Statistical Relational Artificial Intelligence: Logic, Probability, and Computation

Many important real-world applications of machine learning, statistical physics, constraint programming and information theory can be formulated using graphical models that involve determinism and cycles. Accurate and efficient inference and training of such graphical models remains a key challenge. Markov logic networks (MLNs) have recently emerged as a popular framework for expressing a number of problems which exhibit these properties. While loopy belief propagation (LBP) can be an effective solution in some cases; unfortunately, when both determinism and cycles are present, LBP frequently fails to converge or converges to inaccurate results. As such, sampling based algorithms have been found to be more effective and are more popular for general inference tasks in MLNs. In this paper, we introduce Generalized arc-consistency Expectation Maximization Message-Passing (GEM-MP), a novel message-passing approach to inference in an extended factor graph that combines constraint programming techniques with variational methods. We focus our experiments on Markov logic and Ising models but the method is applicable to graphical models in general. In contrast to LBP, GEM-MP formulates the message-passing structure as steps of variational expectation maximization. Moreover, in the algorithm we leverage the local structures in the factor graph by using generalized arc consistency when performing a variational mean-field approximation. Thus each such update increases a lower bound on the model evidence. Our experiments on Ising grids, entity resolution and link prediction problems demonstrate the accuracy and convergence of GEM-MP over existing state-of-the-art inference algorithms such as MC-SAT, LBP, and Gibbs sampling, as well as convergent message passing algorithms such as the concave---convex procedure, residual BP, and the L2-convex method.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

Markov Logic Networks (MLNs) represent relational knowledge using a combination of first-order logic and probabilistic models. In this paper, we develop an approach to explain the results of probabilistic inference in MLNs. Unlike approaches such as LIME and SHAP that explain black-box classifiers, explaining M LN inference is harder since the data is interconnected. We develop an explanation framework that computes importance weights for MLN formulas based on their influence on the marginal likelihood. However, it turns out that computing these importance weights exactly is a hard problem and even approximate sampling methods are unreliable when the MLN is large resulting in non-interpretable explanations. Therefore, we develop an approach where we reduce the large MLN into simpler coalitions of formulas that approximately preserve relational dependencies and generate explanations based on these coalitions. We then weight explanations from different coalitions and combine them into a single explanation. Our experiments illustrate that our approach generates more interpretable explanations in several text processing problems as compared to other state-of-the-art methods.

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

This paper presents the application of Markov Logic Networks(MLN) for the the recognition of Activities of Daily Living (ADL) in a smart home. We describe a procedure that uses raw data from non visual and non wearable sensors in order to create a classification model leveraging logic formal representation and probabilistic inference. SVM and Naive Bayes methods were used as baselines to compare the performance of our implementation, as they have proved to be highly efficient in classification tasks. The evaluation was carried out on a real smart home where 21 participants performed ADLs. Results show not only the appreciable capacities of MLN as a classifier, but also its potential to be easily integrable into a formal knowledge representation framework.

Situational awareness requires continual learning from observations and adaptive reasoning from domain and contextual knowledge. The integration of reasoning and learning has been a standing goal of machine learning and AI in general, and a pressing need for real-world situational awareness in particular. Representative techniques among the numerous methods proposed include integrating logics with learning formalisms, whether probabilistic graphical models or neural methods. These techniques are motivated by the need to model and exploit the symmetry, regularities and complex relations between entities exhibited in real world scenarios (in the form of relational or graph data) for effective reasoning and learning. In this work, we investigate the benefits of integrating two prominent methods for reasoning and learning with relational/graph data, Markov Logic Networks (or simply Markov Logic) and Graph Neural Networks. The former is well-recognised for its powerful representation and uncertainty handling, while the latter have gained much attention due to their efficiency in handling large-scale graph datasets. This paper reports on the potential benefits of combining their respective strengths and applying them to a use case illustration in the maritime domain, together with empirical results.

A new method is proposed to increase the reliability of generating symbolic plans by extending the Semantic-Knowledge Based (SKB) plan generation to take into account the amount of information and uncertainty related to existing objects, their types and properties, as well as their relationships with each other. This approach constructs plans by depending on probabilistic values which are derived from learning statistical relational models such as Markov Logic Networks (MLN). An MLN module is established for probabilistic learning and inference together with semantic information to provide a basis for plausible learning and reasoning services in support of robot task-planning. The MLN module is constructed by using an algorithm to transform the knowledge stored in SKB to types, predicates and formulas which represent the main building block for this module. Following this, the semantic domain knowledge is used to derive implicit expectations of world states and the effects of the action which is nominated for insertion into the task plan. The expectations are matched with MLN output.

