Tian Gao

Yue Yu, Jie Chen, Tian Gao et al.

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al., 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at \url{https://github.com/fishmoon1234/DAG-GNN}.

Haifeng Qian, Radu Marinescu, Alexander Gray et al.

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.

Yue Yu, Tian Gao, Naiyu Yin et al.

Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve efficiency, we propose a novel learning framework to model and learn the weighted adjacency matrices in the DAG space directly. Specifically, we first show that the set of weighted adjacency matrices of DAGs are equivalent to the set of weighted gradients of graph potential functions, and one may perform structure learning by searching in this equivalent set of DAGs. To instantiate this idea, we propose a new algorithm, DAG-NoCurl, which solves the optimization problem efficiently with a two-step procedure: 1) first we find an initial cyclic solution to the optimization problem, and 2) then we employ the Hodge decomposition of graphs and learn an acyclic graph by projecting the cyclic graph to the gradient of a potential function. Experimental studies on benchmark datasets demonstrate that our method provides comparable accuracy but better efficiency than baseline DAG structure learning methods on both linear and generalized structural equation models, often by more than one order of magnitude.

Rui Chen, Sanjeeb Dash, Tian Gao

The problem of finding an ancestral acyclic directed mixed graph (ADMG) that represents the causal relationships between a set of variables is an important area of research on causal inference. Most existing score-based structure learning methods focus on learning directed acyclic graph (DAG) models without latent variables. A number of score-based methods have recently been proposed for the ADMG learning, yet they are heuristic in nature and do not guarantee an optimal solution. We propose a novel exact score-based method that solves an integer programming (IP) formulation and returns a score-maximizing ancestral ADMG for a set of continuous variables that follow a multivariate Gaussian distribution. We generalize the state-of-the-art IP model for DAG learning problems and derive new classes of valid inequalities to formulate an IP model for ADMG learning. Empirically, our model can be solved efficiently for medium-sized problems and achieves better accuracy than state-of-the-art score-based methods as well as benchmark constraint-based methods.

Dennis Wei, Tian Gao, Yue Yu

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.

Lu Zhang, Mo Yu, Tian Gao et al.

Multi-hop reasoning approaches over knowledge graphs infer a missing relationship between entities with a multi-hop rule, which corresponds to a chain of relationships. We extend existing works to consider a generalized form of multi-hop rules, where each rule is a set of relation chains. To learn such generalized rules efficiently, we propose a two-step approach that first selects a small set of relation chains as a rule and then evaluates the confidence of the target relationship by jointly scoring the selected chains. A game-theoretical framework is proposed to this end to simultaneously optimize the rule selection and prediction steps. Empirical results show that our multi-chain multi-hop (MCMH) rules result in superior results compared to the standard single-chain approaches, justifying both our formulation of generalized rules and the effectiveness of the proposed learning framework.

Zijun Cui, Pavan Kapanipathi, Kartik Talamadupula et al.

Knowledge graphs (KGs) are of great importance to many real world applications, but they generally suffer from incomplete information in the form of missing relations between entities. Knowledge graph completion (also known as relation prediction) is the task of inferring missing facts given existing ones. Most of the existing work is proposed by maximizing the likelihood of observed instance-level triples. Not much attention, however, is paid to the ontological information, such as type information of entities and relations. In this work, we propose a type-augmented relation prediction (TaRP) method, where we apply both the type information and instance-level information for relation prediction. In particular, type information and instance-level information are encoded as prior probabilities and likelihoods of relations respectively, and are combined by following Bayes' rule. Our proposed TaRP method achieves significantly better performance than state-of-the-art methods on four benchmark datasets: FB15K, FB15K-237, YAGO26K-906, and DB111K-174. In addition, we show that TaRP achieves significantly improved data efficiency. More importantly, the type information extracted from a specific dataset can generalize well to other datasets through the proposed TaRP model.

Tian Gao, Dharmashankar Subramanian, Karthikeyan Shanmugam et al.

