Generating and Sampling Orbits for Lifted Probabilistic Inference

A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient inference and seek to scale with the degree of symmetry of a probability model. A limitation of existing exact lifted inference techniques is that they do not apply to non-relational representations like factor graphs. In this work we provide the first example of an exact lifted inference algorithm for arbitrary discrete factor graphs. In addition we describe a lifted Markov-Chain Monte-Carlo algorithm that provably mixes rapidly in the degree of symmetry of the distribution

Probabilistic Program Abstractions

Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete program, which is difficult to analyze, and an abstract program, which is more tractable. Program abstractions, however, are typically not probabilistic. We generalize non-deterministic program abstractions to probabilistic program abstractions by explicitly quantifying the non-deterministic choices. Our framework upgrades key definitions and properties of abstractions to the probabilistic context. We also discuss preliminary ideas for performing inference on probabilistic abstractions and general probabilistic programs

Symbolic Exact Inference for Discrete Probabilistic Programs

The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact inference on discrete-valued finite-domain imperative probabilistic programs. We leverage and generalize efficient inference procedures for Bayesian networks, which exploit the structure of the network to decompose the inference task, thereby avoiding full path enumeration. To do this, we first compile probabilistic programs to a symbolic representation. Then we adapt techniques from the probabilistic logic programming and artificial intelligence communities in order to perform inference on the symbolic representation. We formalize our approach, prove it sound, and experimentally validate it against existing exact and approximate inference techniques. We show that our inference approach is competitive with inference procedures specialized for Bayesian networks, thereby expanding the class of probabilistic programs that can be practically analyzed

Logical Abstractions for Noisy Variational Quantum Algorithm Simulation

Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms, which are among the leading candidates for useful quantum computation. Existing quantum circuit simulators do not address the common traits of variational algorithms, namely: 1) their ability to work with noisy qubits and operations, 2) their repeated execution of the same circuits but with different parameters, and 3) the fact that they sample from circuit final wavefunctions to drive a classical optimization routine. We present a quantum circuit simulation toolchain based on logical abstractions targeted for simulating variational algorithms. Our proposed toolchain encodes quantum amplitudes and noise probabilities in a probabilistic graphical model, and it compiles the circuits to logical formulas that support efficient repeated simulation of and sampling from quantum circuits for different parameters. Compared to state-of-the-art state vector and density matrix quantum circuit simulators, our simulation approach offers greater performance when sampling from noisy circuits with at least eight to 20 qubits and with around 12 operations on each qubit, making the approach ideal for simulating near-term variational quantum algorithms. And for simulating noise-free shallow quantum circuits with 32 qubits, our simulation approach offers a $66\times$ reduction in sampling cost versus quantum circuit simulation techniques based on tensor network contraction.Comment: ASPLOS '21, April 19-23, 2021, Virtual, US

Type Prediction With Program Decomposition and Fill-in-the-Type Training

TypeScript and Python are two programming languages that support optional type annotations, which are useful but tedious to introduce and maintain. This has motivated automated type prediction: given an untyped program, produce a well-typed output program. Large language models (LLMs) are promising for type prediction, but there are challenges: fill-in-the-middle performs poorly, programs may not fit into the context window, generated types may not type check, and it is difficult to measure how well-typed the output program is. We address these challenges by building OpenTau, a search-based approach for type prediction that leverages large language models. We propose a new metric for type prediction quality, give a tree-based program decomposition that searches a space of generated types, and present fill-in-the-type fine-tuning for LLMs. We evaluate our work with a new dataset for TypeScript type prediction, and show that 47.4% of files type check (14.5% absolute improvement) with an overall rate of 3.3 type errors per file. All code, data, and models are available at: https://github.com/GammaTauAI/opentau

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool Dice. Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio -- with Rubicon as a first step towards integrating both perspectives.Comment: Technical Report. Accepted at CAV 202

Exploiting Program Structure for Scaling Probabilistic Programming

Probabilistic modeling and reasoning are central tasks in artificial intelligence and machine learning. A probabilistic model is a rough description of the world: the model-builder attempts to capture as much detail about the world’s complexities as she can, and when no more detail can be given the rest is left as probabilistic uncertainty. Once constructed, the goal of a model is to perform automated inference: compute the probability that some particular fact is true about the world. It is natural for the model-builder to want a flexible expressive language – the world is a complex thing to describe – and over time this has led to a trend of increasingly powerful modeling languages. This trend is taken to its apex by probabilistic programming languages (PPLs), which enable modelers to specify probabilistic models using the facilities of a full programming language. However, this expressivity comes at a cost: the computational cost of inference is in direct tension with the flexibility of the modeling language, and so it becomes increasingly difficult to design automated inference algorithms that scale to the kinds of systems that model builders want to create.This thesis focuses on the central question: how can we design effective probabilistic programming languages that profitably trade-off expressivity and tractability for inference? The approach taken here is first to identify and exploit important structure that a probabilistic program may possess. The kinds of structure considered here are discrete program structure and symmetry. Programs are heterogeneous objects, so different parts of programs may exhibit different kinds of structure; in the second part of the thesis I show how to decompose heterogeneous probabilistic program inference using a notion of program abstraction. These contributions enable new applications of probabilistic programs in domains such as text analysis, verification of probabilistic systems, and classical simulation of quantum algorithms

Exploiting Program Structure for Scaling Probabilistic Programming

Probabilistic modeling and reasoning are central tasks in artificial intelligence and machine learning. A probabilistic model is a rough description of the world: the model-builder attempts to capture as much detail about the world’s complexities as she can, and when no more detail can be given the rest is left as probabilistic uncertainty. Once constructed, the goal of a model is to perform automated inference: compute the probability that some particular fact is true about the world. It is natural for the model-builder to want a flexible expressive language – the world is a complex thing to describe – and over time this has led to a trend of increasingly powerful modeling languages. This trend is taken to its apex by probabilistic programming languages (PPLs), which enable modelers to specify probabilistic models using the facilities of a full programming language. However, this expressivity comes at a cost: the computational cost of inference is in direct tension with the flexibility of the modeling language, and so it becomes increasingly difficult to design automated inference algorithms that scale to the kinds of systems that model builders want to create.This thesis focuses on the central question: how can we design effective probabilistic programming languages that profitably trade-off expressivity and tractability for inference? The approach taken here is first to identify and exploit important structure that a probabilistic program may possess. The kinds of structure considered here are discrete program structure and symmetry. Programs are heterogeneous objects, so different parts of programs may exhibit different kinds of structure; in the second part of the thesis I show how to decompose heterogeneous probabilistic program inference using a notion of program abstraction. These contributions enable new applications of probabilistic programs in domains such as text analysis, verification of probabilistic systems, and classical simulation of quantum algorithms

Probabilistic Program Abstractions

Abstraction is a fundamental tool for reasoning about a complex system. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of a program abstraction is a connection between the abstract program, which is simple to analyze, and the concrete program, which may be extremely complex. Program abstractions, however, are typically not probabilistic. In this thesis I generalize a particular class of non- deterministic program abstractions known as sound over-approximations to the probabilistic context. Sound over-approximations are a family of abstract programs which are guaranteed to contain the original program as a subset of their behavior. This thesis shows that when imbued with a probabilistic semantics, sound over-approximations define a family of probabilistic programs which capture key properties of the original program. It then introduces a mechanism for generating sound probabilistic over-approximations as a generalization of a well-known program abstraction technique known as predicate abstraction. Finally, the problem of inference and learning in the context of probabilistic program abstractions are briefly described