The Libra Toolkit for Probabilistic Models

The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to other toolkits, Libra places a greater emphasis on learning the structure of tractable models in which exact inference is efficient. It also includes a variety of algorithms for learning graphical models in which inference is potentially intractable, and for performing exact and approximate inference. Libra is released under a 2-clause BSD license to encourage broad use in academia and industry

Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory

To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited to \emph{negation-free} programs. In this paper, we show how to extend it to general logic programs under the well-founded semantics. We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks

Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). Code and data available at: https://github.com/ralphabb/NeuralDNF

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

Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures

Probabilistic graphical models are a central tool in AI; however, they are generally not as expressive as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic models such as sum-product networks (SPNs) capture joint distributions in a tractable fashion, but still lack the expressive power of intractable models based on deep neural networks. Therefore, we introduce conditional SPNs (CSPNs), conditional density estimators for multivariate and potentially hybrid domains which allow harnessing the expressive power of neural networks while still maintaining tractability guarantees. One way to implement CSPNs is to use an existing SPN structure and condition its parameters on the input, e.g., via a deep neural network. This approach, however, might misrepresent the conditional independence structure present in data. Consequently, we also develop a structure-learning approach that derives both the structure and parameters of CSPNs from data. Our experimental evidence demonstrates that CSPNs are competitive with other probabilistic models and yield superior performance on multilabel image classification compared to mean field and mixture density networks. Furthermore, they can successfully be employed as building blocks for structured probabilistic models, such as autoregressive image models.Comment: 13 pages, 6 figure