Interpretable Explanations for Probabilistic Inference in Markov Logic

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.

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.

We propose a system to recognize objects with a camera network in a smart home. Recognizing objects in a home environment from images is challenging, due to the variation in object appearances such as chairs, as well as the clutters in the scene. Therefore, we propose to recognize objects through user interactions. A hierarchical activity analysis is first performed in the system to recognize fine-grained activities including eating, typing, cutting etc. The object-activity relationship is encoded in the knowledge base of a Markov logic network (MLN). MLN has the advantage of encoding relationships in an intuitive way with first-order logic syntax. It can also deal with both soft and hard constraints by associating weights to the formulas in the knowledge base. With activity observations, the defined MLN is grounded and turned into a dynamic Bayesian network (DBN) to infer object type probabilities. We expedite inference by decomposing the MLN into smaller separate domains that relates to the active activity. Experimental results are presented with our testbed smart home environment.

Chapter 3 - Plan Recognition Using Statistical–Relational Models

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.

Link mining problems are characterized by high complexity (since linked objects are not statistically independent) and uncertainty (since data is noisy and incomplete). Thus they necessitate a modeling language that is both probabilistic and relational. Markov logic provides this by attaching weights to formulas in first-order logic and viewing them as templates for features of Markov networks. Many link mining problems can be elegantly formulated and efficiently solved using Markov logic. Inference algorithms for Markov logic draw on ideas from satisfiability testing, Markov chain Monte Carlo, belief propagation, and resolution. Learning algorithms are based on convex optimization, pseudo-likelihood, and inductive logic programming. Markov logic has been used successfully in a wide variety of link mining applications and is the basis of the open-source Alchemy system.

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.

We propose using a statistical-relational model, the Markov Logic Network, for knowledge transfer in reinforcement learning. Our goal is to extract relational knowledge from a source task and use it to speed up learning in a related target task. We show that Markov Logic Networks are effective models for capturing both source-task Q-functions and source-task policies. We apply them via demonstration, which involves using them for decision making in an initial stage of the target task before continuing to learn. Through experiments in the RoboCup simulated-soccer domain, we show that transfer via Markov Logic Networks can significantly improve early performance in complex tasks, and that transferring policies is more effective than transferring Q-functions.

Recent years have seen a surge of interest in Statistical Relational Learning (SRL) models that combine logic with probabilities. One prominent and highly expressive SRL model is Markov Logic Networks (MLNs), but the expressivity comes at the cost of learning complexity. Most of the current methods for learning MLN structure follow a two-step approach where first they search through the space of possible clauses (i.e. structures) and then learn weights via gradient descent for these clauses. We present a functional-gradient boosting algorithm to learn both the weights (in closed form) and the structure of the MLN simultaneously. Moreover most of the learning approaches for SRL apply the closed-world assumption, i.e., whatever is not observed is assumed to be false in the world. We attempt to open this assumption. We extend our algorithm for MLN structure learning to handle missing data by using an EM-based approach and show this algorithm can also be used to learn Relational Dependency Networks and relational policies. Our results in many domains demonstrate that our approach can effectively learn MLNs even in the presence of missing data.

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.

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.

: 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.

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.

Table-top scene analysis using knowledge-supervised MCMC

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.