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Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

The end-to-end ASR model is often desired in the streaming multilingual scenario since it is easier to deploy and can benefit from pre-trained speech models such as powerful foundation models. Meanwhile, the heterogeneous nature and imbalanced data abundance of different languages may cause performance degradation, leading to asynchronous peak performance for different languages during training, especially on tail ones. Sometimes even the data itself may become unavailable as a result of the enhanced privacy protection. Existing work tend to significantly increase the model size or learn language-specific decoders to accommodate each language separately. In this study, we explore simple yet effective Language-Dependent Adapter (LDA) finetuning under a cascaded Conformer transducer framework enhanced by teacher pseudo-labeling for tail languages in the streaming multilingual ASR. The adapter only accounts for 0.4% of the full model per language. It is plugged into the frozen foundation model and is the only trainable module during the finetuning process with noisy student training. The final model merges the adapter parameters from different checkpoints for different languages. The model performance is validated on a challenging multilingual dictation dataset, which includes 39 tail languages across Latin, Greek, Arabic, etc. Our proposed method brings 12.2% word error rate reduction on average and up to 37.5% on a single locale. Furthermore, we show that our parameter-efficient LDA can match the quality of the full model finetuning, thus greatly alleviating the asynchronous peak performance issue.

To enhance the intelligence degree in operation and maintenance, a novel method for fault detection in power grids is proposed. The proposed GNN-based approach first identifies fault nodes through a specialized feature extraction method coupled with a knowledge graph. By incorporating temporal data, the method leverages the status of nodes from preceding and subsequent time periods to help current fault detection. To validate the effectiveness of the node features, a correlation analysis of the output features from each node was conducted. The results from experiments show that this method can accurately locate fault nodes in simulation scenarios with a remarkable accuracy. Additionally, the graph neural network based feature modeling allows for a qualitative examination of how faults spread across nodes, which provides valuable insights for analyzing fault nodes.

While including pairwise interactions in a regression model can better approximate response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often leads to extremely large-scale interaction modeling problem, where the challenge is posed to identify important interactions among millions or even billions of candidate interactions. While several methods have recently been proposed to tackle this challenge, they are mostly designed by (1) assuming the hierarchy assumption among the important interactions and (or) (2) focusing on the case in linear models with interactions and (sub)Gaussian errors. In practice, however, neither of these two building blocks has to hold. In this paper, we propose an interaction modeling framework in generalized linear models (GLMs) which is free of any assumptions on hierarchy. We develop a non-trivial extension of the reluctance interaction selection principle to the GLMs setting, where a main effect is preferred over an interaction if all else is equal. Our proposed method is easy to implement, and is highly scalable to large-scale datasets. Theoretically, we demonstrate that it possesses screening consistency under high-dimensional setting. Numerical studies on simulated datasets and a real dataset show that the proposed method does not sacrifice statistical performance in the presence of significant computational gain.

A recurring challenge in the application of redistricting simulation algorithms lies in extracting useful summaries and comparisons from a large ensemble of districting plans. Researchers often compute summary statistics for each district in a plan, and then study their distribution across the plans in the ensemble. This approach discards rich geographic information that is inherent in districting plans. We introduce the projective average, an operation that projects a district-level summary statistic back to the underlying geography and then averages this statistic across plans in the ensemble. Compared to traditional district-level summaries, projective averages are a powerful tool for geographically granular, sub-district analysis of districting plans along a variety of dimensions. However, care must be taken to account for variation within redistricting ensembles, to avoid misleading conclusions. We propose and validate a multiple-testing procedure to control the probability of incorrectly identifying outlier plans or regions when using projective averages.

Attribution scores can be applied in data management to quantify the contribution of individual items to conclusions from the data, as part of the explanation of what led to these conclusions. In Artificial Intelligence, Machine Learning, and Data Management, some of the common scores are deployments of the Shapley value, a formula for profit sharing in cooperative game theory. Since its invention in the 1950s, the Shapley value has been used for contribution measurement in many fields, from economics to law, with its latest researched applications in modern machine learning. Recent studies investigated the application of the Shapley value to database management. This article gives an overview of recent results on the computational complexity of the Shapley value for measuring the contribution of tuples to query answers and to the extent of inconsistency with respect to integrity constraints. More specifically, the article highlights lower and upper bounds on the complexity of calculating the Shapley value, either exactly or approximately, as well as solutions for realizing the calculation in practice.

Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation and can be computed even when the target density has an intractable normalizing constant. Notable applications include the diagnosis of approximate MCMC samplers and goodness-of-fit tests for unnormalized statistical models. The present work analyzes the convergence control properties of KSDs. We first show that standard KSDs used for weak convergence control fail to control moment convergence. To address this limitation, we next provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence. As an immediate consequence we develop, for each $q > 0$, the first KSDs known to exactly characterize $q$-Wasserstein convergence.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.