Note

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Anesthetized cat V1 simple cell

The code below uses an online algorithm to estimate the linear receptive field of a simple cell recorded from an anesthetized cat, as described in “Touryan, Jon and Felsen, Gidon and Dan, Yang (2005). Spatial structure of complex cell receptive fields measured with natural images. Neuron 45 (5), 781-791.”

Import requirments

import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt

import lds.inference

/home/runner/work/lds_python/lds_python/src/lds/inference.py:7: SyntaxWarning: invalid escape sequence '\ '
  """
/home/runner/work/lds_python/lds_python/src/lds/inference.py:67: SyntaxWarning: invalid escape sequence '\i'
  """Updates the current state and covariance.
/home/runner/work/lds_python/lds_python/src/lds/inference.py:152: SyntaxWarning: invalid escape sequence '\ '
  """
/home/runner/work/lds_python/lds_python/src/lds/inference.py:198: SyntaxWarning: invalid escape sequence '\i'
  """Updates the current state and covariance.

Define variables

n_samples_to_use = 1000
response_delay_samples = 1
prior_precision_coef = 2.0
likelihood_precision_coef = 0.1
fig_update_delay = 0.1
images_filename = "https://www.gatsby.ucl.ac.uk/~rapela/neuroinformatics/2024/worksheets/linearRegression/data/equalpower_C2_25hzPP.dat"
responses_filename = "https://www.gatsby.ucl.ac.uk/~rapela/neuroinformatics/2024/worksheets/linearRegression/data/040909.a.c06.C2_nsSumSpikeRates.dat"

Get data

images = pd.read_csv(images_filename, sep="\s+").to_numpy()
responses = pd.read_csv(responses_filename, sep="\s+").to_numpy().flatten()
Phi = np.column_stack((np.ones(len(images)), images))
n_pixels = images.shape[1]
image_width = int(np.sqrt(n_pixels))
image_height = image_width

Phi = Phi[:-response_delay_samples,]
responses = responses[response_delay_samples:]

n_samples_to_use = min(Phi.shape[0], n_samples_to_use)
print(f"Using {n_samples_to_use} out of {Phi.shape[0]} samples")
Phi = Phi[:n_samples_to_use,]
responses = responses[:n_samples_to_use]

/home/runner/work/lds_python/lds_python/examples/sphinx_gallery/onlineBayesianLinearRegression/plotOnlineBayesianLinearRegressionSimpleCell.py:38: SyntaxWarning: invalid escape sequence '\s'
  images = pd.read_csv(images_filename, sep="\s+").to_numpy()
/home/runner/work/lds_python/lds_python/examples/sphinx_gallery/onlineBayesianLinearRegression/plotOnlineBayesianLinearRegressionSimpleCell.py:39: SyntaxWarning: invalid escape sequence '\s'
  responses = pd.read_csv(responses_filename, sep="\s+").to_numpy().flatten()
Using 1000 out of 23998 samples

Build Kalman filter matrices

B = np.eye(N=n_pixels+1)
Q = np.zeros(shape=((n_pixels+1, n_pixels+1)))
R = np.array([[1.0/likelihood_precision_coef]])

Estimate posterior

# set prior
m0 = np.zeros((n_pixels+1,), dtype=np.double)
S0 = 1.0 / prior_precision_coef * np.eye(n_pixels+1, dtype=np.double)
indices = np.arange(len(m0))

fig = plt.figure()
ax1 = fig.add_subplot(2, 1, 1, adjustable="box", aspect=1)
ax2 = fig.add_subplot(2, 1, 2)

mn = m0
Sn = S0
kf = lds.inference.TimeVaryingOnlineKalmanFilter()
for n, t in enumerate(responses):
    print(f"Processing {n}/({len(responses)})")
    # update posterior
    mn, Sn = kf.predict(x=mn, P=Sn, B=B, Q=Q)
    mn, Sn = kf.update(y=t, x=mn, P=Sn, Z=Phi[n, :].reshape((1, Phi.shape[1])), R=R)

    # plot posterior
    stds = np.sqrt(np.diag(Sn))
    ax1.clear()
    ax1.contourf(mn[1:].reshape((image_width, image_height)))
    title = (r"$\alpha={:.02f},\beta={:.02f},\lambda={:.02f},"
             "{:d}/{:d}$".format(
                 prior_precision_coef, likelihood_precision_coef,
                 prior_precision_coef/likelihood_precision_coef,
                 n, len(responses)))
    ax1.set_title(title)
    ax2.clear()
    ax2.errorbar(x=indices, y=mn, yerr=1.96*stds)
    ax2.axhline(y=0)
    ax2.set_xlabel("Pixel index")
    ax2.set_ylabel("Pixel value")
    # Note that using time.sleep does *not* work here!
    plt.pause(fig_update_delay)

$\alpha=2.00,\beta=0.10,\lambda=20.00,999/1000$

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Total running time of the script: (3 minutes 51.370 seconds)

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