#ax.legend(loc=1);
# Calculate class membership, by using hmc_trace and logp_normal function:
#confidenceThreshold = 0.95
#class0LogProb = [logp_normal(np.mean(hmc_trace.get_values('mu_0')), np.mean(hmc_trace.get_values('sigma')[:,0]) , data[k,channel]) for k in np.where(sectionNumber == section)]
#class1LogProb = [logp_normal(np.mean(hmc_trace.get_values('mu_1')), np.mean(hmc_trace.get_values('sigma')[:,1]) , data[k,channel]) for k in np.where(sectionNumber == section)]
#normalizedProbs = [exp_normalize(np.array((class0LogProb[0][i], class1LogProb[0][i]))) for i in range(len(class0LogProb[0]))]
#maxProbs = [max(normalizedProbs[i]) for i in range(len(normalizedProbs))]
#classMembership = [np.argmax(normalizedProbs[i]) for i in range(len(normalizedProbs))]
#confidentClass = [2 if maxProbs[i] < confidenceThreshold else classMembership[i] for i in range(len(classMembership))]
# Calculate class membership, by using advi_trace and logp_normal function:
confidenceThreshold = 0.95
class0LogProb = [
logp_normal(np.mean(advi_trace.get_values('mu')[:, 0]),
np.mean(advi_trace.get_values('sigma')[:, 0]),
data[k, channel]) for k in range(np.shape(data)[0])
]
class1LogProb = [
logp_normal(np.mean(advi_trace.get_values('mu')[:, 1]),
np.mean(advi_trace.get_values('sigma')[:, 1]),
data[k, channel]) for k in range(np.shape(data)[0])
]
normalizedProbs = [
exp_normalize(np.array((class0LogProb[i], class1LogProb[i])))
for i in range(len(class0LogProb))
]
maxProbs = [
max(normalizedProbs[i]) for i in range(len(normalizedProbs))
]
classMembership = [
def logp_(value):
logps = [tt.log(pi[i]) + logp_normal(mus[i], sigmas[i], value)
for i in range(3)]
return tt.sum(logsumexp(tt.stacklists(logps), axis=0))
def logp_gmix(mus, pi, sigmas):
def logp_(value):
logps = [tt.log(pi[i]) + logp_normal(mus[i], sigmas[i], value)
for i in range(3)]
return tt.sum(logsumexp(tt.stacklists(logps), axis=0))
return logp_
with pm.Model() as model:
w = pm.Dirichlet('w', alpha)
mus = pm.Normal('mu', mu = mean_priorMean, sigma = mean_priorSigma, shape = (n_components, n_dimensions))
sigmas = pm.Gamma('sigma', mu = sigma_priorMean, sigma = sigma_priorSigma, shape = (n_components, n_dimensions))
c = pm.Normal('c', mu = spectralSignature_priorMean, sigma = spectralSignature_priorSigma, shape = (n_dimensions, n_dimensions))
prior = sample_prior(samples = 1000)
data_corrected = tt.log(tt.dot(data,tt.inv(c)))
x = pm.DensityDist('x', logp_gmix(mus, w, sigmas), observed=data_corrected)
# Plot prior for some parameters:
f = plt.figure()
plt.hist(prior['mu'][:,:,0])
plt.show()
f.savefig("figures/" + slideNames[slide] + "/" + "muPriorSection" + str(section) + "channel" + str(channel) + ".png", bbox_inches='tight')
plt.close(f)
f = plt.figure()
plt.hist(prior['taus_0'][:,1])
plt.show()
f.savefig("figures/" + slideNames[slide] + "/" + "sigmaPriorSection" + str(section) + "channel" + str(channel) + ".png", bbox_inches='tight')
plt.close(f)
f = plt.figure()
plt.hist(prior['w'])
plt.show()
f.savefig("figures/" + slideNames[slide] + "/" + "wPriorSection" + str(section) + "channel" + str(channel) + ".png", bbox_inches='tight')
plt.close(f)
# Fit:
with model:
advi_fit = pm.fit(n=500, obj_optimizer=pm.adagrad(learning_rate=1e-1), method = 'advi')
