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probabilistic programming in Python using PyMC3

PEERJ COMPUTER SCIENCE 2016年第4期2016卷

作者： Salvatier, John Wiecki, Thomas, V Fonnesbeck, Christopher AI Impacts Berkeley CA USA Quantopian Inc Boston MA 02110 USA Vanderbilt Univ Dept Biostat 221 Kirkland Hall Nashville TN 37235 USA

probabilistic programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamiltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new 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. Contrary to other probabilistic programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.

关键词： Bayesian statistic probabilistic programming Python Markov chain Monte Carlo Statistical modeling

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A probabilistic programming Approach for Outlier Detection in Healthcare Claims 15

A Probabilistic Programming Approach for Outlier Detection i...

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15th IEEE International Conference on Machine Learning and Applications (ICMLA)

作者： Bauder, Richard A. Khoshgoftaar, Taghi M. Florida Atlantic Univ Boca Raton FL 33431 USA

ISBN: (纸本)9781509061679

Healthcare is an integral component in people's lives, especially for the rising elderly population. Medicare is one such healthcare program that provides for the needs of the elderly. It is imperative that these healthcare programs are affordable, but this is not always the case. Out of the many possible factors for the rising cost of healthcare, claims fraud is a major contributor, but its impact can be lessened through effective fraud detection. We propose a general outlier detection model, based on Bayesian inference, using probabilistic programming. Our model provides probability distributions rather than just point values, as with most common outlier detection methods. Credible intervals are also generated to further enhance confidence that the detected outliers should in fact be considered outliers. Two case studies are presented demonstrating our model's effectiveness in detecting outliers. The first case study uses temperature data in order to provide a clear comparison of several outlier detection techniques. The second case study uses a Medicare dataset to showcase our proposed outlier detection model. Our results show that the successful detection of outliers, which indicate possible fraudulent activities, can provide effective and meaningful results for further investigation within medical specialties or by using real-world, medical provider fraud investigation cases.

关键词： Fraud Detection Outlier Detection Healthcare Fraud Bayesian Inference probabilistic programming

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Gen: A General-Purpose probabilistic programming System with Programmable Inference 2019

Gen: A General-Purpose Probabilistic Programming System with...

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40th ACM SIGPLAN Conference on programming Language Design and Implementation (PLDI) part of ACM's Federated Computing Research Conference (FCRC)

作者： Cusumano-Towner, Marco F. Saad, Feras A. Lew, Alexander K. Mansinghka, Vikash K. MIT Cambridge MA 02139 USA

ISBN: (纸本)9781450367127

Although probabilistic programming is widely used for some restricted classes of statistical models, existing systems lack the flexibility and efficiency needed for practical use with more challenging models arising in fields like computer vision and robotics. This paper introduces Gen, a generalpurpose probabilistic programming system that achieves modeling flexibility and inference efficiency via several novel language constructs: (i) the generative function interface for encapsulating probabilistic models;(ii) interoperable modeling languages that strike different flexibility/efficiency tradeoffs;(iii) combinators that exploit common patterns of conditional independence;and (iv) an inference library that empowers users to implement efficient inference algorithms at a high level of abstraction. We show that Gen outperforms state-of-the-art probabilistic programming systems, sometimes by multiple orders of magnitude, on diverse problems including object tracking, estimating 3D body pose from a depth image, and inferring the structure of a time series.

关键词： probabilistic programming Markov chain Monte Carlo sequential Monte Carlo variational inference

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Optimization Framework with Minimum Description Length Principle for probabilistic programming 8th

Optimization Framework with Minimum Description Length Princ...

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8th International Conference on Artificial General Intelligence (AGI)

作者： Potapov, Alexey Batishcheva, Vita Rodionov, Sergey ITMO Univ St Petersburg Russia St Petersburg State Univ St Petersburg 199034 Russia AIDEUS Moscow Russia Aix Marseille Univ CNRS UMR 7326 LAM F-13388 Marseille France

ISBN: (纸本)9783319213651;9783319213644

Application of the Minimum Description Length principle to optimization queries in probabilistic programming was investigated on the example of the C++ probabilistic programming library under development. It was shown that incorporation of this criterion is essential for optimization queries to behave similarly to more common queries performing sampling in accordance with posterior distributions and automatically implementing the Bayesian Occam's razor. Experimental validation was conducted on the task of blood cell detection on microscopic images. Detection appeared to be possible using genetic programming query, and automatic penalization of candidate solution complexity allowed to choose the number of cells correctly avoiding overfitting.

