Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic graph is used to specify hierarchical constraints on the allowable configurations of the discrete latent attributes. In this paper, we consider the important yet unaddressed problem of testing the existence of latent hierarchical structures in CDMs. We first introduce the concept of testability of hierarchical structures in CDMs and present sufficient conditions. Then we study the asymptotic behaviors of the likelihood ratio test (LRT) statistic, which is widely used for testing nested models. Due to the irregularity of the problem, the asymptotic distribution of LRT becomes nonstandard and tends to provide unsatisfactory finite sample performance under practical conditions. We provide statistical insights on such failures, and propose to use parametric bootstrap to perform the testing. We also demonstrate the effectiveness and superiority of parametric bootstrap for testing the latent hierarchies over non-parametric bootstrap and the na\"ive Chi-squared test through comprehensive simulations and an educational assessment dataset.
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We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected information, which we show exists at points of singular information under regularity conditions. Similar results have previously only been obtained for scalar parameters, under conditions stronger than ours, and applications to mixed models have not been considered. In simulations our confidence regions have near-nominal coverage with as few as $n = 20$ independent observations, regardless of how close to the boundary the true parameter is. It is a corollary of our main results that the proposed test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of tested parameters, even if they are on the boundary of the parameter set.
Structure information extraction refers to the task of extracting structured text fields from web pages, such as extracting a product offer from a shopping page including product title, description, brand and price. It is an important research topic which has been widely studied in document understanding and web search. Recent natural language models with sequence modeling have demonstrated state-of-the-art performance on web information extraction. However, effectively serializing tokens from unstructured web pages is challenging in practice due to a variety of web layout patterns. Limited work has focused on modeling the web layout for extracting the text fields. In this paper, we introduce WebFormer, a Web-page transFormer model for structure information extraction from web documents. First, we design HTML tokens for each DOM node in the HTML by embedding representations from their neighboring tokens through graph attention. Second, we construct rich attention patterns between HTML tokens and text tokens, which leverages the web layout for effective attention weight computation. We conduct an extensive set of experiments on SWDE and Common Crawl benchmarks. Experimental results demonstrate the superior performance of the proposed approach over several state-of-the-art methods.
We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero if, and only if, the causal effect is identifiable via covariate adjustment. We show that under some restrictions on the structural equations, the causal bias can be estimated efficiently and allows for causal regularization of predictive probabilistic models. We demonstrate the effectiveness of our method for causal bias quantification in various settings where (not) controlling for certain covariates would introduce causal bias.
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of stagnation are observed. We introduce the subordinated Cox-Ross-Rubinstein model and prove that the price of the underlying in that model converges in distribution to the price of underlying in the subordinated Black-Scholes model defined in [26]. Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.
Hierarchical forecasting problems arise when time series have a natural group structure, and predictions at multiple levels of aggregation and disaggregation across the groups are needed. In such problems, it is often desired to satisfy the aggregation constraints in a given hierarchy, referred to as hierarchical coherence in the literature. Maintaining hierarchical coherence while producing accurate forecasts can be a challenging problem, especially in the case of probabilistic forecasting. We present a novel method capable of accurate and coherent probabilistic forecasts for hierarchical time series. We call it Deep Poisson Mixture Network (DPMN). It relies on the combination of neural networks and a statistical model for the joint distribution of the hierarchical multivariate time series structure. By construction, the model guarantees hierarchical coherence and provides simple rules for aggregation and disaggregation of the predictive distributions. We perform an extensive empirical evaluation comparing the DPMN to other state-of-the-art methods which produce hierarchically coherent probabilistic forecasts on multiple public datasets. Compared to existing coherent probabilistic models, we obtained a relative improvement in the overall Continuous Ranked Probability Score (CRPS) of 17.1% on Australian domestic tourism data, 24.2 on the Favorita grocery sales dataset, and 6.9% on a San Francisco Bay Area highway traffic dataset.
Meta learning is a promising solution to few-shot learning problems. However, existing meta learning methods are restricted to the scenarios where training and application tasks share the same out-put structure. To obtain a meta model applicable to the tasks with new structures, it is required to collect new training data and repeat the time-consuming meta training procedure. This makes them inefficient or even inapplicable in learning to solve heterogeneous few-shot learning tasks. We thus develop a novel and principled HierarchicalMeta Learning (HML) method. Different from existing methods that only focus on optimizing the adaptability of a meta model to similar tasks, HML also explicitly optimizes its generalizability across heterogeneous tasks. To this end, HML first factorizes a set of similar training tasks into heterogeneous ones and trains the meta model over them at two levels to maximize adaptation and generalization performance respectively. The resultant model can then directly generalize to new tasks. Extensive experiments on few-shot classification and regression problems clearly demonstrate the superiority of HML over fine-tuning and state-of-the-art meta learning approaches in terms of generalization across heterogeneous tasks.
In this paper, we investigate the challenges of using reinforcement learning agents for question-answering over knowledge graphs for real-world applications. We examine the performance metrics used by state-of-the-art systems and determine that they are inadequate for such settings. More specifically, they do not evaluate the systems correctly for situations when there is no answer available and thus agents optimized for these metrics are poor at modeling confidence. We introduce a simple new performance metric for evaluating question-answering agents that is more representative of practical usage conditions, and optimize for this metric by extending the binary reward structure used in prior work to a ternary reward structure which also rewards an agent for not answering a question rather than giving an incorrect answer. We show that this can drastically improve the precision of answered questions while only not answering a limited number of previously correctly answered questions. Employing a supervised learning strategy using depth-first-search paths to bootstrap the reinforcement learning algorithm further improves performance.
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. However, methods for evaluating clusterability vary radically, making it challenging to select a suitable measure. In this paper, we perform an extensive comparison of measures of clusterability and provide guidelines that clustering users can reference to select suitable measures for their applications.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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