A Refinement of Lasso Regression Applied to Temperature Forecasting

© 2018 The Authors. Published by Elsevier B.V. Model predictive controllers use accurate temperature forecasts to save energy by optimally controlling heating, ventilation and air conditioning equipment while achieving comfort for occupants. In a smart building, i.e. one that is outfitted with sensors, temperature forecasts are computed from data gathered by these sensors. Recently, accurate temperature forecasts have been generated using relatively few observations from each sensor. However, long sensor histories are available in smart houses. In this paper we consider improving forecast accuracy by using up to 24 hours of quarter-hourly readings. In particular, we overcome forecast inaccuracy that arises from the one standard error heuristic (1SE) in lasso regression. When there are many historical observations, low variance in the error estimations can result in excessively high values for the lasso hyperparameter λ. We propose the midfel refinement of lasso regression, which adjusts λ based on the shape of the error curve, resulting in improved forecast accuracy. We illustrate its effect in a setting where lasso regression is used to select sensors based on forecast accuracy. In this setting, midfel lasso regression using many historical observations has two effects: its improves accuracy and uses fewer sensors. Thus it potentially reduces costs arising both from energy usage and from sensor installation

Forecasting Temperature in a Smart Home with Segmented Linear Regression

The 9th International Conference on Sustainable Energy Information Technology (SEIT), August 19-21, 2019, Halifax, Nova Scotia, Canad

Forecasting Temperature in a Smart Home with Segmented Linear Regression

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Conference Program Chairs. The efficiency of heating, ventilation and cooling operations in a home are improved when they are controlled by a system that takes into account an accurate forecast of temperature in the house. Temperature forecasts are informed by data from sensors that report on activities and conditions in and around the home. Using publicly available data, we apply linear models based on LASSO regression and our recently developled MIDFEL LASSO regression. These models take into account the past 24 hours of the sensors\u27 data. We have previously identified the most influential sensors in a forecast over the next 48 hours. In this paper, we compute 48 separate one-hour forecast and for each hour we identify the sensors that are most influential. This improves forecast accuracy and reveals which sensors are most valuable to install

Mathematical programming for piecewise linear regression analysis

In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our proposed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method can benefit expert systems in various applications by automatically acquiring knowledge from databases to improve the quality of knowledge base

Uncertainty in mesoscale numerical weather prediction : probabilistic forecasting of precipitation

Over the last decade, advances in numerical weather prediction (NWP) led to forecasts on even finer horizontal scales and a better representation of mesoscale processes. High-resolution mod- els provide the user with realistic weather patterns on the km-scale. However, the evaluation of such small-scale model output remains still a challenge in forecast verification and the quan- tification of forecast uncertainty. Ensembles are the main tool to assess uncertainty from NWP models. The first operational mesoscale NWP ensemble was developed by the German Meteo- rological Service (DWD) in 2010. The German-focused COSMO-DE-EPS is especially designed to improve quantitative precipitation forecasts, which is still one of the most difficult weather variables to predict. This study investigates the potential of mesoscale NWP ensembles to predict quantitative pre- cipitation. To comprise the uncertainty inherent in NWP, precipitation forecasts should take the form of probabilistic predictions. Typical point forecasts for precipitation are the probability that a certain threshold will be exceeded as well as quantiles. Quantiles are very suitable to predict quantitative precipitation and do not depend an a priori defined thresholds, as is necessary for the probability forecasts. Various statistical methods are explored to transform the ensemble forecast into probabilistic predictions, either in terms of probabilities or quantiles. An enhanced framework for statistical postprocessing of quantitative precipitation quantile predictions is de- veloped based on a Bayesian inference of quantile regression. For a further investigation of the predictive performance of quantile forecasts, the pool of verification methods is expanded by the decomposition and graphical exploration of the quantile score. The decomposition allows to attribute changes in the predictive performance of quantile forecasts either to the reliability or the information content of a forecasting scheme. Together with the Bayesian quantile regression model, this study contributes to an enhanced framework of statistical postprocessing and probabilistic forecast verification of quantitative precipitation quantile predictions derived from mesoscale NWP ensembles