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We present a novel bottom-up method for the synthesis of functional recursive programs. While bottom-up synthesis techniques can work better than top-down methods in certain settings, there is no prior technique for synthesizing recursive programs from logical specifications in a purely bottom-up fashion. The main challenge is that effective bottom-up methods need to execute sub-expressions of the code being synthesized, but it is impossible to execute a recursive subexpression of a program that has not been fully constructed yet. In this paper, we address this challenge using the concept of angelic semantics. Specifically, our method finds a program that satisfies the specification under angelic semantics (we refer to this as angelic synthesis), analyzes the assumptions made during its angelic execution, uses this analysis to strengthen the specification, and finally reattempts synthesis with the strengthened specification. Our proposed angelic synthesis algorithm is based on version space learning and therefore deals effectively with many incremental synthesis calls made during the overall algorithm. We have implemented this approach in a prototype called Burst and evaluate it on synthesis problems from prior work. Our experiments show that Burst is able to synthesize a solution to 95% of the benchmarks in our benchmark suite, outperforming prior work.

Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of adversarial attacks. We take another step forward in relating the architectural structure of neural networks from a graph theoretic perspective to their robustness. We aim to investigate any existing correlations between graph theoretic properties and the robustness of Sparse Neural Networks. Our hypothesis is, that graph theoretic properties as a prior of neural network structures are related to their robustness. To answer to this hypothesis, we designed an empirical study with neural network models obtained through random graphs used as sparse structural priors for the networks. We additionally investigated the evaluation of a randomly pruned fully connected network as a point of reference. We found that robustness measures are independent of initialization methods but show weak correlations with graph properties: higher graph densities correlate with lower robustness, but higher average path lengths and average node eccentricities show negative correlations with robustness measures. We hope to motivate further empirical and analytical research to tightening an answer to our hypothesis.

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are subject to mutual time warping. That is, the component processes exhibit a similar shape but are subject to systematic phase variation across their time domains. We introduce a novel model for multivariate functional data that incorporates such mutual time warping via nonlinear transport functions. This model allows for meaningful interpretation and is well suited to represent functional vector data. The proposed approach combines a random amplitude factor for each component with population based registration across the components of a multivariate functional data vector and also includes a latent population function, which corresponds to a common underlying trajectory as well as subject-specific warping component. We also propose estimators for all components of the model. The proposed approach not only leads to a novel representation for multivariate functional data, but is also useful for downstream analyses such as Fr\'echet regression. Rates of convergence are established when curves are fully observed or observed with measurement error. The usefulness of the model, interpretations and practical aspects are illustrated in simulations and with application to multivariate human growth curves as well as multivariate environmental pollution data.

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.

We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or countable infinite set of variables. In the finite case the underlying graph can be recovered with probability one, while in the countable infinite case we can recover any finite sub-graph with probability one, by allowing the candidate neighborhoods to grow with the sample size n and provided the penalizing constant is sufficiently large. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We evaluate the performance of the estimator on simulated data and we apply the methodology to a real dataset of stock index markets in different countries.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Path-based relational reasoning over knowledge graphs has become increasingly popular due to a variety of downstream applications such as question answering in dialogue systems, fact prediction, and recommender systems. In recent years, reinforcement learning (RL) has provided solutions that are more interpretable and explainable than other deep learning models. However, these solutions still face several challenges, including large action space for the RL agent and accurate representation of entity neighborhood structure. We address these problems by introducing a type-enhanced RL agent that uses the local neighborhood information for efficient path-based reasoning over knowledge graphs. Our solution uses graph neural network (GNN) for encoding the neighborhood information and utilizes entity types to prune the action space. Experiments on real-world dataset show that our method outperforms state-of-the-art RL methods and discovers more novel paths during the training procedure.

BERT-based architectures currently give state-of-the-art performance on many NLP tasks, but little is known about the exact mechanisms that contribute to its success. In the current work, we focus on the interpretation of self-attention, which is one of the fundamental underlying components of BERT. Using a subset of GLUE tasks and a set of handcrafted features-of-interest, we propose the methodology and carry out a qualitative and quantitative analysis of the information encoded by the individual BERT's heads. Our findings suggest that there is a limited set of attention patterns that are repeated across different heads, indicating the overall model overparametrization. While different heads consistently use the same attention patterns, they have varying impact on performance across different tasks. We show that manually disabling attention in certain heads leads to a performance improvement over the regular fine-tuned BERT models.

Medical knowledge graph is the core component for various medical applications such as automatic diagnosis and question-answering. However, medical knowledge usually associates with certain conditions, which can significantly affect the performance of the supported applications. In the light of this challenge, we propose a new truth discovery method to explore medical-related texts and infer trustworthiness degrees of knowledge triples associating with different conditions. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed truth discovery method.

Recurrent models for sequences have been recently successful at many tasks, especially for language modeling and machine translation. Nevertheless, it remains challenging to extract good representations from these models. For instance, even though language has a clear hierarchical structure going from characters through words to sentences, it is not apparent in current language models. We propose to improve the representation in sequence models by augmenting current approaches with an autoencoder that is forced to compress the sequence through an intermediate discrete latent space. In order to propagate gradients though this discrete representation we introduce an improved semantic hashing technique. We show that this technique performs well on a newly proposed quantitative efficiency measure. We also analyze latent codes produced by the model showing how they correspond to words and phrases. Finally, we present an application of the autoencoder-augmented model to generating diverse translations.