We use an artificial neural network to analyze asymmetric noisy random telegraph signals, and extract underlying transition rates. We demonstrate that a long short-term memory neural network can outperform other methods, particularly for noisy signals and measurements with limited bandwidths. Our technique gives reliable results as the signal-to-noise ratio approaches one, and over a wide range of underlying transition rates. We apply our method to random telegraph signals generated by quasiparticle poisoning in a superconducting double dot, allowing us to extend our measurement of quasiparticle dynamics to new temperature regimes.