关键词： probabilistic programming MDL Image interpretation AGI

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Etalumis: Bringing probabilistic programming to Scientific Simulators at Scale 19

Etalumis: Bringing Probabilistic Programming to Scientific S...

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International Conference for High Performance Computing, Networking, Storage and Analysis (SC)

作者： Baydin, Atilim Gunes Shao, Lei Bhimji, Wahid Heinrich, Lukas Meadows, Lawrence Liu, Jialin Munk, Andreas Naderiparizi, Saeid Gram-Hansen, Bradley Louppe, Gilles Ma, Mingfei Zhao, Xiaohui Torr, Philip Lee, Victor Cranmer, Kyle Prabhat Wood, Frank Univ Oxford Oxford England Intel Corp Santa Clara CA 95051 USA Lawrence Berkeley Natl Lab Berkeley CA USA CERN Geneva Switzerland Univ British Columbia Vancouver BC Canada Univ Liege Liege Belgium NYU New York NY 10003 USA

ISBN: (数字)9781450362290

ISBN: (纸本)9781450362290

probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting complex scientific simulators in a PPL, the computational cost of inference, and the lack of scalable implementations. To address these, we present a novel PPL framework that couples directly to existing scientific simulators through a cross-platform probabilistic execution protocol and provides Markov chain Monte Carlo (MCMC) and deep-learning-based inference compilation (IC) engines for tractable inference. To guide IC inference, we perform distributed training of a dynamic 3DCNN-LSTM architecture with a PyTorch-MPI-based framework on 1,024 32-core CPU nodes of the Cori supercomputer with a global minibatch size of 128k: achieving a performance of 450 Tflop/s through enhancements to PyTorch. We demonstrate a Large Hadron Collider (LHC) use-case with the C++ Sherpa simulator and achieve the largest-scale posterior inference in a Turing-complete PPL.

关键词： probabilistic programming simulation inference deep learning

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Multivariate outlier detection in medicare claims payments applying probabilistic programming methods

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HEALTH SERVICES AND OUTCOMES RESEARCH METHODOLOGY 2017年第3-4期17卷 256-289页

作者： Bauder, Richard A. Khoshgoftaar, Taghi M. Florida Atlantic Univ Boca Raton FL 33431 USA

The rising elderly population continues to demand more cost-effective healthcare programs. In particular, Medicare is a vital program serving the needs of the elderly in the United States. The growing number of people enrolled in healthcare programs such as Medicare, along with the enormous volume of money in the healthcare industry, increases the appeal for, and risk of, fraudulent activities. Out of the many possible factors for the rising cost of healthcare, fraud is a major contributor, but its impacts can be lessened through the use of fraud detection methods. In this paper, we assess possible illegitimate activities by looking at the amounts paid to providers for services rendered to patients. We propose a novel method for fraud detection that focuses on discovering outliers in Medicare payment data using multiple predictors as model inputs. Our multivariate outlier detection approach is twofold: (1) create a Multivariate Adaptive Regression Splines model to produce studentized residuals and, (2) use the residuals as input into a general univariate outlier detection model, based on full Bayesian inference, using probabilistic programming. Using this approach, we are able to incorporate multiple variables to detect outliers with a model that provides probability distributions, with credible intervals, rather than just point values, as with most common outlier detection methods. Additionally, these credible intervals further enhance confidence that the detected outliers should in fact be considered outlying values, thus possibly fraudulent activities. Our results show that the successful detection of these possibly fraudulent activities can provide effective and meaningful results for further investigation within various medical specialties.

关键词： Medicare fraud Multivariate outlier detection Regression Bayesian inference probabilistic programming

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Bayesian Object Models for Robotic Interaction with Differentiable probabilistic programming 6

Bayesian Object Models for Robotic Interaction with Differen...

