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Electricity price forecasting is essential for the market participants in their decision making. Nevertheless, the accuracy of such forecasting cannot be guaranteed due to the high variability of the price data. For this reason, in many cases, rather than merely point forecasting results, market participants are more interested in the probabilistic price forecasting results, i.e., the prediction intervals of the electricity price. Focusing on this issue, this paper proposes a new model for the probabilistic electricity price forecasting. This model is based on the active learning technique and the variational heteroscedastic Gaussian process (VHGP). It provides the heteroscedastic Gaussian prediction intervals, which effectively quantify the heteroscedastic uncertainties associated with the price data. Because the high computational effort of VHGP hinders its application to the large-scale electricity price forecasting tasks, we design an active learning algorithm to select a most informative training subset from the whole available training set. By constructing the forecasting model on this smaller subset, the computational efforts can be significantly reduced. In this way, the practical applicability of the proposed model is enhanced. The forecasting performance and the computational time of the proposed model are evaluated using the real-world electricity price data, which is obtained from the ANEM, PJM, and New England ISO. [ABSTRACT FROM AUTHOR]