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Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In this article, we study the FQR model for densely sampled, high-dimensional functional data without relying on parametric error or independent stochastic process assumptions, with the focus being on statistical inference under this challenging regime along with scalable implementation. This is achieved by a simple but powerful distributed strategy, in which we first perform separate quantile regression to compute $M$-estimators at each sampling location, and then carry out estimation and inference for the entire coefficient functions by properly exploiting the uncertainty quantification and dependence structures of $M$-estimators. We derive a uniform Bahadur representation and a strong Gaussian approximation result for the $M$-estimators on the discrete sampling grid, leading to dimension reduction and serving as the basis for inference. An interpolation-based estimator with minimax optimality and a Bayesian alternative to improve upon finite sample performance are discussed. Large sample properties for point and simultaneous interval estimators are established. The obtained minimax optimal rate under the FQR model shows an interesting phase transition phenomenon that has been previously observed in functional mean regression. The proposed methods are illustrated via simulations and an application to a mass spectrometry proteomics dataset.

Reservoir simulations are computationally expensive in the well control and well placement optimization. Generally, numerous simulation runs (realizations) are needed in order to achieve the optimal well locations. In this paper, we propose a graph neural network (GNN) framework to build a surrogate feed-forward model which replaces simulation runs to accelerate the optimization process. Our GNN framework includes an encoder, a process, and a decoder which takes input from the processed graph data designed and generated from the simulation raw data. We train the GNN model with 6000 samples (equivalent to 40 well configurations) with each containing the previous step state variable and the next step state variable. We test the GNN model with another 6000 samples and after model tuning, both one-step prediction and rollout prediction achieve a close match with the simulation results. Our GNN framework shows great potential in the application of well-related subsurface optimization including oil and gas as well as carbon capture sequestration (CCS).

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.

The ability to scale out training workloads has been one of the key performance enablers of deep learning. The main scaling approach is data-parallel GPU-based training, which has been boosted by hardware and software support for highly efficient inter-GPU communication, in particular via bandwidth overprovisioning. This support comes at a price: there is an order of magnitude cost difference between "cloud-grade" servers with such support, relative to their "consumer-grade" counterparts, although server-grade and consumer-grade GPUs can have similar computational envelopes. In this paper, we investigate whether the expensive hardware overprovisioning approach can be supplanted via algorithmic and system design, and propose a framework called CGX, which provides efficient software support for communication compression. We show that this framework is able to remove communication bottlenecks from consumer-grade multi-GPU systems, in the absence of hardware support: when training modern models and tasks to full accuracy, CGX provides self-speedups of 2-3X for an 8-GPU commodity node, enabling it to surpass the throughput of a much more expensive NVIDIA DGX-1 server. In the multi-node setting, CGX enables significant additional speedups by identifying and solving the novel adaptive compression problem, in which we can automatically set compression levels in a layer-wise fashion, balancing speedup and accuracy recovery.

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure, namely a manifold. Manifold learning is an emerging field for learning the underlying structure. The study of manifold learning can be split into two main branches: dimension reduction and manifold fitting. With the aim of combining statistics and geometry, we address the problem of manifold fitting in the ambient space. Inspired by the relation between the eigenvalues of the Laplace-Beltrami operator and the geometry of a manifold, we aim to find a small set of points that preserve the geometry of the underlying manifold. From this relationship, we extend the idea of subsampling to sample points in high-dimensional space and employ the Moving Least Squares (MLS) approach to approximate the underlying manifold. We analyze the two core steps in our proposed method theoretically and also provide the bounds for the MLS approach. Our simulation results and theoretical analysis demonstrate the superiority of our method in estimating the underlying manifold.

