In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature's number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data.

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary weighted set, defined as the sum of weights of all elements in the set. Our technique provides upper and lower bounds on a novel generalization of Rademacher complexity to the weighted setting in terms of the weighted set size. This generalizes Massart’s Lemma, a known upper bound on the Rademacher complexity in terms of the unweighted set size. We show that the weighted Rademacher complexity can be estimated by solving a randomly perturbed optimization problem, allowing us to derive high probability bounds on the size of any weighted set. We apply our method to the problems of calculating the partition function of an Ising model and computing propositional model counts (#SAT). Our experiments demonstrate that we can produce tighter bounds than competing methods in both the weighted and unweighted settings.

Weight learning is a challenging problem in Markov Logic Networks (MLNs) due to the large size of the ground propositional probabilistic graphical model that underlies the first-order representation of MLNs. Though more sophisticated weight learning methods that use lifted inference have been proposed, such methods can typically scale up only in the absence of evidence, namely in generative weight learning. In discriminative learning, where the evidence typically destroys symmetries, existing approaches are lacking in scalability. In this paper, we propose a novel, intuitive approach for learning MLNs discriminatively by utilizing approximate symmetries. Specifically, we reduce the size of the training database by clustering approximately symmetric atoms together and selecting a representative atom from each cluster. However, each choice made from the clusters induces a different distribution, increasing the uncertainty in our learned model. To reduce this uncertainty, we learn a finite mixture model by stacking the different distributions, where the parameters of the model are learned using an EM approach. Our results on several benchmarks show that our approach is much more scalable and accurate as compared to existing state-of-the-art MLN learning methods.

Consider a policymaker who wants to decide which intervention to perform in order to change a currently undesirable situation. The policymaker has at her disposal a team of experts, each with their own understanding of the causal dependencies between different factors contributing to the outcome. The policymaker has varying degrees of confidence in the experts’ opinions. She wants to combine their opinions in order to decide on the most effective intervention. We formally define the notion of an effective intervention, and then consider how experts’ causal judgments can be combined in order to determine the most effective intervention. We define a notion of two causal models being compatible , and show how compatible causal models can be combined. We then use it as the basis for combining experts causal judgments. We illustrate our approach on a number of real-life examples.

Decentralized (PO)MDPs provide a rigorous framework for sequential multiagent decision making under uncertainty. However, their high computational complexity limits the practical impact. To address scalability and real-world impact, we focus on settings where a large number of agents primarily interact through complex joint-rewards that depend on their entire histories of states and actions. Such history-based rewards encapsulate the notion of events or tasks such that the team reward is given only when the joint-task is completed. Algorithmically, we contribute---1) A nonlinear programming (NLP) formulation for such event-based planning model; 2) A probabilistic inference based approach that scales much better than NLP solvers for a large number of agents; 3) A policy gradient based multiagent reinforcement learning approach that scales well even for exponential state-spaces. Our inference and RL-based advances enable us to solve a large real-world multiagent coverage problem modeling schedule coordination of agents in a real urban subway network where other approaches fail to scale.

Bayesian inference methods for probabilistic topic models can quantify uncertainty in the parameters, which has primarily been used to increase the robustness of parameter estimates. In this work, we explore other rich information that can be obtained by analyzing the posterior distributions in topic models. Experimenting with latent Dirichlet allocation on two datasets, we propose ideas incorporating information about the posterior distributions at the topic level and at the word level. At the topic level, we propose a metric called topic stability that measures the variability of the topic parameters under the posterior. We show that this metric is correlated with human judgments of topic quality as well as with the consistency of topics appearing across multiple models. At the word level, we experiment with different methods for adjusting individual word probabilities within topics based on their uncertainty. Humans prefer words ranked by our adjusted estimates nearly twice as often when compared to the traditional approach. Finally, we describe how the ideas presented in this work could potentially applied to other predictive or exploratory models in future work.

Typically, neural conversation systems generate replies based on the sequence-to-sequence (seq2seq) model. seq2seq tends to produce safe and universal replies, which suffers from the lack of diversity and information. Determinantal Point Processes (DPPs) is a probabilistic model defined on item sets, which can select the items with good diversity and quality. In this paper, we investigate the diversity issue in two different aspects, namely query-level and system-level diversity. We propose a novel framework which organically combines seq2seq model with Determinantal Point Processes (DPPs). The new framework achieves high quality in generated reply and significantly improves the diversity among them. Experiments show that our model achieves the best performance among various baselines in terms of both quality and diversity.

Neural machine translation (NMT) heavily relies on parallel bilingual data for training. Since large-scale, high-quality parallel corpora are usually costly to collect, it is appealing to exploit monolingual corpora to improve NMT. Inspired by the law of total probability, which connects the probability of a given target-side monolingual sentence to the conditional probability of translating from a source sentence to the target one, we propose to explicitly exploit this connection to learn from and regularize the training of NMT models using monolingual data. The key technical challenge of this approach is that there are exponentially many source sentences for a target monolingual sentence while computing the sum of the conditional probability given each possible source sentence. We address this challenge by leveraging the dual translation model (target-to-source translation) to sample several mostly likely source-side sentences and avoid enumerating all possible candidate source sentences. That is, we transfer the knowledge contained in the dual model to boost the training of the primal model (source-to-target translation), and we call such an approach dual transfer learning. Experiment results on English-French and German-English tasks demonstrate that dual transfer learning achieves significant improvement over several strong baselines and obtains new state-of-the-art results.

Pre-trained distributed word representations have been proven to be useful in various natural language processing (NLP) tasks. However, the geometric basis of word representations and their relations to the representations of word's contexts has not been carefully studied yet. In this study, we first investigate such geometric relationship under a general framework, which is abstracted from some typical word representation learning approaches, and find out that only the directions of word representations are well associated to their context vector representations while the magnitudes are not. In order to make better use of the information contained in the magnitudes of word representations, we propose a hierarchical Gaussian model combined with maximum a posteriori estimation to learn word representations, and extend it to represent polysemous words. Our word representations have been evaluated on multiple NLP tasks, and the experimental results show that the proposed model achieved promising results, comparing to several popular word representations.

Dynamic topic models (DTM) are commonly used for mining latent topics in evolving web corpora. In this paper, we note that a major limitation of the conventional DTM based models is that they assume a predetermined and fixed scale of topics. In reality, however, topics may have varying spans and topics of multiple scales can co-exist in a single web or social media data stream. Therefore, DTMs that assume a fixed epoch length may not be able to effectively capture latent topics and thus negatively affect accuracy. In this paper, we propose a Multi-Scale Dynamic Topic Model (MS-DTM) and a complementary Incremental Multi-Scale Dynamic Topic Model (IMS-DTM) inference method that can be used to capture latent topics and their dynamics simultaneously, at different scales. In this model, topic specific feature distributions are generated based on a multi-scale feature distribution of the previous epochs; moreover, multiple scales of the current epoch are analyzed together through a novel multi-scale incremental Gibbs sampling technique. We show that the proposed model significantly improves efficiency and effectiveness compared to the single scale dynamic DTMs and prior models that consider only multiple scales of the past.