Figure 4.

Recapitulation of stretched-exponential rate spectra from noisy time series. (top) Noisy data sets (s = 0.05, blue) with best-fit time traces ŷ (shown are the results from ridge regression; best-fits from lasso and elastic net are nearly indistinguighable) for various stretching parameters γ = 0.3, 0.5, 0.7 and 0.9. (bottom) Regularized rate spectra (shown here as the expectation over all posterior samples of λ) for ridge, lasso and elastic net regression. The ridge and elastic net rate spectra correspond well to the analytical results (red line), while lasso regression consistently describes the data with the smallest possible number of timescales. Note that the elastic net posterior takes longer to converge, as can be seen in by the larger error estimates from posterior sampling.