RockIt is a maximum a-posteriori (MAP) query engine for statistical relational models. MAP inference in graphical models is an optimization problem which can be compiled to integer linear programs (ILPs). We describe several advances in translating MAP queries to ILP instances and present the novel meta-algorithm cutting plane aggregation (CPA). CPA exploits local context-specific symmetries and bundles up sets of linear constraints. The resulting counting constraints lead to more compact ILPs and make the symmetry of the ground model more explicit to state-of-the-art ILP solvers. Moreover, RockIt parallelizes most parts of the MAP inference pipeline taking advantage of ubiquitous shared-memory multi-core architectures. We report on extensive experiments with Markov logic network (MLN) benchmarks showing that RockIt outperforms the state-of-the-art systems Alchemy, Markov TheBeast, and Tuffy both in terms of efficiency and quality of results.
There are several lifted inference approaches such as lifted message passing @cite_9 @cite_17 , variants of lifted knowledge compilation and theorem proving @cite_15 @cite_18 , and lifted MCMC @cite_36 @cite_14 approaches. While there are some generic parallel machine learning architectures such as @cite_10 which could in principle be used for parallel MAP inference, is the first system that parallelizes MAP inference in SRL models combining CPI and CPA.
@cite_18 @cite_14 @cite_36 @cite_9 @cite_15 @cite_10 @cite_17
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In this work we present Cutting Plane Inference (CPI), a Maximum A Posteriori (MAP) inference method for Statistical Relational Learning. Framed in terms of Markov Logic and inspired by the Cutting Plane Method, it can be seen as a meta algorithm that instantiates small parts of a large and complex Markov Network and then solves these using a conventional MAP method. We evaluate CPI on two tasks, Semantic Role Labelling and Joint Entity Resolution, while plugging in two different MAP inference methods: the current method of choice for MAP inference in Markov Logic, MaxWalkSAT, and Integer Linear Programming. We observe that when used with CPI both methods are significantly faster than when used alone. In addition, CPI improves the accuracy of MaxWalkSAT and maintains the exactness of Integer Linear Programming. Lifted message passing algorithms exploit repeated structure within a given graphical model to answer queries efficiently. Given evidence, they construct a lifted network of supernodes and superpotentials corresponding to sets of nodes and potentials that are indistinguishable given the evidence. Recently, efficient algorithms were presented for updating the structure of an existing lifted network with incremental changes to the evidence. In the inference stage, however, current algorithms need to construct a separate lifted network for each evidence case and run a modified message passing algorithm on each lifted network separately. Consequently, symmetries across the inference tasks are not exploited. In this paper, we present a novel lifted message passing technique that exploits symmetries across multiple evidence cases. The benefits of this multi-evidence lifted inference are shown for several important AI tasks such as computing personalized PageRanks and Kalman filters via multievidence lifted Gaussian belief propagation. There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic model to speedup inference. In particular, we describe approximate lifted inference techniques that allow the user to trade off inference accuracy for computational efficiency by using a handful of tunable parameters, while keeping the error bounded. Our algorithms are closely related to the graph-theoretic concept of bisimulation. We report experiments on both synthetic and real data to show that in the presence of symmetries, run-times for inference can be improved significantly, with approximate lifted inference providing orders of magnitude speedup over ground inference. Unifying first-order logic and probability is a long-standing goal of AI, and in recent years many representations combining aspects of the two have been proposed. However, inference in them is generally still at the level of propositional logic, creating all ground atoms and formulas and applying standard probabilistic inference methods to the resulting network. Ideally, inference should be lifted as in first-order logic, handling whole sets of indistinguishable objects together, in time independent of their cardinality. Poole (2003) and (2005, 2006) developed a lifted version of the variable elimination algorithm, but it is extremely complex, generally does not scale to realistic domains, and has only been applied to very small artificial problems. In this paper we propose the first lifted version of a scalable probabilistic inference algorithm, belief propagation (loopy or not). Our approach is based on first constructing a lifted network, where each node represents a set of ground atoms that all pass the same messages during belief propagation. We then run belief propagation on this network. We prove the correctness and optimality of our algorithm. Experiments show that it can greatly reduce the cost of inference. Geographic information has spawned many novel Web applications where global positioning system (GPS) plays important roles in bridging the applications and end users. Learning knowledge from users' raw GPS data can provide rich context information for both geographic and mobile applications. However, so far, raw GPS data are still used directly without much understanding. In this paper, an approach based on supervised learning is proposed to automatically infer transportation mode from raw GPS data. The transportation mode, such as walking, driving, etc., implied in a user's GPS data can provide us valuable knowledge to understand the user. It also enables context-aware computing based on user's present transportation mode and design of an innovative user interface for Web users. Our approach consists of three parts: a change point-based segmentation method, an inference model and a post-processing algorithm based on conditional probability. The change point-based segmentation method was compared with two baselines including uniform duration based and uniform length based methods. Meanwhile, four different inference models including Decision Tree, Bayesian Net, Support Vector Machine (SVM) and Conditional Random Field (CRF) are studied in the experiments. We evaluated the approach using the GPS data collected by 45 users over six months period. As a result, beyond other two segmentation methods, the change point based method achieved a higher degree of accuracy in predicting transportation modes and detecting transitions between them. Decision Tree outperformed other inference models over the change point based segmentation method. Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and accurate inference on such problems using Markov chain Monte Carlo (MCMC) techniques with customized proposal distributions. Currently, implementing such a system requires coding MCMC state representations and acceptance probability calculations that are specific to a particular application. An alternative approach, which we pursue in this paper, is to use a general-purpose probabilistic modeling language (such as BLOG) and a generic Metropolis-Hastings MCMC algorithm that supports user-supplied proposal distributions. Our algorithm gains flexibility by using MCMC states that are only partial descriptions of possible worlds; we provide conditions under which MCMC over partial worlds yields correct answers to queries. We also show how to use a context-specific Bayes net to identify the factors in the acceptance probability that need to be computed for a given proposed move. Experimental results on a citation matching task show that our general-purpose MCMC engine compares favorably with an application-specific system. First-order probabilistic models combine the power of first-order logic, the de facto tool for handling relational structure, with probabilistic graphical models, the de facto tool for handling uncertainty. Lifted probabilistic inference algorithms for them have been the subject of much recent research. The main idea in these algorithms is to improve the accuracy and scalability of existing graphical models' inference algorithms by exploiting symmetry in the first-order representation. In this paper, we consider blocked Gibbs sampling, an advanced MCMC scheme, and lift it to the first-order level. We propose to achieve this by partitioning the first-order atoms in the model into a set of disjoint clusters such that exact lifted inference is polynomial in each cluster given an assignment to all other atoms not in the cluster. We propose an approach for constructing the clusters and show how it can be used to trade accuracy with computational complexity in a principled manner. Our experimental evaluation shows that lifted Gibbs sampling is superior to the propositional algorithm in terms of accuracy, scalability and convergence. Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results. This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its conjunctive normal form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations. We propose a novel method called deep convolutional decision jungle (CDJ) and its learning algorithm for image classification. The CDJ maintains the structure of standard convolutional neural networks (CNNs), i.e. multiple layers of multiple response maps fully connected. Each response map-or node-in both the convolutional and fully-connected layers selectively respond to class labels s.t. each data sample travels via a specific soft route of those activated nodes. The proposed method CDJ automatically learns features, whereas decision forests and jungles require pre-defined feature sets. Compared to CNNs, the method embeds the benefits of using data-dependent discriminative functions, which better handles multi-modal heterogeneous data; further,the method offers more diverse sparse network responses, which in turn can be used for cost-effective learning classification. The network is learnt by combining conventional softmax and proposed entropy losses in each layer. The entropy loss,as used in decision tree growing, measures the purity of data activation according to the class label distribution. The back-propagation rule for the proposed loss function is derived from stochastic gradient descent (SGD) optimization of CNNs. We show that our proposed method outperforms state-of-the-art methods on three public image classification benchmarks and one face verification dataset. We also demonstrate the use of auxiliary data labels, when available, which helps our method to learn more discriminative routing and representations and leads to improved classification. Until recently, the lack of ground truth data has hindered the application of discriminative structured prediction techniques to the stereo problem. In this paper we use ground truth data sets that we have recently constructed to explore different model structures and parameter learning techniques. To estimate parameters in Markov random fields (MRFs) via maximum likelihood one usually needs to perform approximate probabilistic inference. Conditional random fields (CRFs) are discriminative versions of traditional MRFs. We explore a number of novel CRF model structures including a CRF for stereo matching with an explicit occlusion model. CRFs require expensive inference steps for each iteration of optimization and inference is particularly slow when there are many discrete states. We explore belief propagation, variational message passing and graph cuts as inference methods during learning and compare with learning via pseudolikelihood. To accelerate approximate inference we have developed a new method called sparse variational message passing which can reduce inference time by an order of magnitude with negligible loss in quality. Learning using sparse variational message passing improves upon previous approaches using graph cuts and allows efficient learning over large data sets when energy functions violate the constraints imposed by graph cuts. There has been an increased growth in a number of applications that naturally generate large volumes of uncertain data. By the advent of such applications, the support of advanced analysis queries such as the skyline and its variant operators for big