We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is given by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program. It is well-defined when each random sample uniquely determines the truth values of all logical atoms. Argumentation problems, however, represent an interesting practical application where this is not always the case. SMProbLog generalizes the semantics of ProbLog to the setting where multiple truth assignments are possible for a randomly sampled program, and implements the corresponding algorithms for both inference and learning tasks. We then show how this novel framework can be used to reason about probabilistic argumentation problems. Therefore, the key contribution of this paper are: a more general semantics for ProbLog programs, its implementation into a probabilistic programming framework for both inference and parameter learning, and a novel approach to probabilistic argumentation problems based on such framework.
We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).
ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2021 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualization. Implementation: Compilation, Virtual machines, Memory management, Parallel and Distributed execution, Constraint handling rules, Tabling, Foreign interfaces, User interfaces. Related Paradigms and Synergies: Inductive and coinductive logic programming, Constraint logic programming, Answer set programming, Interaction with SAT, SMT and CSP solvers, Theorem proving, Argumentation, Probabilistic programming, Machine learning. Applications: Databases, Big data, Data integration and federation, Software engineering, Natural language processing, Web and semantic web, Agents, Artificial intelligence, Computational life sciences, Cyber-security, Robotics, Education.
This paper summarizes our formal approach to testing autonomous vehicles (AVs) in simulation for the IEEE AV Test Challenge. We demonstrate a systematic testing framework leveraging our previous work on formally-driven simulation for intelligent cyber-physical systems. First, to model and generate interactive scenarios involving multiple agents, we used Scenic, a probabilistic programming language for specifying scenarios. A Scenic program defines an abstract scenario as a distribution over configurations of physical objects and their behaviors over time. Sampling from an abstract scenario yields many different concrete scenarios which can be run as test cases for the AV. Starting from a Scenic program encoding an abstract driving scenario, we can use the VerifAI toolkit to search within the scenario for failure cases with respect to multiple AV evaluation metrics. We demonstrate the effectiveness of our testing framework by identifying concrete failure scenarios for an open-source autopilot, Apollo, starting from a variety of realistic traffic scenarios.
It is well known that reinforcement learning can be cast as inference in an appropriate probabilistic model. However, this commonly involves introducing a distribution over agent trajectories with probabilities proportional to exponentiated rewards. In this work, we formulate reinforcement learning as Bayesian inference without resorting to rewards, and show that rewards are derived from agent's preferences, rather than the other way around. We argue that agent preferences should be specified stochastically rather than deterministically. Reinforcement learning via inference with stochastic preferences naturally describes agent behaviors, does not require introducing rewards and exponential weighing of trajectories, and allows to reason about agents using the solid foundation of Bayesian statistics. Stochastic conditioning, a probabilistic programming paradigm for conditioning models on distributions rather than values, is the formalism behind agents with probabilistic preferences. We demonstrate realization of our approach on case studies using both a two-agent coordinate game and a single agent acting in a noisy environment, showing that despite superficial differences, both cases can be modeled and reasoned about based on the same principles.
With the recent rapid progress in the study of deep generative models (DGMs), there is a need for a framework that can implement them in a simple and generic way. In this research, we focus on two features of DGMs: (1) deep neural networks are encapsulated by probability distributions, and (2) models are designed and learned based on an objective function. Taking these features into account, we propose a new Python library to implement DGMs called Pixyz. This library adopts a step-by-step implementation method with three APIs, which allows us to implement various DGMs more concisely and intuitively. In addition, the library introduces memoization to reduce the cost of duplicate computations in DGMs to speed up the computation. We demonstrate experimentally that this library is faster than existing probabilistic programming languages in training DGMs.
Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman-Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox.
When observing task demonstrations, human apprentices are able to identify whether a given task is executed correctly long before they gain expertise in actually performing that task. Prior research into learning from demonstrations (LfD) has failed to capture this notion of the acceptability of a task's execution; meanwhile, temporal logics provide a flexible language for expressing task specifications. Inspired by this, we present Bayesian specification inference, a probabilistic model for inferring task specification as a temporal logic formula. We incorporate methods from probabilistic programming to define our priors, along with a domain-independent likelihood function to enable sampling-based inference. We demonstrate the efficacy of our model for inferring specifications, with over 90% similarity observed between the inferred specification and the ground truth, both within a synthetic domain and during a real-world table setting task.