# Sample:
with model:
%time hmc_trace = pm.sample(draws=20, tune=50, cores=15)
# Show results advi:
f = plt.figure()
advi_elbo = pd.DataFrame(
{'log-ELBO': -np.log(advi_fit.hist),
'n': np.arange(advi_fit.hist.shape[0])})
_ = sns.lineplot(y='log-ELBO', x='n', data=advi_elbo)
f.savefig("figures/" + slideNames[slide] + "/" + "adviElbo_Section" + str(section) + "_channel" + str(channel) + ".png", bbox_inches='tight')
plt.close(f)
advi_trace = advi_fit.sample(10000)
pm.summary(advi_trace, include_transformed=False)
# Plot of all component distributions in each channel
f, axis = plt.subplots(n_components,n_dimensions, figsize=(n_components*2.5,n_dimensions*2.5))
plt.rcParams['axes.titlesize'] = 10
plt.rcParams['axes.facecolor'] = 'white'
dotSize = 0.5
colours = ('gold', 'pink','green', 'red', 'blue')
x_min = 6
x_max = 12
x = np.linspace(x_min, x_max, 100)
for i in range(n_components):
for j in range(n_dimensions):
axis[i,j].plot(x, scipy.stats.norm.pdf(x,np.mean(advi_trace.get_values('mu')[:,i,j]), np.mean(advi_trace.get_values('sigma')[:,i,j])), color=colours[j])
mean_posteriorMean = np.zeros((n_components,n_dimensions))
for i in range(n_components):
for j in range(n_dimensions):
mean_posteriorMean[i,j] = np.mean(advi_trace.get_values('mu')[:,i,j])
# Show results hmc:
f, axis = plt.subplots(n_components,n_dimensions, figsize=(n_components*2.5,n_dimensions*2.5))
plt.rcParams['axes.titlesize'] = 10
plt.rcParams['axes.facecolor'] = 'white'
dotSize = 0.5
colours = ('gold', 'pink','green', 'red', 'blue')
x_min = 6
x_max = 12
x = np.linspace(x_min, x_max, 100)
for i in range(n_components):
for j in range(n_dimensions):
axis[i,j].plot(x, scipy.stats.norm.pdf(x,np.mean(hmc_trace.get_values('mu')[:,i,j]), np.mean(hmc_trace.get_values('sigma')[:,i,j])), color=colours[j])
mean_posteriorMean = np.zeros((n_components,n_dimensions))
for i in range(n_components):
for j in range(n_dimensions):
mean_posteriorMean[i,j] = np.mean(hmc_trace.get_values('mu')[:,i,j])
# Save trace means:
advi_mus = np.array([[np.mean(advi_trace.get_values('mu')[:,i,j]) for i in range(n_components)] for j in range(n_dimensions)])
advi_sigmas = np.array([[np.mean(advi_trace.get_values('sigma')[:,i,j]) for i in range(n_components)] for j in range(n_dimensions)])
advi_w = np.array([np.mean(advi_trace.get_values('w')[:,i]) for i in range(n_components)])
advi_data = {"advi_mu": advi_mus,
"advi_sigma": advi_sigmas,
"advi_w": advi_w}
pickle_out = open("data/" + slideNames[slide] + '_AdviFitResults.pickle',"wb")
pickle.dump(advi_data, pickle_out)
pickle_out.close()
# Calculate class membership, by using advi_trace and logp_normal function:
confidenceThreshold = 0.66
class0LogProb = [logp_normal(np.mean(advi_trace.get_values('mu')[:,0]), np.mean(advi_trace.get_values('sigma')[:,0]) , data[k,channel]) for k in np.where(sectionNumber == section)]
class1LogProb = [logp_normal(np.mean(advi_trace.get_values('mu')[:,1]), np.mean(advi_trace.get_values('sigma')[:,1]) , data[k,channel]) for k in np.where(sectionNumber == section)]
normalizedProbs = [exp_normalize(np.array((class0LogProb[0][i], class1LogProb[0][i]))) for i in range(len(class0LogProb[0]))]
