fastASD

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

• Download: zipped archive fastASD-master.zip
• Clone: clone the repository from github: git clone [email protected]:pillowlab/fastASD.git

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 )

Notes

• 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.