Event datasets are sequences of events of various types occurring irregularly over the time-line, and they are increasingly prevalent in numerous domains. Existing work for modeling events using conditional intensities rely on either using some underlying parametric form to capture historical dependencies, or on non-parametric models that focus primarily on tasks such as prediction. We propose a non-parametric deep neural network approach in order to estimate the underlying intensity functions. We use a novel multi-channel RNN that optimally reinforces the negative evidence of no observable events with the introduction of fake event epochs within each consecutive inter-event interval. We evaluate our method against state-of-the-art baselines on model fitting tasks as gauged by log-likelihood. Through experiments on both synthetic and real-world datasets, we find that our proposed approach outperforms existing baselines on most of the datasets studied.

Haoyu Wang, Mo Yu, Xiaoxiao Guo et al.

General Question Answering (QA) systems over texts require the multi-hop reasoning capability, i.e. the ability to reason with information collected from multiple passages to derive the answer. In this paper we conduct a systematic analysis to assess such an ability of various existing models proposed for multi-hop QA tasks. Specifically, our analysis investigates that whether providing the full reasoning chain of multiple passages, instead of just one final passage where the answer appears, could improve the performance of the existing QA models. Surprisingly, when using the additional evidence passages, the improvements of all the existing multi-hop reading approaches are rather limited, with the highest error reduction of 5.8% on F1 (corresponding to 1.3% absolute improvement) from the BERT model. To better understand whether the reasoning chains could indeed help find correct answers, we further develop a co-matching-based method that leads to 13.1% error reduction with passage chains when applied to two of our base readers (including BERT). Our results demonstrate the existence of the potential improvement using explicit multi-hop reasoning and the necessity to develop models with better reasoning abilities.

Ameya Godbole, Dilip Kavarthapu, Rajarshi Das et al.

Multi-hop question answering (QA) requires an information retrieval (IR) system that can find \emph{multiple} supporting evidence needed to answer the question, making the retrieval process very challenging. This paper introduces an IR technique that uses information of entities present in the initially retrieved evidence to learn to `\emph{hop}' to other relevant evidence. In a setting, with more than \textbf{5 million} Wikipedia paragraphs, our approach leads to significant boost in retrieval performance. The retrieved evidence also increased the performance of an existing QA model (without any training) on the \hotpot benchmark by \textbf{10.59} F1.

Dennis Wei, Sanjeeb Dash, Tian Gao et al.

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences and interactions. Our problem formulation accordingly trades off rule set complexity and prediction accuracy. Column generation is used to optimize over an exponentially large space of rules without pre-generating a large subset of candidates or greedily boosting rules one by one. The column generation subproblem is solved using either integer programming or a heuristic optimizing the same objective. In experiments involving logistic and linear regression, the proposed methods obtain better accuracy-complexity trade-offs than existing rule ensemble algorithms. At one end of the trade-off, the methods are competitive with less interpretable benchmark models.

Tian Gao, Jie Chen, Vijil Chenthamarakshan et al.

Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are not readily applicable to set-valued outputs because of the growth rate of the output space; and because conventional sequence generation doesn't reflect sets' order-free nature. In this paper, we propose a unified framework--sequential set generation (SSG)--that can handle output sets of labels and sequences. SSG is a meta-algorithm that leverages any probabilistic learning method for label or sequence prediction, but employs a proper regularization such that a new label or sequence is generated repeatedly until the full set is produced. Though SSG is sequential in nature, it does not penalize the ordering of the appearance of the set elements and can be applied to a variety of set output problems, such as a set of classification labels or sequences. We perform experiments with both benchmark and synthetic data sets and demonstrate SSG's strong performance over baseline methods.

Clemens Rosenbaum, Tian Gao, Tim Klinger

In this paper we present a new dataset and user simulator e-QRAQ (explainable Query, Reason, and Answer Question) which tests an Agent's ability to read an ambiguous text; ask questions until it can answer a challenge question; and explain the reasoning behind its questions and answer. The User simulator provides the Agent with a short, ambiguous story and a challenge question about the story. The story is ambiguous because some of the entities have been replaced by variables. At each turn the Agent may ask for the value of a variable or try to answer the challenge question. In response the User simulator provides a natural language explanation of why the Agent's query or answer was useful in narrowing down the set of possible answers, or not. To demonstrate one potential application of the e-QRAQ dataset, we train a new neural architecture based on End-to-End Memory Networks to successfully generate both predictions and partial explanations of its current understanding of the problem. We observe a strong correlation between the quality of the prediction and explanation.