brevity, we brush aside qualifiers that appear in statements like the following: 'We wish to emphasize that recourse problems characterize almost all (sic) real decision problems involving risk.' Except for possibly affording some degree of protection to HMT, we do not see that such qualifiers serve any useful purpose.

In the probabilistic-programming paradigm, the application logic is specified by means of a description of a probabilistic model (by stating how a sample is being produced) using a Probabilistic Programming Language (PPL). The principal value one obtains from a probabilistic program lies in the inference thereof, that is, reasoning about the entire probability distribution that the program defines (e.g., finding a likely event or estimating its marginal probability). The PPAML kickoff meeting highlighted several research challenges regarding the development of inference infrastructure for PPL, for both increasing software efficiency and reducing software complexity, towards the goal of broadening the PPL applications and the community of implementers and programmers. These challenges include the design of an Application Program Interface (API), or alternatively an Intermediate Representation Language (IRL), that would allow new solvers to be plugged into existing PPLs, and for PPL engines to be able to pick from and combine solvers for a given problem.

This Bachelor's thesis, written in Russian, is devoted to a relatively new direction in the field of machine learning and artificial intelligence, namely probabilistic programming. The thesis gives a brief overview to the already existing probabilistic programming languages: Church, Venture, and Anglican. It also describes the results of the first experiments on the automatic induction of probabilistic programs. The thesis was submitted, in June 2014, in partial fulfilment of the requirements for the degree of Bachelor of Science in Mathematics in the Department of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia. The work, which is described in this thesis, has been performing in 2012-2014 in the Massachusetts Institute of Technology and in the University of Oxford by the colleagues of the author and by himself.

The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and $m$ constraints ($n>m$), where all elements of the vectors and matrices are normally distributed is studied. The convergence time of a flow to the fixed point representing the optimal solution is computed. The cumulative distribution ${\cal F}^{(n,m)}(\Delta)$ of the convergence rate $\Delta_{min}$ to this point is calculated analytically, in the asymptotic limit of large $(n,m)$, in the framework of Random Matrix Theory. In this limit ${\cal F}^{(n,m)}(\Delta)$ is found to be a scaling function, namely it is a function of one variable that is a combination of $n$, $m$ and $\Delta$ rather then a function of these three variables separately. From numerical simulations also the distribution of the computation times is calculated and found to be a scaling function as well.

Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.

Machine Learning has demonstrated the potential to transform many areas of science, commerce, and the military. However, creating and maintaining successful machine learning systems is an arduous task that requires a doctoral degree and heroic software engineering efforts. Probabilistic Programming for Advancing Machine Learning (PPAML) by creating probabilistic programming systems and associated solvers-aimed to make existing machine learning applications easier to build and to greatly extend the range of problems that can be successfully solved by machine learning. This effort acted as the voice of the user: (a) exposing the probabilistic programming, machine learning and inference engine performers to a breadth of user scenarios over a wide a variety of domains, (b) evaluated and produced feedback on PPS tools to enable the performer teams to understand user perspectives and spur them to enhance their PPS for future users, and (c) developed a community of users in multiple distinct application areas who are invested in the future developments of PPSs.

In this paper we explore the application of some notable Boolean methods, namely the Disjunctive Normal Form representation of logic table expansions, and apply them to a real-valued logic model which utilizes quantities on the range [0,1] to produce a probabilistic programming of a game character's logic in mathematical form.

Existing decision-theoretic reasoning frameworks such as decision networks use simple data structures and processes. However, decisions are often made based on complex data structures, such as social networks and protein sequences, and rich processes involving those structures. We present a framework for representing decision problems with complex data structures using probabilistic programming, allowing probabilistic models to be created with programming language constructs such as data structures and control flow. We provide a way to use arbitrary data types with minimal effort from the user, and an approximate decision-making algorithm that is effective even when the information space is very large or infinite. Experimental results show our algorithm working on problems with very large information spaces.