Ground-based solar image restoration is a computationally expensive procedure that involves nonlinear optimization techniques. The presence of atmospheric turbulence produces perturbations in individual images that make it necessary to apply blind deconvolution techniques. These techniques rely on the observation of many short exposure frames that are used to simultaneously infer the instantaneous state of the atmosphere and the unperturbed object. We have recently explored the use of machine learning to accelerate this process, with promising results. We build upon this previous work to propose several interesting improvements that lead to better models. As well, we propose a new method to accelerate the restoration based on algorithm unrolling. In this method, the image restoration problem is solved with a gradient descent method that is unrolled and accelerated aided by a few small neural networks. The role of the neural networks is to correct the estimation of the solution at each iterative step. The model is trained to perform the optimization in a small fixed number of steps with a curated dataset. Our findings demonstrate that both methods significantly reduce the restoration time compared to the standard optimization procedure. Furthermore, we showcase that these models can be trained in an unsupervised manner using observed images from three different instruments. Remarkably, they also exhibit robust generalization capabilities when applied to new datasets. To foster further research and collaboration, we openly provide the trained models, along with the corresponding training and evaluation code, as well as the training dataset, to the scientific community.
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With the rapid growth in the demand for plug-in electric vehicles (EVs), the corresponding charging infrastructures are expanding. These charging stations are located at various places and with different congestion levels. EV drivers face an important decision in choosing which charging station to go to in order to reduce their overall time costs. However, existing literature either assumes a flat charging rate and hence overlooks the physical characteristics of an EV battery where charging rate is typically reduced as the battery charges, or ignores the effect of other drivers on an EV's decision making process. In this paper, we consider both the predetermined exogenous wait cost and the endogenous congestion induced by other drivers' strategic decisions, and propose a differential equation based approach to find the optimal strategies. We analytically characterize the equilibrium strategies and find that co-located EVs may make different decisions depending on the charging rate and/or remaining battery levels. Through numerical experiments, we investigate the impact of charging rate characteristics, modeling parameters and the consideration of endogenous congestion levels on the optimal charging decisions. Finally, we conduct numerical studies on real-world data and find that some EV users with slower charging rates may benefit from the participation of fast-charging EVs.
We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact representation to the well-known Neural Tangent Kernel (NTK) and discuss approximation error relative to the NTK and other non-exact path kernel formulations. We experimentally demonstrate that the kernel can be computed for realistic networks up to machine precision. We use this exact kernel to show that our theoretical contribution can provide useful insights into the predictions made by neural networks, particularly the way in which they generalize.
The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated under a more general setting, and two estimators for estimating the parameters have been proposed. Since both estimators are obtained iterative fashion, several numerical schemes are investigated and the best initial guess is determined. Furthermore, the constraint Cram\'{e} Rao lower bound for this problem is derived and it is compared with the variance of each estimator. Finally, our theory is assessed and validated by a series of numerical experiments on both real and synthetic data.
Understanding how helpful a visualization is from experimental results is difficult because the observed performance is confounded with aspects of the study design, such as how useful the information that is visualized is for the task. We develop a rational agent framework for designing and interpreting visualization experiments. Our framework conceives two experiments with the same setup: one with behavioral agents (human subjects), and the other one with a hypothetical rational agent. A visualization is evaluated by comparing the expected performance of behavioral agents to that of a rational agent under different assumptions. Using recent visualization decision studies from the literature, we demonstrate how the framework can be used to pre-experimentally evaluate the experiment design by bounding the expected improvement in performance from having access to visualizations, and post-experimentally to deconfound errors of information extraction from errors of optimization, among other analyses.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
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.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.
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