uncertain data has become important. In this paper, we propose the effective parallel algorithms using MapReduce to process the probabilistic skyline queries for uncertain data modeled by both discrete and continuous models. We present three filtering methods to identify probabilistic non-skyline objects in advance. We next develop a single MapReduce phase algorithm PS-QP-MR by utilizing space partitioning based on a variant of quadtrees to distribute the instances of objects effectively and the enhanced algorithm PS-QPF-MR by applying the three filtering methods additionally. We also propose the workload balancing technique to balance the workload of reduce functions based on the number of machines available. Finally, we present the brute-force algorithms PS-BR-MR and PS-BRF-MR with partitioning randomly and applying the filtering methods. In our experiments, we demonstrate the efficiency and scalability of PS-QPF-MR compared to the other algorithms. Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SGMCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key components: i) adaptive preconditioners (as in ADAgrad or RMSprop), and ii) adaptive element-wise momentum weights. The zerotemperature limit gives a novel stochastic optimization method with adaptive elementwise momentum weights, while conventional optimization methods only have a shared, static momentum weight. Under certain assumptions, our theoretical analysis suggests the proposed simulated annealing approach converges close to the global optima. Experiments on several deep neural network models show state-of-the-art results compared to related stochastic optimization algorithms. Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly nongaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hit-and-run” algorithm performed better than other MCMC methods. Using these algorithms, we show that for this latter class of priors, the posterior mean estimate can have a considerably lower average error than MAP, whereas for gaussian priors, the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting nonmarginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators. Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficient relational variational inference algorithm that factors largescale probability models into simpler variational models, composed of mixtures of iid (Bernoulli) random variables. The algorithm takes probability relational models of largescale hybrid systems and converts them to a close-to-optimal variational models. Then, it efficiently calculates marginal probabilities on the variational models by using a latent (or lifted) variable elimination or a lifted stochastic sampling. This inference is unique because it maintains the relational structure upon individual observations and during inference steps. We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules. Probabilistic logics are receiving a lot of attention today because of their expressive power for knowledge representation and learning. However, this expressivity is detrimental to the tractability of inference, when done at the propositional level. To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. Despite the existence of various lifted inference approaches, there are currently no completeness results about these algorithms. The key contribution of this paper is that we introduce a formal definition of lifted inference that allows us to reason about the completeness of lifted inference algorithms relative to a particular class of probabilistic models. We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables. Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such methods tend to be blurry, over-smoothed and generally appear implausible. A more desirable approach would employ Maximum a Posteriori (MAP) inference, preferring solutions that always have a high probability under the image prior, and thus appear more plausible. Direct MAP estimation for SR is non-trivial, as it requires us to build a model for the image prior from samples. Furthermore, MAP inference is often performed via optimisation-based iterative algorithms which don't compare well with the efficiency of neural-network-based alternatives. Here we introduce new methods for amortised MAP inference whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models. We propose three methods to solve this optimisation problem: (1) Generative Adversarial Networks (GAN) (2) denoiser-guided SR which backpropagates gradient-estimates from denoising to train the network, and (3) a baseline method using a maximum-likelihood-trained image prior. Our experiments show that the GAN based approach performs best on real image data. Lastly, we establish a connection between GANs and amortised variational inference as in e.g. variational autoencoders. Most current statistical natural language processing models use only local features so as to permit dynamic programming in inference, but this makes them unable to fully account for the long distance structure that is prevalent in language use. We show how to solve this dilemma with Gibbs sampling, a simple Monte Carlo method used to perform approximate inference in factored probabilistic models. By using simulated annealing in place of Viterbi decoding in sequence models such as HMMs, CMMs, and CRFs, it is possible to incorporate non-local structure while preserving tractable inference. We use this technique to augment an existing CRF-based information extraction system with long-distance dependency models, enforcing label consistency and extraction template consistency constraints. This technique results in an error reduction of up to 9 over state-of-the-art systems on two established information extraction tasks. The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedule, where larger steps discover new modes, and smaller steps characterize each mode. We prove that our proposed learning rate schedule provides faster convergence to samples from a stationary distribution than SG-MCMC with standard decaying schedules. Moreover, we provide extensive experimental results to demonstrate the effectiveness of cyclical SG-MCMC in learning complex multimodal distributions, especially for fully Bayesian inference with modern deep neural networks.