Review of automated time series forecasting pipelines

Time series forecasting is fundamental for various use cases in different domains such as energy systems and economics. Creating a forecasting model for a specific use case requires an iterative and complex design process. The typical design process includes the five sections (1) data pre-processing, (2) feature engineering, (3) hyperparameter optimization, (4) forecasting method selection, and (5) forecast ensembling, which are commonly organized in a pipeline structure. One promising approach to handle the ever-growing demand for time series forecasts is automating this design process. The present paper, thus, analyzes the existing literature on automated time series forecasting pipelines to investigate how to automate the design process of forecasting models. Thereby, we consider both Automated Machine Learning (AutoML) and automated statistical forecasting methods in a single forecasting pipeline. For this purpose, we firstly present and compare the proposed automation methods for each pipeline section. Secondly, we analyze the automation methods regarding their interaction, combination, and coverage of the five pipeline sections. For both, we discuss the literature, identify problems, give recommendations, and suggest future research. This review reveals that the majority of papers only cover two or three of the five pipeline sections. We conclude that future research has to holistically consider the automation of the forecasting pipeline to enable the large-scale application of time series forecasting

Review of automated time series forecasting pipelines

Time series forecasting is fundamental for various use cases in different domains such as energy systems and economics. Creating a forecasting model for a specific use case requires an iterative and complex design process. The typical design process includes the five sections (1) data pre-processing, (2) feature engineering, (3) hyperparameter optimization, (4) forecasting method selection, and (5) forecast ensembling, which are commonly organized in a pipeline structure. One promising approach to handle the ever-growing demand for time series forecasts is automating this design process. The present paper, thus, analyzes the existing literature on automated time series forecasting pipelines to investigate how to automate the design process of forecasting models. Thereby, we consider both Automated Machine Learning (AutoML) and automated statistical forecasting methods in a single forecasting pipeline. For this purpose, we firstly present and compare the proposed automation methods for each pipeline section. Secondly, we analyze the automation methods regarding their interaction, combination, and coverage of the five pipeline sections. For both, we discuss the literature, identify problems, give recommendations, and suggest future research. This review reveals that the majority of papers only cover two or three of the five pipeline sections. We conclude that future research has to holistically consider the automation of the forecasting pipeline to enable the large-scale application of time series forecasting

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

37^th plenary meeting report of the scientific, technical and economic committee for fisheries (PLEN-11-02)

The Scientific, Technical and Economic Committee for Fisheries hold its 37th plenary on 11-15 July 2011 in Copenhagen (Denmark). The terms of reference included both issues assessments of STECF Expert Working Group reports and additional requests submitted to the STECF by the Commission. Topics dealt with ranged from fisheries economics to management plan evaluation issues

Identifying the validity domain of machine learning models in building energy systems

The building sector significantly contributes to climate change. To improve its carbon footprint, applications like model predictive control and predictive maintenance rely on system models. However, the high modeling effort hinders practical application. Machine learning models can significantly reduce this modeling effort. To ensure a machine learning model’s reliability in all operating states, it is essential to know its validity domain. Operating states outside the validity domain might lead to extrapolation, resulting in unpredictable behavior. This paper addresses the challenge of identifying extrapolation in data-driven building energy system models and aims to raise knowledge about it. For that, a novel approach is proposed that calibrates novelty detection algorithms towards the machine learning model. Suitable novelty detection algorithms are identified through a literature review and a benchmark test with 15 candidates. A subset of five algorithms is then evaluated on building energy systems. First, on two-dimensional data, displaying the results with a novel visualization scheme. Then on more complex multi-dimensional use cases. The methodology performs well, and the validity domain could be approximated. The visualization allows for a profound analysis and an improved understanding of the fundamental effects behind a machine learning model’s validity domain and the extrapolation regimes

Safe operation of online learning data driven model predictive control of building energy systems

Model predictive control is a promising approach to reduce the CO2 emissions in the building sector. However, the vast modeling effort hampers the widescale practical application. Here, data-driven process models, like artificial neural networks, are well-suited to automatize the modeling. However, the underlying data set strongly determines the quality and reliability of artificial neural networks. In general, the validity domain of a machine learning model is limited to the data that was used to train it. Predictions based on system states outside that domain, so-called extrapolations, are unreliable and can negatively influence the control quality.We present a safe operation approach combined with online learning to deal with extrapolation in data-driven model predictive control. Here, the k-nearest neighbor algorithm is used to detect extrapolation to switch to a robust fallback controller. By continuously retraining the artificial neural networks during operation, we successively increase the validity domain of the artificial neural networks and the control quality.We apply the approach to control a building energy system provided by the BOPTEST framework. We compare controllers based on two data sets, one with extensive system excitation and one with baseline operation. The system is controlled to a fixed temperature set point in baseline operation. Therefore, the artificial neural networks trained on this data set tend to extrapolate in other operating points. We show that safe operation in combination with online learning significantly improves performance