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  1. In this work, we tackle two widespread challenges in real applications for time series forecasting that have been largely understudied: distribution shifts and missing data. We propose SpectraNet, a novel multivariate time-series forecasting model that dynamically infers a latent space spectral decomposition to capture current temporal dynamics and correlations on the recent observed history. A Convolution Neural Network maps the learned representation by sequentially mixing its components and refining the output. Our proposed approach can simultaneously produce forecasts and interpolate past observations and can, therefore, greatly simplify production systems by unifying imputation and forecasting tasks into a single model. SpectraNet achieves SoTA performance simultaneously on both tasks on five benchmark datasets, compared to forecasting and imputation models, with up to 92% fewer parameters and comparable training times. On settings with up to 80% missing data, SpectraNet has average performance improvements of almost 50% over the second-best alternative. 
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  2. Multivariate time series anomaly detection has become an active area of research in recent years, with Deep Learning models outperforming previous approaches on benchmark datasets. Among reconstruction-based models, most previous work has focused on Variational Autoencoders and Generative Adversarial Networks. This work presents DGHL, a new family of generative models for time series anomaly detection, trained by maximizing the observed likelihood by posterior sampling and alternating back-propagation. A top-down Convolution Network maps a novel hierarchical latent space to time series windows, exploiting temporal dynamics to encode information efficiently. Despite relying on posterior sampling, it is computationally more efficient than current approaches, with up to 10x shorter training times than RNN based models. Our method outperformed current state-of-the-art models on four popular benchmark datasets. Finally, DGHL is robust to variable features between entities and accurate even with large proportions of missing values, settings with increasing relevance with the advent of IoT. We demonstrate the superior robustness of DGHL with novel occlusion experiments in this literature. Our code is available at https://github. com/cchallu/dghl. 
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  3. The aim of this work is to examine the environmental dependence of K‐band luminosity in the Main, Low Redshift (LOWZ), and Constant Mass (CMASS) galaxy samples of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10). Overall, the environmental dependence of K‐band luminosity is very mild. In two volume‐limited Main samples with the luminosity −20.5 ≤Mr≤ −18.5 and −22.5 ≤Mr≤ −20.5, respectively, we find that the environmental dependence of K‐band luminosity in the luminous volume‐limited Main galaxy sample still can be observed, but this dependence in the faint volume‐limited Main galaxy sample is very weak. Considering the disadvantages of the use of volume‐limited samples, we apply the apparent magnitude‐limited Main galaxy sample, divide the Main galaxy sample of the SDSS DR10 into subsamples with a redshift binning size of Δz=0.01, and then analyze the environmental dependence of K‐band luminosity of subsamples in each redshift bin. Such a method also is used in the LOWZ and CMASS galaxy samples. K‐band luminosity of the Main galaxies shows substantial correlation with the local environment in many redshift bins. In the LOWZ galaxy sample, K‐band luminosity of galaxies shows substantial correlation with the local environment only in the redshift region 0.16 ≤z≤ 0.21, while K‐band luminosity of CMASS galaxy sample is only weakly correlated with the local environment. Statistical results also show that in the apparent magnitude‐limited main galaxy sample and the LOWZ galaxy sample, environmental dependence of K‐band luminosity becomes weak with increasing redshift.

     
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