## 1 Introduction  
Electric load forecasting (LF) is an indispensable task for electric utilities in the long term [1]. As a fundamental business problem, LF is associated with decision-making processes in power system plannings, operations, energy trading and so forth [2; 3]. Prediction of future load demand is a tendency forecasting subject based on actual load data. Methods of tendency forecasting are generally classified into three categories: the physical approaches, the statistical approaches and the artificial intelligence (AI) approaches [4]. In practice, the diversity of data sources makes it impossible to build physical models for LF [5]. Moreover, since the load demand is affected by the chaotic nature of weather conditions, statistical approaches such as exponential smoothing, auto regression (AR), moving average (MA) and their variants are insufficient to address the nonlinearity and randomness properties of load data [6]. Consequently, AI approaches have become the mainstream of LF methods. Traditional LF studies apply AI-based methods of neural network [7; 8; 9], support vector machine [10; 11; 12] and other methods [13; 14] to forecast the load demand with exactly values. Although the performance of traditional LF models can be improved by optimizing the AI model, the forecasting uncertainty at each load point is unknown [15]. To develop efficient strategies for power market management, more detail about forecasting results should be provided [16]. Preferably, an emerging technique called probabilistic forecasting can offer much more comprehensive information about future tendency, and thus is more effective for decision-makingin the dynamic environment [17]. Over the past few years, numerous probabilistic forecasting methods have been proposed and employed to achieve probabilistic forecasts in the industrial tendency analysis [18]. Generally, more steps are involved in generating probabilistic intervals than point forecasting. Hence, gradient-based methods with long training time are improper for probabilistic forecasting [19; 20]. In the field of LF, common forms of probabilistic load forecasting (PLF) refer to providing output with quantile, interval and density function [21]. It is noticed that the interval methods include prediction interval (PI) and confidence interval (CI). Despite the investigations of PLF published in Global Energy Forecasting Competition 2014 (GEFCom2014) [22; 23; 24], advanced techniques for PLF are quite limited. In addition, most of the investigations focus on the quantile and interval methods. Typical research on introducing the quantile regression averaging (QRA) to PLF can be found in [21], which employed the QRA technique in point forecasts for PLF tasks. In addition, an advanced quantile regression technique called gradient boosting machine (GBM) is proved to outperform QRA techniques in terms of robustness and accessibility [25]. However, a large amount of time in training 99 required quantiles is unpalatable for short-term load demand forecasting. The emerging technique of quantile regression neural network (QRNN) seems to be a cure for reducing the time cost by optimizing a single forecasting model with overall pinball loss [26]. Nevertheless, the massive computation brought by a large data set is unsustainable. The PI method mentioned in [27] estimated the variance of forecasting errors with load forecasts based on weather ensembles. In [28], the generalized extreme learning machine (ELM) was developed to predict the load interval. Both the prediction error and the noise uncertainty were taken into account in this ELM. Since the PIs are obtained by prediction, the accuracy of PI methods is only guaranteed for fixed interval size. Moreover, the two-stage neural network [29] and the bootstrapping technique [30] provide a statistical approach to generate CIs, of which the interval size can be adjusted flexibly with various confidence levels. The width of CIs highly depends on the behavior of forecasting process.