Respiratory rate monitoring has become necessary for people with respiratory diseases, especially those living alone. Sudden changes in respiratory rate (RR) in these individuals may indicate a severe illness. Hence, estimating the RR is essential for cardiopulmonary health conditions. Capnography is a well-known standard technique for measuring RR. This study presents a novel methodology that uses an automatic feature extraction algorithm integrated with a robust feature selection technique based on exact Gaussian process regression (EGPR) for RR and uncertainty estimations. As EGPR is vital to noisy data and is naturally normalized, it can generate uncertainty estimates. Uncertainty estimation is essential for estimating physiological parameters. In the proposed methodology, data dimension is obtained using a power spectral density feature based on an autocorrelation function; subsequently, the long-resampled wave signal is split to increase the number of input data samples. Selecting an appropriate high-dimensional feature is necessary to predict a response effectively. Herein, we use a robust feature selection method based on neighbor component analysis. The proposed EGPR with automatic feature extraction is more accurate than conventional algorithms for RR and confidence intervals (CIs) estimations. The proposed methodology proves superior to conventional algorithms in terms of saving computer resources. We confirm that the proposed methodology, 2.085 breath per minute (bpm), and EGPR with robust feature selection, 2.049 bpm, show the lowest mean absolute error compared to the conventional algorithms in the Beth Israel Deaconess Medical Center data set.INDEX TERMS respiratory rate estimation, automatic feature extraction, exact Gaussian process regression, robust neighbor component analysis, confidence intervals.