Despite great recent advances achieved by deep neural networks (DNNs), they are often vulnerable to adversarial attacks. Intensive research efforts have been made to improve the robustness of DNNs; however, most empirical defenses can be adaptively attacked again, and the theoretically certified robustness is limited, especially on large-scale datasets. One potential root cause of such vulnerabilities for DNNs is that although they have demonstrated powerful expressiveness, they lack the reasoning ability to make robust and reliable predictions. In this paper, we aim to integrate domain knowledge to enable robust learning with the reasoning paradigm. In particular, we propose a certifiably robust learning with reasoning pipeline (CARE), which consists of a learning component and a reasoning component. Concretely, we use a set of standard DNNs to serve as the learning component to make semantic predictions (e.g., whether the input is furry), and we leverage the probabilistic graphical models, such as Markov logic networks (MLN), to serve as the reasoning component to enable knowledge/logic reasoning (e.g., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{IsPanda} \Longrightarrow \text{IsFurry}$</tex> ). However, it is known that the exact inference of MLN (reasoning) is #P-complete, which limits the scalability of the pipeline. To this end, we propose to approximate the MLN inference via variational inference based on an efficient expectation maximization algorithm. In particular, we leverage graph convolutional networks (GCNs) to encode the posterior distribution during variational inference and update the parameters of GCNs (E-step) and the weights of knowledge rules in MLN (M-step) iteratively. We conduct extensive experiments on different datasets such as AwA2, Word50, GTSRB, and PDF malware, and we show that CARE achieves significantly higher certified robustness (e.g., the certified accuracy is improved from 36.0% to 61.8% under <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{2}$</tex> radius 2.0 on AwA2) compared with the state-of-the-art baselines. We additionally conducted different ablation studies to demonstrate the empirical robustness of CARE and the effectiveness of different knowledge integration. The official code is available at https://github.com/javyduck/CARE.

Multiply sectioned Bayesian networks (MSBNs) extend Bayesian networks (BNs) to graphical models that provide a coherent framework for probabilistic inference in cooperative multiagent distributed interpretation systems. Observation plays an important role in the inference with graphical models. Since observation of each observable variable has a cost, it would be helpful if we can find the most relevant variables to observe. In a probabilistic model, a Markov boundary of a variable provides a minimal set of variables that shields the variable from the influence of all other variables. However, the concept cannot be used directly for observation. First, it is generally intractable to verify conditional independencies in a probabilistic model. Second, the Markov boundary members may not be observable. Third, it is defined only for a single variable. Finally, it is not unique. By revising the concept to address these issues, we introduce the concept of observable Markov boundary of a set of nodes defined on d-separation of graphical models. The observable Markov boundary captures all relevant variables to observe for probabilistic inference with graphical models. In an MSBN, the observable Markov boundary of a set of nodes may span across all Bayesian subnets. We present an algorithm for cooperative computation of the observable Markov boundary of a set of nodes in an MSBN without revealing subnet structures.

Gait recognition is a newly developing bio-metric which has potential to recognize people at a distance when application of other biometrics might not be feasible. We propose a new technique to represent and learn various gait component relationships using a recently developing statistical relational learning technique called Markov Logic Networks. Markov Logic Network is a robust statistical learning technique that fuses expressive first-order logic with probabilistic graphical models and prove to be efficient in handling noisy and uncertain data. Initially we derive component based pattern classifiers in the imaging domain using an automatic segmentation scheme and represent gait components and their relationships using firstorder logic. Then we model and learn their characteristics using undirected graphs to finally classify gaits based on standard inference techniques. The proposed approach enables automatic gait recognition from low resolution videos and differs from conventional techniques which rely on manual markings on videos. We show that the proposed representation provide intuitive means to reason gait component relationships. Our results show that the proposed approach competes well with other state-of-the-art techniques.