maxProbs = [max(normalizedProbs[i]) for i in range(len(normalizedProbs))]
classMembership = [np.argmax(normalizedProbs[i]) for i in range(len(normalizedProbs))]
confidentClass = [2 if maxProbs[i] < confidenceThreshold else classMembership[i] for i in range(len(classMembership))]
# Class membership probability:
pickle_out = open("data/" + slideNames[slide] + "Probability-" + celltypeOrder[channel] + '.pickle',"wb")
pickle.dump(normalizedProbs, pickle_out)
pickle_out.close()
### Plot results:
# Histograms:
if sum(np.array(confidentClass) == 1) > 0:
boundary1 = min(data[sectionNumber == section,channel][np.array(confidentClass) == 1])
else:
boundary1 = np.inf
if sum(np.array(confidentClass) == 2) > 0:
boundary2 = min(data[sectionNumber == section,channel][np.array(confidentClass) == 2])
else:
boundary2 = 0
fig = plt.figure()
fig, ax = plt.subplots()
N, bins, patches = ax.hist(data[sectionNumber == section,channel], edgecolor='white', linewidth=1, bins = 100)
for i in range(0, len(patches)):
if bins[i] < boundary2:
patches[i].set_facecolor('b')
elif bins[i] < boundary1:
patches[i].set_facecolor('black')
else:
patches[i].set_facecolor('r')
plt.gca().set_title('Log Intensity and Classification Channel ' + channelOrder[channel])
plt.show()
fig.savefig("figures/" + slideNames[slide] + "/" + "HistogramIntensityAndClassification" + "Section" + str(section) + "channel" + str(channel) + ".png", bbox_inches='tight')
plt.close(fig)
# Scatterplots:
colours = np.repeat('black', sum(sectionNumber == section))
if sum(np.array(confidentClass) == 1) > 0:
colours[np.array(confidentClass) == 1] = 'red'
fig = plt.figure()
plt.scatter(kptn_data[sectionNumber == section,0], np.exp(data[sectionNumber == section,channel]), c = colours, s = 0.1)
plt.gca().set_title('Intensity and Classification Channel ' + channelOrder[channel])
plt.show()
fig.savefig("figures/" + slideNames[slide] + "/" + "ScatterPlotIntensityAndClassification" + "Section" + str(section) + "channel" + channelOrder[channel] + ".png", bbox_inches='tight')
plt.close(fig)
fig = plt.figure()
plt.scatter(kptn_data[sectionNumber == section,0], data[sectionNumber == section,channel], c = colours, s = 0.1)
plt.gca().set_title('Log Intensity and Classification Channel ' + channelOrder[channel])
plt.show()
fig.savefig("figures/" + slideNames[slide] + "/" + "ScatterPlotLOGIntensityAndClassification" + "Section" + str(section) + "channel" + channelOrder[channel] + ".png", bbox_inches='tight')
plt.close(fig)
# Slide location of each cell type (including unclassified):
fig = plt.figure()
plt.scatter(kptn_data[sectionNumber == section,0][np.array(confidentClass) == 1], kptn_data[sectionNumber == section,1][np.array(confidentClass) == 1], s = 0.05)
plt.gca().set_title('Nuclei Positive Classification Slide ' + str(slide) + " Section " + str(section) + " Channel " + channelOrder[channel] + ".png")
plt.show()
fig.savefig("figures/" + slideNames[slide] + "/" + "PositiveClassificationPosition" + str(slide) + "section" + str(section) + "channel" + channelOrder[channel] + ".png", bbox_inches='tight')
plt.close(fig)
def logp_(value):
logps = [tt.log(pi[i]) + logp_normal(mus[i,:], taus[i], value) for i in range(n_components)]
