Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete causal discovery algorithms have been previously introduced, where a directed acyclic graph (DAG), or its equivalence class, representing causal relations is searched. However, in real-world cases, only finite training data is available, which limits the power of statistical tests used by these algorithms, leading to errors in the inferred causal model. This is commonly addressed by devising a strategy for using as few as possible statistical tests. In this paper, we introduce such a strategy in the form of a recursive wrapper for existing constraint-based causal discovery algorithms, which preserves soundness and completeness. It recursively clusters the observed variables using the normalized min-cut criterion from the outset, and uses a baseline causal discovery algorithm during backtracking for learning local sub-graphs. It then combines them and ensures completeness. By an ablation study, using synthetic data, and by common real-world benchmarks, we demonstrate that our approach requires significantly fewer statistical tests, learns more accurate graphs, and requires shorter run-times than the baseline algorithm.
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Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome variable. It allows estimation of both discrete and continuous treatment effects. Furthermore, it allows for the inclusion of additional numerical confounding factors next to text data. To this end, we combine a supervised Bayesian topic model with a Bayesian regression framework and perform supervised representation learning for the text features jointly with the regression parameter training, respecting the Frisch-Waugh-Lovell theorem. Our paper makes two main contributions. First, we provide a regression framework that allows causal inference in settings when both text and numerical confounders are of relevance. We show with synthetic and semi-synthetic datasets that our joint approach recovers ground truth with lower bias than any benchmark model, when text and numerical features are correlated. Second, experiments on two real-world datasets demonstrate that a joint and supervised learning strategy also yields superior prediction results compared to strategies that estimate regression weights for text and non-text features separately, being even competitive with more complex deep neural networks.
In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $\sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the "linear association" conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.
Motivated by establishing theoretical foundations for various manifold learning algorithms, we study the problem of Mahalanobis distance (MD), and the associated precision matrix, estimation from high-dimensional noisy data. By relying on recent transformative results in covariance matrix estimation, we demonstrate the sensitivity of \MD~and the associated precision matrix to measurement noise, determining the exact asymptotic signal-to-noise ratio at which MD fails, and quantifying its performance otherwise. In addition, for an appropriate loss function, we propose an asymptotically optimal shrinker, which is shown to be beneficial over the classical implementation of the MD, both analytically and in simulations. The result is extended to the manifold setup, where the nonlinear interaction between curvature and high-dimensional noise is taken care of. The developed solution is applied to study a multiscale reduction problem in the dynamical system analysis.
We present an objective function for similarity based hierarchical clustering of partially ordered data that preserves the partial order in the sense that if $x \leq y$, and if $[x]$ and $[y]$ are the respective clusters of $x$ and $y$, then there is an order relation $\leq'$ on the clusters for which $[x] \leq' |y]$. The model distinguishes itself from existing methods and models for clustering of ordered data in that the order relation and the similarity are combined to obtain an optimal hierarchical clustering seeking to satisfy both, and that the order relation is equipped with a pairwise level of comparability in the range $[0,1]$. In particular, if the similarity and the order relation are not aligned, then order preservation may have to yield in favor of clustering. Finding an optimal solution is NP-hard, so we provide a polynomial time approximation algorithm, with a relative performance guarantee of $O(\log^{3/2}n)$, based on successive applications of directed sparsest cut. The model is an extension of the Dasgupta cost function for divisive hierarchical clustering.
Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been shown to achieve superior results on some sequence modeling tasks such as machine translation, with the added advantage that they concurrently process all inputs in the sequence, leading to easy parallelization and faster training times. Despite these successes, however, popular feed-forward sequence models like the Transformer fail to generalize in many simple tasks that recurrent models handle with ease, e.g. copying strings or even simple logical inference when the string or formula lengths exceed those observed at training time. We propose the Universal Transformer (UT), a parallel-in-time self-attentive recurrent sequence model which can be cast as a generalization of the Transformer model and which addresses these issues. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. We also add a dynamic per-position halting mechanism and find that it improves accuracy on several tasks. In contrast to the standard Transformer, under certain assumptions, UTs can be shown to be Turing-complete. Our experiments show that UTs outperform standard Transformers on a wide range of algorithmic and language understanding tasks, including the challenging LAMBADA language modeling task where UTs achieve a new state of the art, and machine translation where UTs achieve a 0.9 BLEU improvement over Transformers on the WMT14 En-De dataset.
Although neural network approaches achieve remarkable success on a variety of NLP tasks, many of them struggle to answer questions that require commonsense knowledge. We believe the main reason is the lack of commonsense \mbox{connections} between concepts. To remedy this, we provide a simple and effective method that leverages external commonsense knowledge base such as ConceptNet. We pre-train direct and indirect relational functions between concepts, and show that these pre-trained functions could be easily added to existing neural network models. Results show that incorporating commonsense-based function improves the baseline on three question answering tasks that require commonsense reasoning. Further analysis shows that our system \mbox{discovers} and leverages useful evidence from an external commonsense knowledge base, which is missing in existing neural network models and help derive the correct answer.
In this paper, we propose a novel end-to-end neural architecture for ranking candidate answers, that adapts a hierarchical recurrent neural network and a latent topic clustering module. With our proposed model, a text is encoded to a vector representation from an word-level to a chunk-level to effectively capture the entire meaning. In particular, by adapting the hierarchical structure, our model shows very small performance degradations in longer text comprehension while other state-of-the-art recurrent neural network models suffer from it. Additionally, the latent topic clustering module extracts semantic information from target samples. This clustering module is useful for any text related tasks by allowing each data sample to find its nearest topic cluster, thus helping the neural network model analyze the entire data. We evaluate our models on the Ubuntu Dialogue Corpus and consumer electronic domain question answering dataset, which is related to Samsung products. The proposed model shows state-of-the-art results for ranking question-answer pairs.
Human conversation is a complex mechanism with subtle nuances. It is hence an ambitious goal to develop artificial intelligence agents that can participate fluently in a conversation. While we are still far from achieving this goal, recent progress in visual question answering, image captioning, and visual question generation shows that dialog systems may be realizable in the not too distant future. To this end, a novel dataset was introduced recently and encouraging results were demonstrated, particularly for question answering. In this paper, we demonstrate a simple symmetric discriminative baseline, that can be applied to both predicting an answer as well as predicting a question. We show that this method performs on par with the state of the art, even memory net based methods. In addition, for the first time on the visual dialog dataset, we assess the performance of a system asking questions, and demonstrate how visual dialog can be generated from discriminative question generation and question answering.
A number of recent works have proposed attention models for Visual Question Answering (VQA) that generate spatial maps highlighting image regions relevant to answering the question. In this paper, we argue that in addition to modeling "where to look" or visual attention, it is equally important to model "what words to listen to" or question attention. We present a novel co-attention model for VQA that jointly reasons about image and question attention. In addition, our model reasons about the question (and consequently the image via the co-attention mechanism) in a hierarchical fashion via a novel 1-dimensional convolution neural networks (CNN). Our model improves the state-of-the-art on the VQA dataset from 60.3% to 60.5%, and from 61.6% to 63.3% on the COCO-QA dataset. By using ResNet, the performance is further improved to 62.1% for VQA and 65.4% for COCO-QA.
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