Inference of nonlinear receptive field subunits with spike-triggered clustering
- Stanford University, United States
- Stanford School of Medicine, United States
- University of California, Santa Cruz, United States
- New York University, United States
- Howard Hughes Medical Institute, United States
Figures
Figure 1 with 1 supplement
Spiking response model, and estimation through spike-triggered stimulus clustering.
(A) The model is constructed as a cascade of two linear-nonlinear (LN) stages. In the first stage, subunit activations are computed by linearly filtering the stimulus () with kernels () followed …
Figure 1—figure supplement 1
Validation of the subunit fitting algorithm on simulated RGC data.
(A) Receptive field obtained via spike-triggered average of a simulated RGC with cascaded linear nonlinear units. The stimulus is temporally filtered by 64 photoreceptors organized on a jittered …
Figure 2 with 1 supplement
Estimated subunit properties.
(A) Subunits, shown as grayscale images, estimated from OFF parasol cell responses to 24 min of white noise. Each pixel was temporally prefiltered with a kernel derived from the spike-triggered …
Figure 2—figure supplement 1
Gradual partitioning of the receptive field into subunits by hierarchical clustering.
Different number of subunits (rows) estimated by splitting one parent subunit into two subunits at each step. Children subunits estimated by soft-clustering the simulated spikes of the parent …
Figure 3
Spatially localized subunit estimation.
Comparison of different regularizers for estimating subunits using limited data. Examples of OFF parasol cells are shown. (A) Five subunits (most frequent optimum across cells from Figure 2) …
Figure 4
Joint estimation of subunits across multiple nearby cells.
(A) Gaussian fits to the subunits estimated for an entire OFF parasol cell population (5 subunits per cell, with poorly estimated subunits removed). Lines connect center of each cell to its …
Figure 5
Cells respond to stimulus in null space of receptive field.
(A) Construction of null stimulus, depicted in a two-dimensional stimulus space. Each dimension of stimulus space consists of intensity along a particular pixel. A stimulus frame is represented as a …
Figure 6
Subunits improve prediction of responses to null stimuli.
(A) Rasters for recorded responses of an OFF parasol cell to 30 presentations of a 5 s long null stimulus (top row). Predictions of models with increasing (1 to 10) number of subunits (subsequent …
Figure 7
Subunits improve response prediction accuracy for naturalistic stimuli.
(A) Top row: Rasters of responses for an OFF parasol cell from 40 presentations for 30 s long naturalistic stimuli. Natural scene images are presented and spatially jittered, with a new image every …
Figure 8
Application of subunit model to V1.
(A) Hierarchical relationship between subunits estimated using responses to flickering bar stimuli for the complex cell featured in Rust et al. (2005). Rows show estimated spatio-temporal filters …
Figure 9
Comparison with spike-triggered non-negative matrix factorization.
(A) Spatial filters for five simulated subunits. Responses are generated by linearly projecting white noise stimulus onto these spatial filters, followed by exponential subunit nonlinearity, …
Figure 10 with 1 supplement
Comparison with convolutional subunit model.
Subunits estimated for the retinal ganglion cell from Figure 1A using a convolutional model, similar to Vintch et al. (2015). The visual stimulus is convolved with a 4 × 4 spatial filter, separately …
Figure 10—figure supplement 1
Comparison between spike triggered clustering and convolutional subunit model (Vintch et al., 2015) with quadratic nonlinearity.
Dashed lines correspond to models with exponential nonlinearity (same as Figure 10C); solid lines correspond to quadratic nonlinearity. For the convolutional model, the stimulus is passed through a …
Figure 11
Iterative fitting of subunits, partitioned into four steps.
The subunit kernels () and weights () are randomly initialized, and used to compute soft cluster assignments ( upper left), followed by cluster centroid computation ( - upper right), …
Author response image 1
Convergence of PSTH variance.
(A) PSTH variance (y-axis), averaged over ON and OFF populations for white noise (black) and null stimulus (red) as a function of the number of randomly sampled trials (x-axis). Line thickness …
Tables
Key resources table
| Reagent type (species) or resource | Designation | Source or reference | Identifiers | Additional information |
|---|---|---|---|---|
| Biological Sample | Macaque retina | UC Davis Primate Research Center | ||
| Biological Sample | Macaque retina | Stanford University | ||
| Biological Sample | Macaque retina | University of California Berkeley | ||
| Biological Sample | Macaque retina | Salk Institue | ||
| Biological Sample | Macaque retina | The Scripps Research Institute | ||
| Chemical compound, drug | Ames' medium | Sigma-Aldrich | Cat #1420 | |
| Software, algorithm | MGL | Gardner Lab | http://gru.stanford.edu/doku.php/mgl/overview | |
| Software, algorithm | MATLAB | Mathworks | ||
| Software, algorithm | Python | https://www.python.org/ | ||
| Software, algorithm | Intaglio | Purgatory Design | ||
| Software, algorithm | Custom spike sorting software | Chichilnisky Lab |
