Independent component analysis (ICA) estimates a demixing matrix that can recover statistically independent sources from linear mixtures. FastICA is a popular ICA algorithm due to its efficiency, but its performance strongly depends on a user-chosen nonlinear function matched to the source distribution. When the source distribution is unknown, this function must be guessed at, and incorrect guesses can lead to significant drops in performance. We remove the need to guess by estimating a suitable function directly from the observed data. Our experiments show that the separation error stays close to the best fixed choice across synthetic mixtures comprising heavy-tailed or discrete sources while retaining a FastICA-like runtime.