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Fast inference for high-D receptive fields using Automatic Smoothness Determination (ASD) in Matlab

  • general method for regression problems with smooth weights

Description: Performs evidence optimization for hyperparameters in a Gaussian linear regression model with a Gaussian Process (GP) prior on the regression weights, and returns maximum a posteriori (MAP) estimate of the weights given optimal hyperparameters.

Original reference:

Sahani, M. & Linden, J. Evidence optimization techniques for estimating stimulus-response functions. NIPS (2003).

Reference for this implementation

Aoi MC & Pillow JW. Scalable Bayesian inference for high-dimensional neural receptive fields. bioRxiv (2017)


  • Download: zipped archive
  • Clone: clone the repository from github: git clone

Getting started

  • Launch matlab and cd into the directory containing the code
    (e.g. cd fastASD/).

  • Run script "setpaths.m" to set local paths:
    > setpaths

  • cd to directory demos:
    > cd demos

  • Examine the demo scripts for example application to simulated data:

    • test_fastASD_1D.m - illustrate estimation of a 1D (e.g. purely temporal) receptive field using fastASD.
    • test_fastASD_2D.m - for 2D (e.g. 1D space x time ) receptive field with same length scale (i.e. smoothness level) along each axis.
    • test_fastASD_2Dnonisotropic.m - for 2D receptive field, but with different length scale (smoothness) along each axis.
    • test_fastASD_3D.m - for 3D (e.g. 2D space x time) receptive field.
  • More advanced demo scripts:

    • test_fastASD_1Dgroupedcoeffs.m - model with multiple vectors of regression weights for different covariates, each of which should be smooth (e.g. 1 filter governing stimulus and 1 governing running speed).

    • test_fastASD_1Dnonuniform.m - run ASD for weight vectors which are not evenly spaced in time (or space),

    • test_fastASD_2Dnonunif.m - same but for non-uniformly sampled 2D data, e.g. for inferring a rat hippocampal place fields from location data that does not sit on a 2D grid. (See, e.g., Muragan et al 2017 )


  • The ASD model includes three hyperparameters (for 1D or isotropic prior):

    • rho - prior variance of the regression weights
    • len - length scale, governing smoothness (larger => smoother).
    • sig^2 - variance of the observation noise (from Gaussian likelihood term).
  • The only change for non-isotropic version is to have a different length scale governing smoothness in each direction.

  • code returns MAP estimate of RF, posterior confidence intervals of the RF, and confidence intervals on hyperparameters based on the inverse Hessian of the marginal likelihood.

  • Computational efficiency of this implementation comes from using a spectral (Fourier basis) representation of the ASD prior, which is also known as Gaussian, or Radial Basis Function (RBF), or "squared exponential" covariance function.