In this paper, for efficient data collection with limited bandwidth, data-aided sensing is applied to Gaussian process regression that is used to learn data sets collected from sensors in Internet-of-Things systems. We focus on the interpolation of sensors' measurements from a small number of measurements uploaded by a fraction of sensors using Gaussian process regression with data-aided sensing. Thanks to active sensor selection, it is shown that Gaussian process regression with data-aided sensing can provide a good estimate of a complete data set compared to that with random selection. With multichannel ALOHA, data-aided sensing is generalized for distributed selective uploading when sensors can have feedback of predictions of their measurements so that each sensor can decide whether or not it uploads by comparing its measurement with the predicted one. Numerical results show that modified multichannel ALOHA with predictions can help improve the performance of Gaussian process regression with data-aided sensing compared to conventional multichannel ALOHA with equal uploading probability.