Object recognition from images in a home environment is challenging since the object usually has low resolution in the image and the scene is usually cluttered. However, many objects have specific functions to the user and the interactions between the user and the object provides useful contextual information to recognize the object. In this paper, we use Markov logic network (MLN) to model such context information as relationship between the objects and user activities. We demonstrate that Markov logic network provides a flexible way in the syntax of first-order logic to incorporate relational context information. It is also a probabilistic graphical model which handles uncertainty in the knowledge base, observations and decisions. In our experiment, objects in the living room and kitchen in a home are recognized based on only user's activity. The user's activity is analyzed from images of cameras installed in the home. Relationship between user activity and objects is defined in a knowledge base with MLN. Experiments show that objects in the home can be recognized irrespective of their position, size and appearance in the image.

Probabilistic logics combine the ability to reason about complex scenes, with a rigorous approach to uncertainty. This paper explores the construction of probabilistic spatial logics through the combination of established qualitative spatial calculi together with Markov logic networks (MLNs). Qualitative spatial calculi provide the basis for automated representation and reasoning with complex spatial scenes; MLNs provide a rigorous basis for handling uncertainty and driving probabilistic inference. Our approach focuses specifically on the combination of an uncertain knowledge base with a certain spatial reasoning rule-base. The experiments explore how uncertain knowledge propagates through certain qualitative spatial inferences, using the specific example of reasoning with cardinal directions. The results provide a template for probabilistic qualitative spatial reasoning more generally, with applications to a wide range of common scenarios for situational awareness and automated reasoning under uncertainty.

Protein fold recognition is the problem of determining whether a given protein sequence folds into a previously observed structure. An uncertainty complication is that it is not always true that the structure has been previously observed. Markov logic networks (MLNs) are a powerful representation that combines first-order logic and probability by attaching weights to first-order formulas and using these as templates for features of Markov networks. In this chapter, we describe a simple temporal extension of MLNs that is able to deal with sequences of logical atoms. We also propose iterated robust tabu search (IRoTS) for maximum a posteriori (MAP) inference and Markov Chain-IRoTS (MC-IRoTS) for conditional inference in the new framework. We show how MC-IRoTS can also be used for discriminative weight learning. We describe how sequences of protein secondary structure can be modeled through the proposed language and show through some preliminary experiments the promise of our approach for the problem of protein fold recognition from these sequences.

Statistical Relational Models are state-of-the-art representation formalisms at the intersection of logical and statistical machine learning. One of the most promising models is Markov Logic (ML) which combines Markov networks (MNs) and first-order logic by attaching weights to first-order formulas and using these as templates for features of MNs. MAP inference in ML is the task of finding the most likely state of a set of output variables given the state of the input variables and this problem is NP-hard. In this paper we present an algorithm for this inference task based on the Iterated Local Search (ILS) and Robust Tabu Search (RoTS) metaheuristics. The algorithm performs a biased sampling of the set of local optima by using RoTS as a local search procedure and repetitively jumping in the search space through a perturbation operator, focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for the optimization engine. We show through extensive experiments in real-world domains that it improves over the state-of-the-art algorithm in terms of solution quality and inference time.

: Natural language (supplemented with diagrams and some mathematical notations) is convenient for succinct communication of technical descriptions between the various stakeholders (e.g., customers, designers, implementers) involved in the design of software systems. However, natural language descriptions can be informal, incomplete, imprecise and ambiguous, and cannot be processed easily by design and analysis tools. Formal languages, on the other hand, formulate design requirements in a precise and unambiguous mathematical notation, but are more difficult to master and use. We propose a methodology for connecting semi-formal requirements with formal descriptions through an intermediate representation. We have implemented this methodology in a research prototype called Automatic Requirements Specification Extraction from Natural Language (ARSENAL). The main novelty of ARSENAL lies in its ability to generate a fully-specified complete formal model automatically from natural language requirements. ARSENAL extracts relations from text using semantic parsing and progressively refines them over multiple stages to create a final composite model. Currently, ARSENAL generates formal models in linear-time temporal logic (LTL), but the approach can be adapted for other models, e.g., probabilistic relational models like Markov Logic Networks (MLN). The formal models of the requirements can be used to check important design and system properties, e.g., consistency, satisfiability, realizability. ARSENAL has a modular and flexible architecture that facilitates porting it from one domain to another. We evaluated ARSENAL on complex requirements from two real-world case studies: the Time-Triggered Ethernet (TTEthernet) communication platform used in space, and FAA-Isolette infant incubators used in NICU. We systematically evaluated various aspects of ARSENAL -- the accuracy of the natural language processing stage, the degree of automation, and robustness to noise.