return tt.sum(logsumexp(tt.stacklists(logps)[:, :n_samples], axis=0))
# Fit:
with model:
advi_fit = pm.fit(n=2000, obj_optimizer=pm.adagrad(learning_rate=1e-1), method = 'advi')
# Show results advi:
advi_elbo = pd.DataFrame(
{'log-ELBO': -np.log(advi_fit.hist),
'n': np.arange(advi_fit.hist.shape[0])})
_ = sns.lineplot(y='log-ELBO', x='n', data=advi_elbo)
advi_trace = advi_fit.sample(10000)
pm.summary(advi_trace, include_transformed=False)
# Calculate class membership, by using advi_trace and logp_normal function:
confidenceThreshold = 0.95
class0LogProb = [logp_normal(np.mean(advi_trace.get_values('mu')[:,0]), np.mean(advi_trace.get_values('sigma')[:,0]) , data[k,channel]) for k in np.where(sectionNumber == section)]
class1LogProb = [logp_normal(np.mean(advi_trace.get_values('mu')[:,1]), np.mean(advi_trace.get_values('sigma')[:,1]) , data[k,channel]) for k in np.where(sectionNumber == section)]
normalizedProbs = [exp_normalize(np.array((class0LogProb[0][i], class1LogProb[0][i]))) for i in range(len(class0LogProb[0]))]
maxProbs = [max(normalizedProbs[i]) for i in range(len(normalizedProbs))]
classMembership = [np.argmax(normalizedProbs[i]) for i in range(len(normalizedProbs))]
confidentClass = [2 if maxProbs[i] < confidenceThreshold else classMembership[i] for i in range(len(classMembership))]
# i.e. a value of 2 corresponds to a classification below our confidence threshold, unlike values 0 or 1
### Plot results:
# Histograms:
if sum(np.array(confidentClass) == 1) > 0:
boundary1 = min(data[sectionNumber == section,channel][np.array(confidentClass) == 1])
# i.e. what's the minimum value to confidently classify a cell as positive for this marker?
else:
boundary1 = np.inf
#ax.legend(loc=1);
# Calculate class membership, by using hmc_trace and logp_normal function:
#confidenceThreshold = 0.95
#class0LogProb = [logp_normal(np.mean(hmc_trace.get_values('mu_0')), np.mean(hmc_trace.get_values('sigma')[:,0]) , data[k,channel]) for k in np.where(sectionNumber == section)]
#class1LogProb = [logp_normal(np.mean(hmc_trace.get_values('mu_1')), np.mean(hmc_trace.get_values('sigma')[:,1]) , data[k,channel]) for k in np.where(sectionNumber == section)]
#normalizedProbs = [exp_normalize(np.array((class0LogProb[0][i], class1LogProb[0][i]))) for i in range(len(class0LogProb[0]))]
#maxProbs = [max(normalizedProbs[i]) for i in range(len(normalizedProbs))]
#classMembership = [np.argmax(normalizedProbs[i]) for i in range(len(normalizedProbs))]
#confidentClass = [2 if maxProbs[i] < confidenceThreshold else classMembership[i] for i in range(len(classMembership))]
# Calculate class membership, by using advi_trace and logp_normal function:
confidenceThreshold = 0.95
class0LogProb = [
logp_normal(np.mean(advi_trace.get_values('mu')[:, 0]),
np.mean(advi_trace.get_values('sigma')[:, 0]),
data[k, channel])
for k in np.where(sectionNumber == section)
]
class1LogProb = [
logp_normal(np.mean(advi_trace.get_values('mu')[:, 1]),
np.mean(advi_trace.get_values('sigma')[:, 1]),
data[k, channel])
for k in np.where(sectionNumber == section)
]
normalizedProbs = [
exp_normalize(
np.array((class0LogProb[0][i], class1LogProb[0][i])))
for i in range(len(class0LogProb[0]))
]
maxProbs = [