Quantum Enhanced Inference in Markov Logic Networks

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.

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.

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.

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.

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.

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.

The epidemic of COVID-19 has been effectively controlled in China, which provides an empirical basis for intervention analysis. An extended SIR transmission model with heterogeneous force of infectiousness is presented including three fractals sub-models of Wuhan, Hubei and China. The model is built upon the data from January 20 to March 23, 2020. The Markov chain Monte Carlo (MCMC) Gibbs sampling and machine learning of Gaussian process regression are applied to solve the parameters estimation and the sensitivity analysis is used in various scenarios. The model has a breakthrough in parameter setting and accuracy optimization. It is found that contact reduction is the most effective core lever to control the epidemic, with 3.5 times or more sensitivity as much as other levers. The asymmetric marginal effect in strong and weak scenarios proves that Chinese controlling strategy is close to the Pareto Optimality. The intervention effectiveness of COVID-19 in China is evaluated by simulation analysis. The result provides valuable reference for China and other countries to judge the epidemic risk, control the intervention pace, and formulate prevention strategies in the future.

Chapter 3 - Plan Recognition Using Statistical–Relational Models

Recognizing inference in texts (RITE) attracts growing attention of natural language processing (NLP) researchers in recent years. In this article, we propose a novel approach to recognize inference with probabilistic logical reasoning. Our approach is built on Markov logic networks (MLNs) framework, which is a probabilistic extension of first-order logic. We design specific semantic rules based on the surface, syntactic, and semantic representations of texts, and map these rules to logical representations. We also extract information from some knowledge bases as common sense logic rules. Then we utilize MLNs framework to make predictions with combining statistical and logical reasoning. Experiment results shows that our system can achieve better performance than state-of-the-art RITE systems.

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.

ABSTRACTWith diverse online media emerging, there is a growing concern of sentiment classification problem. At present, text sentiment classification mainly utilizes supervised machine learning methods, which feature certain domain dependency. On the basis of Markov logic networks (MLNs), this study proposed a cross-domain multi-task text sentiment classification method rooted in transfer learning. Through many-to-one knowledge transfer, labeled text sentiment classification, knowledge was successfully transferred into other domains, and the precision of the sentiment classification analysis in the text tendency domain was improved. The experimental results revealed the following: (1) the model based on a MLN demonstrated higher precision than the single individual learning plan model. (2) Multi-task transfer learning based on Markov logical networks could acquire more knowledge than self-domain learning. The cross-domain text sentiment classification model could significantly improve the precision and efficiency of text sentiment classification.

Clustering is a fundamental problem in statistics and machine learning, whose solution is commonly computed by the Expectation-Maximization (EM) method, which finds a locally optimal solution for an objective function called log-likelihood. Since the surface of the log-likelihood function is non convex, a stochastic search with Markov Chain Monte Carlo (MCMC) methods can help escaping locally optimal solutions. In this article, we tackle two fundamental conflicting goals: Finding higher quality solutions and achieving faster convergence. With that motivation in mind, we introduce an efficient algorithm that combines elements of the EM and MCMC methods to find clustering solutions that are qualitatively better than those found by the standard EM method. Moreover, our hybrid algorithm allows tuning model parameters and understanding the uncertainty in their estimation. The main issue with MCMC methods is that they generally require a very large number of iterations to explore the posterior of each model parameter. Convergence is accelerated by several algorithmic improvements which include sufficient statistics, simplified model parameter priors, fixing covariance matrices and iterative sampling from small blocks of the data set. A brief experimental evaluation shows promising results.

This paper presents an overview of Markov Chain Monte Carlo (MCMC) methods for statistical inference and applications. The article begins by describing ordinary Monte Carlo methods, which in principle has the same goals as the MCMC but can hardly be implemented in practice. Following that basic Markov Chain Monte Carlo is discussed, which is founded on the Hastings algorithm and includes Metropolis method and the Gibbs sampler as special cases. Finally, various special applications of Markov Chain Monte Carlo methods are briefly mentioned and some recent development of MCMC are covered in final remarks section.KeywordsReal EstateMarkov Chain Monte CarloGibbs SamplerDetailed BalanceMarkov Chain Monte Carlo MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

Markov chain Monte Carlo methods, in particular, the Gibbs sampler, are widely used algorithms both in application and theoretical works in the classical and Bayesian paradigms. However, these algorithms are often computer intensive. Samawi et al. [Steady-state ranked Gibbs sampler. J. Stat. Comput. Simul. 2012;82(8), 1223–1238. doi:10.1080/00949655.2011.575378] demonstrate through theory and simulation that the dependent steady-state Gibbs sampler is more efficient and accurate in model parameter estimation than the original Gibbs sampler. This paper proposes the independent steady-state Gibbs sampler (ISSGS) approach to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in multidimensional problems.