Learning effective policies for real-world problems is still an open challenge for the field of reinforcement learning (RL). The main limitation being the amount of data needed and the pace at which that data can be obtained. In this paper, we study how to build lightweight simulators of complicated systems that can run sufficiently fast for deep RL to be applicable. We focus on domains where agents interact with a reduced portion of a larger environment while still being affected by the global dynamics. Our method combines the use of local simulators with learned models that mimic the influence of the global system. The experiments reveal that incorporating this idea into the deep RL workflow can considerably accelerate the training process and presents several opportunities for the future.

Controllable generation is one of the key requirements for successful adoption of deep generative models in real-world applications, but it still remains as a great challenge. In particular, the compositional ability to generate novel concept combinations is out of reach for most current models. In this work, we use energy-based models (EBMs) to handle compositional generation over a set of attributes. To make them scalable to high-resolution image generation, we introduce an EBM in the latent space of a pre-trained generative model such as StyleGAN. We propose a novel EBM formulation representing the joint distribution of data and attributes together, and we show how sampling from it is formulated as solving an ordinary differential equation (ODE). Given a pre-trained generator, all we need for controllable generation is to train an attribute classifier. Sampling with ODEs is done efficiently in the latent space and is robust to hyperparameters. Thus, our method is simple, fast to train, and efficient to sample. Experimental results show that our method outperforms the state-of-the-art in both conditional sampling and sequential editing. In compositional generation, our method excels at zero-shot generation of unseen attribute combinations. Also, by composing energy functions with logical operators, this work is the first to achieve such compositionality in generating photo-realistic images of resolution 1024x1024.

The concept of smart grid has been introduced as a new vision of the conventional power grid to figure out an efficient way of integrating green and renewable energy technologies. In this way, Internet-connected smart grid, also called energy Internet, is also emerging as an innovative approach to ensure the energy from anywhere at any time. The ultimate goal of these developments is to build a sustainable society. However, integrating and coordinating a large number of growing connections can be a challenging issue for the traditional centralized grid system. Consequently, the smart grid is undergoing a transformation to the decentralized topology from its centralized form. On the other hand, blockchain has some excellent features which make it a promising application for smart grid paradigm. In this paper, we have an aim to provide a comprehensive survey on application of blockchain in smart grid. As such, we identify the significant security challenges of smart grid scenarios that can be addressed by blockchain. Then, we present a number of blockchain-based recent research works presented in different literatures addressing security issues in the area of smart grid. We also summarize several related practical projects, trials, and products that have been emerged recently. Finally, we discuss essential research challenges and future directions of applying blockchain to smart grid security issues.

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper, we consider a specific class of invariant and equivariant networks, for which we prove new universality theorems. More precisely, we consider networks with a single hidden layer, obtained by summing channels formed by applying an equivariant linear operator, a pointwise non-linearity and either an invariant or equivariant linear operator. Recently, Maron et al. (2019) showed that by allowing higher-order tensorization inside the network, universal invariant GNNs can be obtained. As a first contribution, we propose an alternative proof of this result, which relies on the Stone-Weierstrass theorem for algebra of real-valued functions. Our main contribution is then an extension of this result to the equivariant case, which appears in many practical applications but has been less studied from a theoretical point of view. The proof relies on a new generalized Stone-Weierstrass theorem for algebra of equivariant functions, which is of independent interest. Finally, unlike many previous settings that consider a fixed number of nodes, our results show that a GNN defined by a single set of parameters can approximate uniformly well a function defined on graphs of varying size.

Cloud Robotics is one of the emerging area of robotics. It has created a lot of attention due to its direct practical implications on Robotics. In Cloud Robotics, the concept of cloud computing is used to offload computational extensive jobs of the robots to the cloud. Apart from this, additional functionalities can also be offered on run to the robots on demand. Simultaneous Localization and Mapping (SLAM) is one of the computational intensive algorithm in robotics used by robots for navigation and map building in an unknown environment. Several Cloud based frameworks are proposed specifically to address the problem of SLAM, DAvinCi, Rapyuta and C2TAM are some of those framework. In this paper, we presented a detailed review of all these framework implementation for SLAM problem.