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In this paper, we use SEIR equations to make predictions for the number of mortality due to COVID-19 in \.Istanbul. Using excess mortality method, we find the number of mortality for the previous three waves in 2020 and 2021. We show that the predictions of our model is consistent with number of moralities for each wave. Furthermore, we predict the number of mortality for the second wave of 2021. We also extend our analysis for Germany, Italy and Turkey to compare the basic reproduction number $R_0$ for Istanbul. Finally, we calculate the number of infected people in Istanbul for herd immunity.

An effective way to oppose global warming and mitigate climate change is to electrify our energy sectors and supply their electric power from renewable wind and solar. Spatio-temporal predictions of electric load become increasingly important for planning this transition, while deep learning prediction models provide increasingly accurate predictions for it. The data used for training deep learning models, however, is usually collected at random using a passive learning approach. This naturally results in a large demand for data and associated costs for sensors like smart meters, posing a large barrier for electric utilities in decarbonizing their grids. Here, we test active learning where we leverage additional computation for collecting a more informative subset of data. We show how electric utilities can apply active learning to better distribute smart meters and collect their data for more accurate predictions of load with about half the data compared to when applying passive learning.

Current online learning methods suffer issues such as lower convergence rates and limited capability to recover the support of the true features compared to their offline counterparts. In this paper, we present a novel framework for online learning based on running averages and introduce a series of online versions of popular offline methods such as Elastic Net, Minimax Concave Penalty, and Feature Selection with Annealing. The framework can handle an arbitrarily large number of observations with the restriction that the data dimension is not too large, e.g. p<50,000. We prove the equivalence between our online methods and their offline counterparts and give theoretical true feature recovery and convergence guarantees for some of them. In contrast to existing online methods, the proposed methods can extract models with any desired sparsity level at any time. Numerical experiments indicate that our new methods enjoy high true feature recovery accuracy and a fast convergence rate, compared with standard online and offline algorithms. We also show how the running averages framework can be used for model adaptation in the presence of model drift. Finally, we present applications to large datasets where again the proposed framework shows competitive results compared to popular online and offline algorithms.

A reservoir computer (RC) is a type of simplified recurrent neural network architecture that has demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A further advantage of RC is that it reproduces intrinsic dynamical quantities essential for its incorporation into numerical forecasting routines such as the ensemble Kalman filter -- used in numerical weather prediction to compensate for sparse and noisy data. We explore here the architecture and design choices for a "best in class" RC for a number of characteristic dynamical systems, and then show the application of these choices in scaling up to larger models using localization. Our analysis points to the importance of large scale parameter optimization. We also note in particular the importance of including input bias in the RC design, which has a significant impact on the forecast skill of the trained RC model. In our tests, the the use of a nonlinear readout operator does not affect the forecast time or the stability of the forecast. The effects of the reservoir dimension, spinup time, amount of training data, normalization, noise, and the RC time step are also investigated. While we are not aware of a generally accepted best reported mean forecast time for different models in the literature, we report over a factor of 2 increase in the mean forecast time compared to the best performing RC model of Vlachas et.al (2020) for the 40 dimensional spatiotemporally chaotic Lorenz 1996 dynamics, and we are able to accomplish this using a smaller reservoir size.

The recent developments in the machine learning domain have enabled the development of complex multivariate probabilistic forecasting models. Therefore, it is pivotal to have a precise evaluation method to gauge the performance and predictability power of these complex methods. To do so, several evaluation metrics have been proposed in the past (such as Energy Score, Dawid-Sebastiani score, variogram score), however, they cannot reliably measure the performance of a probabilistic forecaster. Recently, CRPS-sum has gained a lot of prominence as a reliable metric for multivariate probabilistic forecasting. This paper presents a systematic evaluation of CRPS-sum to understand its discrimination ability. We show that the statistical properties of target data affect the discrimination ability of CRPS-Sum. Furthermore, we highlight that CRPS-Sum calculation overlooks the performance of the model on each dimension. These flaws can lead us to an incorrect assessment of model performance. Finally, with experiments on the real-world dataset, we demonstrate that the shortcomings of CRPS-Sum provide a misleading indication of the probabilistic forecasting performance method. We show that it is easily possible to have a better CRPS-Sum for a dummy model, which looks like random noise, in comparison to the state-of-the-art method.

Producing an accurate weather forecast and a reliable quantification of its uncertainty is an open scientific challenge. Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts along with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture and quantify different sources of uncertainty, particularly those associated with model errors. In this work proof-of-concept model experiments are conducted to examine the performance of ANNs trained to predict a corrected state of the system and the state uncertainty using only a single deterministic forecast as input. We compare different training strategies: one based on a direct training using the mean and spread of an ensemble forecast as target, the other ones rely on an indirect training strategy using a deterministic forecast as target in which the uncertainty is implicitly learned from the data. For the last approach two alternative loss functions are proposed and evaluated, one based on the data observation likelihood and the other one based on a local estimation of the error. The performance of the networks is examined at different lead times and in scenarios with and without model errors. Experiments using the Lorenz'96 model show that the ANNs are able to emulate some of the properties of ensemble forecasts like the filtering of the most unpredictable modes and a state-dependent quantification of the forecast uncertainty. Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the presence of model error.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

Automated anatomical labeling plays a vital role in coronary artery disease diagnosing procedure. The main challenge in this problem is the large individual variability inherited in human anatomy. Existing methods usually rely on the position information and the prior knowledge of the topology of the coronary artery tree, which may lead to unsatisfactory performance when the main branches are confusing. Motivated by the wide application of the graph neural network in structured data, in this paper, we propose a conditional partial-residual graph convolutional network (CPR-GCN), which takes both position and CT image into consideration, since CT image contains abundant information such as branch size and spanning direction. Two majority parts, a Partial-Residual GCN and a conditions extractor, are included in CPR-GCN. The conditions extractor is a hybrid model containing the 3D CNN and the LSTM, which can extract 3D spatial image features along the branches. On the technical side, the Partial-Residual GCN takes the position features of the branches, with the 3D spatial image features as conditions, to predict the label for each branches. While on the mathematical side, our approach twists the partial differential equation (PDE) into the graph modeling. A dataset with 511 subjects is collected from the clinic and annotated by two experts with a two-phase annotation process. According to the five-fold cross-validation, our CPR-GCN yields 95.8% meanRecall, 95.4% meanPrecision and 0.955 meanF1, which outperforms state-of-the-art approaches.