Receptive Field Inference with Localized Priors
Figure 2
Comparison of estimators for 1D simulated example.
A 1D difference-of-Gaussians receptive field with 100 elements was stimulated with 2000 samples of correlated (1/F) Gaussian noise. Left column: True filter (top), maximum likelihood (linear regression) estimate (middle), and empirical Bayes ridge regression (L2-penalized) estimate (bottom). Middle: Lasso (L1-penalized) estimate (top) and ARD (middle) produce sparse estimates but fail to capture smoothness. The ASD estimate (bottom) captures smoothness, but exhibits spurious oscillations in the tails. Right column: Three variants of automatic locality determination (ALD): Spacetime localization (ALDs, top), which identifies a spatial region in which the filter coefficients are large; frequency localization (ALDf, middle), which identifies a local region of the frequency domain in which Fourier coefficients are large, leading to a smooth estimate that closely resembles ASD; and joint localization in spacetime and frequency (ALDsf, bottom), which simultaneously identifies a local region in spacetime and frequency, yielding an estimate that is both smooth and sparse.