In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings can be very large, making inference and learning computationally expensive. Here we present a first-order probabilistic language which is well-suited to approximate "local" grounding: every query @math can be approximately grounded with a small graph. The language is an extension of stochastic logic programs where inference is performed by a variant of personalized PageRank. Experimentally, we show that the approach performs well without weight learning on an entity resolution task; that supervised weight-learning improves accuracy; and that grounding time is independent of DB size. We also show that order-of-magnitude speedups are possible by parallelizing learning.
Although we have chosen here to compare experimentally to MLNs @cite_6 @cite_18 , ProPPR represents a rather different philosophy toward language design: rather than beginning with a highly-expressive but intractible logical core, we begin with a limited logical inference scheme and add to it a minimal set of extensions that allow probabilistic reasoning, while maintaining stable, efficient inference and learning. While ProPPR is less expressive than MLNs (for instance, it is limited to definite clause theories) it is also much more efficient. This philosophy is similar to that illustrated by probabilistic similarity logic (PSL) @cite_3 ; however, unlike ProPPR, PSL does not include a local'' grounding procedure, which leads to small inference problems, even for large databases.
@cite_18 @cite_3 @cite_6
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Elementary-level science exams pose significant knowledge acquisition and reasoning challenges for automatic question answering. We develop a system that reasons with knowledge derived from textbooks, represented in a subset of firstorder logic. Automatic extraction, while scalable, often results in knowledge that is incomplete and noisy, motivating use of reasoning mechanisms that handle uncertainty. Markov Logic Networks (MLNs) seem a natural model for expressing such knowledge, but the exact way of leveraging MLNs is by no means obvious. We investigate three ways of applying MLNs to our task. First, we simply use the extracted science rules directly as MLN clauses and exploit the structure present in hard constraints to improve tractability. Second, we interpret science rules as describing prototypical entities, resulting in a drastically simplified but brittle network. Our third approach, called Praline, uses MLNs to align lexical elements as well as define and control how inference should be performed in this task. Praline demonstrates a 15 accuracy boost and a 10x reduction in runtime as compared to other MLNbased methods, and comparable accuracy to word-based baseline approaches. We consider the problem of constructing abstract representations for planning in high-dimensional, continuous environments. We assume an agent equipped with a collection of high-level actions, and construct representations provably capable of evaluating plans composed of sequences of those actions. @PARASPLIT We first consider the deterministic planning case, and show that the relevant computation involves set operations performed over sets of states. We define the specific collection of sets that is necessary and sufficient for planning, and use them to construct a grounded abstract symbolic representation that is provably suitable for deterministic planning. The resulting representation can be expressed in PDDL, a canonical high-level planning domain language; we construct such a representation for the Playroom domain and solve it in milliseconds using an off-the-shelf planner. @PARASPLIT We then consider probabilistic planning, which we show requires generalizing from sets of states to distributions over states. We identify the specific distributions required for planning, and use them to construct a grounded abstract symbolic representation that correctly estimates the expected reward and probability of success of any plan. In addition, we show that learning the relevant probability distributions corresponds to specific instances of probabilistic density estimation and probabilistic classification. We construct an agent that autonomously learns the correct abstract representation of a computer game domain, and rapidly solves it. @PARASPLIT Finally, we apply these techniques to create a physical robot system that autonomously learns its own symbolic representation of a mobile manipulation task directly from sensorimotor data---point clouds, map locations, and joint angles---and then plans using that representation. Together, these results establish a principled link between high-level actions and abstract representations, a concrete theoretical foundation for constructing abstract representations with provable properties, and a practical mechanism for autonomously learning abstract high-level representations. This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of behaviors (e.g. "If the speed of the car is greater than 15 m s within 0.5s of brake application, the obstruction will be struck") which can be used to tune designs or to perform on-line monitoring to ensure the desired behavior. We introduce reactive parameter signal temporal logic (rPSTL), a fragment of parameter signal temporal logic (PSTL) that is expressive enough to capture causal, spatial, and temporal relationships in data. We define a partial order over the set of rPSTL formulae that is based on language inclusion. This order enables a directed search over this set, i.e. given a candidate rPSTL formula that does not adequately match the observed data, we can automatically construct a formula that will fit the data at least as well. Two case studies, one involving a cattle herding scenario and one involving a stochastic hybrid gene circuit model, are presented to illustrate our approach. Probabilistic programming languages (PPLs) are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on expensive, approximate sampling-based methods. To alleviate this problem, one could try to learn from past inferences, so that future inferences run faster. This strategy is known as amortized inference; it has recently been applied to Bayesian networks and deep generative models. This paper proposes a system for amortized inference in PPLs. In our system, amortization comes in the form of a parameterized guide program. Guide programs have similar structure to the original program, but can have richer data flow, including neural network components. These networks can be optimized so that the guide approximately samples from the posterior distribution defined by the original program. We present a flexible interface for defining guide programs and a stochastic gradient-based scheme for optimizing guide parameters, as well as some preliminary results on automatically deriving guide programs. We explore in detail the common machine learning pattern in which a 'local' model is specified by 'global' random values and used to generate independent observed data points; this gives rise to amortized local inference supporting global model learning.