Probabilistic programming uses programs to express generative models whose posterior probability is then computed by built-in inference engines. A challenging goal is to develop general purpose inference algorithms that work out-of-the-box for arbitrary programs in a universal probabilistic programming language (PPL). The densities defined by such programs, which may use stochastic branching and recursion, are (in general) nonparametric, in the sense that they correspond to models on an infinite-dimensional parameter space. However standard inference algorithms, such as the Hamiltonian Monte Carlo (HMC) algorithm, target distributions with a fixed number of parameters. This paper introduces the Nonparametric Hamiltonian Monte Carlo (NP-HMC) algorithm which generalises HMC to nonparametric models. Inputs to NP-HMC are a new class of measurable functions called "tree representable", which serve as a language-independent representation of the density functions of probabilistic programs in a universal PPL. We provide a correctness proof of NP-HMC, and empirically demonstrate significant performance improvements over existing approaches on several nonparametric examples.
We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming, the aim of the backend inference engine is to directly estimate expected return values of programs, as opposed to approximating their conditional distributions. This distinction, while subtle, allows us to achieve substantial performance improvements over the standard PPS computational pipeline by tailoring computation to the expectation we care about. We realize a particular instance of our expectation programming concept, Expectation Programming in Turing (EPT), by extending the PPS Turing to allow so-called target-aware inference to be run automatically. We then verify the statistical soundness of EPT theoretically, and show that it provides substantial empirical gains in practice.
We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to \textit{stochastically condition} a complementary model, such that inference on new data yields the same posterior distribution of latent parameters corresponding to the new data as inference on a hierachical model on the combination of both previously available and new data, at a lower computation cost. We frame the approach as a design pattern of probabilistic programming referred to herein as `stump and fungus', and evaluate realization of the pattern on case studies.
Recent findings suggest that humans deploy cognitive mechanism of physics simulation engines to simulate the physics of objects. We propose a framework for bots to deploy probabilistic programming tools for interacting with intuitive physics environments. The framework employs a physics simulation in a probabilistic way to infer about moves performed by an agent in a setting governed by Newtonian laws of motion. However, methods of probabilistic programs can be slow in such setting due to their need to generate many samples. We complement the model with a model-free approach to aid the sampling procedures in becoming more efficient through learning from experience during game playing. We present an approach where combining model-free approaches (a convolutional neural network in our model) and model-based approaches (probabilistic physics simulation) is able to achieve what neither could alone. This way the model outperforms an all model-free or all model-based approach. We discuss a case study showing empirical results of the performance of the model on the game of Flappy Bird.
We present d3p, a software package designed to help fielding runtime efficient widely-applicable Bayesian inference under differential privacy guarantees. d3p achieves general applicability to a wide range of probabilistic modelling problems by implementing the differentially private variational inference algorithm, allowing users to fit any parametric probabilistic model with a differentiable density function. d3p adopts the probabilistic programming paradigm as a powerful way for the user to flexibly define such models. We demonstrate the use of our software on a hierarchical logistic regression example, showing the expressiveness of the modelling approach as well as the ease of running the parameter inference. We also perform an empirical evaluation of the runtime of the private inference on a complex model and find a $\sim$10 fold speed-up compared to an implementation using TensorFlow Privacy.
The development of recommender systems that optimize multi-turn interaction with users, and model the interactions of different agents (e.g., users, content providers, vendors) in the recommender ecosystem have drawn increasing attention in recent years. Developing and training models and algorithms for such recommenders can be especially difficult using static datasets, which often fail to offer the types of counterfactual predictions needed to evaluate policies over extended horizons. To address this, we develop RecSim NG, a probabilistic platform for the simulation of multi-agent recommender systems. RecSim NG is a scalable, modular, differentiable simulator implemented in Edward2 and TensorFlow. It offers: a powerful, general probabilistic programming language for agent-behavior specification; tools for probabilistic inference and latent-variable model learning, backed by automatic differentiation and tracing; and a TensorFlow-based runtime for running simulations on accelerated hardware. We describe RecSim NG and illustrate how it can be used to create transparent, configurable, end-to-end models of a recommender ecosystem, complemented by a small set of simple use cases that demonstrate how RecSim NG can help both researchers and practitioners easily develop and train novel algorithms for recommender systems.