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6th Conference on Robot Learning (CoRL)

作者： Jatavallabhula, Krishna Murthy Macklin, Miles Fox, Dieter Garg, Animesh Ramos, Fabio NVIDIA Santa Clara CA 95050 USA

A hallmark of human intelligence is the ability to build rich mental models of previously unseen objects from very few interactions. To achieve true, continuous autonomy, robots too must possess this ability. Importantly, to integrate with the probabilistic robotics software stack, such models must encapsulate the uncertainty (resulting from noisy dynamics and observation models) in a prescriptive manner. We present Bayesian Object Models (BOMs): generative (probabilistic) models that encode both the structural and kinodynamic attributes of an object. BOMs are implemented in the form of a differentiable probabilistic program that models latent scene structure, object dynamics, and observation models. This allows for efficient and automated Bayesian inference samples (object trajectories) drawn from the BOM are compared with a small set of real-world observations and used to compute a likelihood function. Our model comprises a differentiable tree structure sampler and a differentiable physics engine, enabling gradient computation through this likelihood function. This enables gradient-based Bayesian inference to efficiently update the distributional parameters of our model. BOMs outperform several recent approaches, including differentiable physics-based, gradient-free, and neural inference schemes. (Webpage)

关键词： Simulation probabilistic programming Differentiable physics

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A Lambda-Calculus Foundation for Universal probabilistic programming 2016

A Lambda-Calculus Foundation for Universal Probabilistic Pro...

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21st ACM SIGPLAN International Conference on Functional programming (ICFP)

作者： Borgstrom, Johannes Dal Lago, Ugo Gordon, Andrew D. Szymczak, Marcin Uppsala Univ Uppsala Sweden Univ Bologna I-40126 Bologna Italy INRIA Rocquencourt France Microsoft Res Cambridge England Univ Edinburgh Edinburgh EH8 9YL Midlothian Scotland

ISBN: (纸本)9781450342193

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, and both hard and soft constraints, 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 integration over the space of 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, or for a language with soft constraints.

关键词： probabilistic programming Lambda-calculus MCMC Machine Learning Operational Semantics

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A Functional Account of probabilistic programming with Possible Worlds Declarative Pearl 1

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16th International Symposium on Functional and Logic programming (FLOPS)

作者： van den Berg, Birthe Schrijvers, Tom Katholieke Univ Leuven Leuven Belgium

ISBN: (数字)9783030994617

ISBN: (纸本)9783030994600;9783030994617

While there has been much cross-fertilization between functional and logic programming-e.g., leading to functional models of many Prolog features-this appears to be much less the case regarding probabilistic programming, even though this is an area of mutual interest. Whereas functional programming often focuses on modeling probabilistic processes, logic programming typically focuses on modeling possible worlds. These worlds are made up of facts that each carry a probability and together give rise to a distribution semantics. The latter approach appears to be little-known in the functional programming community. This paper aims to remedy this situation by presenting a functional account of the distribution semantics of probabilistic logic programming that is based on possible worlds. We present a term monad for the monadic syntax of queries together with a natural interpretation in terms of boolean algebras. Then we explain that, because probabilities do not form a boolean algebra, they-and other interpretations in terms of commutative semirings-can only be computed after query normalisation to deterministic, decomposable negation normal form (d-DNNF). While computing the possible worlds readily gives such a normal form, it suffers from exponential blow-up. Using heuristic algorithms yields much better results in practice.

关键词： Possible worlds Monad Functional programming probabilistic programming Logic programming

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Automatic Sampler Discovery via probabilistic programming and Approximate Bayesian Computation 9th

Automatic Sampler Discovery via Probabilistic Programming an...

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9th International Conference on Artificial General Intelligence (AGI) Held as Part of Joint Multi-Conference on Human-Level Intelligence (HLAI)

作者： Perov, Yura Wood, Frank Univ Oxford Dept Engn Sci Oxford England

ISBN: (纸本)9783319416496;9783319416489

We describe an approach to automatic discovery of samplers in the form of human interpretable probabilistic programs. Specifically, we learn the procedure code of samplers for one-dimensional distributions. We formulate a Bayesian approach to this problem by specifying an adaptor grammar prior over probabilistic program code, and use approximate Bayesian computation to learn a program whose execution generates samples that match observed data or analytical characteristics of a distribution of interest. In our experiments we leverage the probabilistic programming system Anglican to perform Markov chain Monte Carlo sampling over the space of programs. Our results are competive relative to state-of-the-art genetic programming methods and demonstrate that we can learn approximate and even exact samplers.

关键词： probabilistic programming Automatic programming Program synthesis Bayesian inference Automatic modelling

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