D-trace estimation of a precision matrix using adaptive Lasso penalties

The accurate estimation of a precision matrix plays a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the ℓ1 norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimate for properly selected penalty parameters. However, the ℓ1 norm penalization often fails to control the bias of obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed ℓ1 norm penalized D-trace loss minimization method. They aim at reducing the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators.We would like to thank the Associate Editor, Coordinating Editor and two anonymous referees for their helpful comments that led to an improvement of this article. We express our gratitude to Teng Zhang and Hui Zou for sharing their Matlab code that solves the L1 norm penalized D-trace loss minimization problem. Andrés M. Alonso gratefully acknowledges financial support from CICYT (Spain) Grants ECO2012-38442 and ECO2015-66593. Francisco J. Nogales and Vahe Avagyan were supported by the Spanish Government through project MTM2013-44902-P. This paper is based on the first author's dissertation submitted to the Universidad Carlos III de Madrid. At the time of publication, Vahe Avagyan is a Postdoctoral fellow at Ghent University

A Single Scalable LSTM Model for Short-Term Forecasting of Massive Electricity Time Series

This article belongs to the Special Issue Forecasting in Electricity Markets with Big Data and Artificial Intelligence.Most electricity systems worldwide are deploying advanced metering infrastructures to collect relevant operational data. In particular, smart meters allow tracking electricity load consumption at a very disaggregated level and at high frequency rates. This data opens the possibility of developing new forecasting models with a potential positive impact on electricity systems. We present a general methodology that can process and forecast many smart-meter time series. Instead of using traditional and univariate approaches, we develop a single but complex recurrent neural-network model with long short-term memory that can capture individual consumption patterns and consumptions from different households. The resulting model can accurately predict future loads (short-term) of individual consumers, even if these were not included in the original training set. This entails a great potential for large-scale applications as once the single network is trained, accurate individual forecast for new consumers can be obtained at almost no computational cost. The proposed model is tested under a large set of numerical experiments by using a real-world dataset with thousands of disaggregated electricity consumption time series. Furthermore, we explore how geo-demographic segmentation of consumers may impact the forecasting accuracy of the model.The authors gratefully acknowledge the financial support from the Spanish government through projects MTM2017-88979-P and PID2019-108311GB-I00/AEI/10.13039/501100011033, and from Fundación Iberdrola through “Ayudas a la Investigación en Energía y Medio Ambiente 2018”