We present a meta-algorithm for learning a posterior-inference algorithm for restricted probabilistic programs. Our meta-algorithm takes a training set of probabilistic programs that describe models with observations, and attempts to learn an efficient method for inferring the posterior of a similar program. A key feature of our approach is the use of what we call a white-box inference algorithm that extracts information directly from model descriptions themselves, given as programs. Concretely, our white-box inference algorithm is equipped with multiple neural networks, one for each type of atomic command, and computes an approximate posterior of a given probabilistic program by analysing individual atomic commands in the program using these networks. The parameters of the networks are learnt from a training set by our meta-algorithm. We empirically demonstrate that the learnt inference algorithm generalises well to programs that are new in terms of both parameters and model structures, and report cases where our approach achieves greater test-time efficiency than alternative approaches such as HMC. The overall results show the promise as well as remaining challenges of our approach.
We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.
Cardinality estimation (CardEst) is an essential component in query optimizers and a fundamental problem in DBMS. A desired CardEst method should attain good algorithm performance, be stable to varied data settings, and be friendly to system deployment. However, no existing CardEst method can fulfill the three criteria at the same time. Traditional methods often have significant algorithm drawbacks such as large estimation errors. Recently proposed deep learning based methods largely improve the estimation accuracy but their performance can be greatly affected by data and often difficult for system deployment. In this paper, we revitalize the Bayesian networks (BN) for CardEst by incorporating the techniques of probabilistic programming languages. We present BayesCard, the first framework that inherits the advantages of BNs, i.e., high estimation accuracy and interpretability, while overcomes their drawbacks, i.e. low structure learning and inference efficiency. This makes BayesCard a perfect candidate for commercial DBMS deployment. Our experimental results on several single-table and multi-table benchmarks indicate BayesCard's superiority over existing state-of-the-art CardEst methods: BayesCard achieves comparable or better accuracy, 1-2 orders of magnitude faster inference time, 1-3 orders faster training time, 1-3 orders smaller model size, and 1-2 orders faster updates. Meanwhile, BayesCard keeps stable performance when varying data with different settings. We also deploy BayesCard into PostgreSQL. On the IMDB benchmark workload, it improves the end-to-end query time by 13.3%, which is very close to the optimal result of 14.2% using an oracle of true cardinality.
It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic programming and concept formation. First it is shown that appropriate averaging-across-situations and renormalization of 4-valued p-bits operating in accordance with Constructible Duality (CD) logic yields PLN (Probabilistic Logic Networks) strength-and-confidence truth values. Then variations on the Curry-Howard correspondence are used to map these paraconsistent and probabilistic logics into probabilistic types suitable for use within dependent type based programming languages. Zach Weber's paraconsistent analysis of the sorites paradox is extended to form a paraconsistent / probabilistic / fuzzy analysis of concept boundaries; and a paraconsistent version of concept formation via Formal Concept Analysis is presented, building on a definition of fuzzy property-value degrees in terms of relative entropy on paraconsistent probability distributions. These general points are fleshed out via reference to the realization of probabilistic reasoning and programming and concept formation in the OpenCog AGI framework which is centered on collaborative multi-algorithm updating of a common knowledge metagraph.
Over 34,000 objects bigger than 10 cm in length are known to orbit Earth. Among them, only a small percentage are active satellites, while the rest of the population is made of dead satellites, rocket bodies, and debris that pose a collision threat to operational spacecraft. Furthermore, the predicted growth of the space sector and the planned launch of megaconstellations will add even more complexity, therefore causing the collision risk and the burden on space operators to increase. Managing this complex framework with internationally agreed methods is pivotal and urgent. In this context, we build a novel physics-based probabilistic generative model for synthetically generating conjunction data messages, calibrated using real data. By conditioning on observations, we use the model to obtain posterior distributions via Bayesian inference. We show that the probabilistic programming approach to conjunction assessment can help in making predictions and in finding the parameters that explain the observed data in conjunction data messages, thus shedding more light on key variables and orbital characteristics that more likely lead to conjunction events. Moreover, our technique enables the generation of physically accurate synthetic datasets of collisions, answering a fundamental need of the space and machine learning communities working in this area.
Single Photon Emission Computed Tomography (SPECT) is one of the nuclear medicine imaging modalities used for functional analysis of animal or human organs. Gamma rays emitted from the scanned body are filtered with collimators and detected by the SPECT head. The conventional reconstruction algorithms do not consider the uncertainty in the process introduced by the field of view of the collimators. In this paper, we incorporate the probabilistic programming approach for SPECT image reconstruction. No-U-Turn Sampler (NUTS) is used to estimate the scanned object system by considering uncertainty. Results indicate that the current work can include uncertainty in reconstruction compared to conventional approaches like MLEM and MAP. However, reconstruction time need to be improved for phantom sizes of 128x128x128 voxels and higher.