def comp_varexp(Y,S,nneuron):
"""
Compute variance explained from the GLM results, with parameters set above
"""
y = np.squeeze(Y[nneuron,:]) #spike train of interest
stimulus = S[:,None] #same stimulus for all neurons
X = build_convolved_matrix(stimulus, Y.T, Ks, couple) #design matrix with features projected onto basis functions
glm = GLMCV(distr="binomial", tol=1e-5, eta=1.0,
score_metric="deviance",
alpha=0., learning_rate=1e-6, max_iter=1000, cv=3, verbose=True) #important to have v slow learning_rate
glm.fit(X, y)
yhat = simulate_glm('binomial', glm.beta0_, glm.beta_, X) #simulate spike rate given the firring results
varexp = np.corrcoef(y,yhat)
return varexp
def test_glmcv(distr):
"""Test GLMCV class."""
raises(ValueError, GLM, distr='blah')
raises(ValueError, GLM, distr='gaussian', max_iter=1.8)
scaler = StandardScaler()
n_samples, n_features = 100, 10
# coefficients
beta0 = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0)
beta = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0, (n_features,))
solvers = ['batch-gradient', 'cdfast']
score_metric = 'pseudo_R2'
learning_rate = 2e-1
for solver in solvers:
if distr == 'gamma' and solver == 'cdfast':
continue
glm = GLMCV(distr,
learning_rate=learning_rate,
solver=solver,
score_metric=score_metric,
cv=2)
assert (repr(glm))
np.random.seed(glm.random_state)
X_train = np.random.normal(0.0, 1.0, [n_samples, n_features])
y_train = simulate_glm(glm.distr, beta0, beta, X_train)
X_train = scaler.fit_transform(X_train)
glm.fit(X_train, y_train)
beta_ = glm.beta_
assert_allclose(beta, beta_, atol=0.5) # check fit
y_pred = glm.predict(scaler.transform(X_train))
assert (y_pred.shape[0] == X_train.shape[0])
# test picky score_metric check within fit().
glm.score_metric = 'bad_score_metric' # reuse last glm
raises(ValueError, glm.fit, X_train, y_train)
def test_glmcv():
"""Test GLMCV class."""
scaler = StandardScaler()
n_samples, n_features = 100, 10
# coefficients
beta0 = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0)
beta = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0, (n_features,))
distrs = ['softplus', 'gaussian', 'poisson', 'binomial', 'probit', 'gamma']
solvers = ['batch-gradient', 'cdfast']
score_metric = 'pseudo_R2'
learning_rate = 2e-1
for solver in solvers:
for distr in distrs:
if distr == 'gamma' and solver == 'cdfast':
continue
glm = GLMCV(distr,
learning_rate=learning_rate,
solver=solver,
score_metric=score_metric)
assert_true(repr(glm))
np.random.seed(glm.random_state)
X_train = np.random.normal(0.0, 1.0, [n_samples, n_features])
y_train = simulate_glm(glm.distr, beta0, beta, X_train)
X_train = scaler.fit_transform(X_train)
glm.fit(X_train, y_train)
beta_ = glm.beta_
assert_allclose(beta, beta_, atol=0.5) # check fit
y_pred = glm.predict(scaler.transform(X_train))
assert_equal(y_pred.shape[0], X_train.shape[0])
def kernel_MSE(Y, S, nneuron, Ks):
"""
Compute MSE from the GLM results, with simulated activity, stimulus, and the ground truth kernel
"""
###GLM
y = np.squeeze(Y[nneuron, :]) #spike train of interest
stimulus = S[:, None] #same stimulus for all neurons
X = build_convolved_matrix(
stimulus, Y.T, Ks,
couple) #design matrix with features projected onto basis functions
glm = GLMCV(distr="binomial",
tol=1e-5,
eta=1.0,
score_metric="deviance",
alpha=0.,
learning_rate=0.1,
max_iter=1000,
cv=3,
verbose=True) #important to have v slow learning_rate
glm.fit(X, y)
###store kernel
theta_rec = glm.beta_[1:]
theta_rec = theta_rec.reshape(nbasis, N + 1)
K_rec = np.zeros((N + 1, pad))
for ii in range(N + 1):
K_rec[ii, :] = np.dot(theta_rec[:, ii], Ks)
###normalize and shift kernels
K_rec_norm = np.array([
K_rec[ii, :] / np.linalg.norm(K_rec[ii, :]) for ii in range(N + 1)
]) #
K_tru_norm = np.array([
allK[nneuron, ii, :] / np.linalg.norm(allK[nneuron, ii, :])
for ii in range(N + 1)
]) #
# K_rec_norm = K_rec_norm.T-K_rec_norm[:,-1]
# K_tru_norm = K_tru_norm.T-K_tru_norm[:,-1]
mses = np.sum((K_rec_norm - K_tru_norm)**2,
axis=1) #measuring MSE for each kernel
return mses
def test_glmcv():
"""Test GLMCV class."""
scaler = StandardScaler()
n_samples, n_features = 100, 10
# coefficients
beta0 = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0)
beta = 1. / (np.float(n_features) + 1.) * \
np.random.normal(0.0, 1.0, (n_features,))
distrs = ['softplus', 'gaussian', 'poisson', 'binomial', 'probit', 'gamma']
solvers = ['batch-gradient', 'cdfast']
score_metric = 'pseudo_R2'
learning_rate = 2e-1
for solver in solvers:
for distr in distrs:
if distr == 'gamma' and solver == 'cdfast':
continue
glm = GLMCV(distr, learning_rate=learning_rate,
solver=solver, score_metric=score_metric)
assert_true(repr(glm))
np.random.seed(glm.random_state)
X_train = np.random.normal(0.0, 1.0, [n_samples, n_features])
y_train = simulate_glm(glm.distr, beta0, beta, X_train)
X_train = scaler.fit_transform(X_train)
glm.fit(X_train, y_train)
beta_ = glm.beta_
assert_allclose(beta, beta_, atol=0.5) # check fit
y_pred = glm.predict(scaler.transform(X_train))
assert_equal(y_pred.shape[0], X_train.shape[0])
# %%
###############################################################################
# %% inference method (single)
nneuron = 2
pad = 100 #window for kernel
nbasis = 7 #number of basis
couple = 1 #wether or not coupling cells considered
Y = np.squeeze(rate[nneuron,:]) #spike train of interest
Ks = (np.fliplr(basis_function1(pad,nbasis).T).T).T #basis function used for kernel approximation
stimulus = stim[:,None] #same stimulus for all neurons
X = build_convolved_matrix(stimulus, rate.T, Ks, couple) #design matrix with features projected onto basis functions
###pyGLMnet function with optimal parameters
glm = GLMCV(distr="binomial", tol=1e-5, eta=1.0,
score_metric="deviance",
alpha=0., learning_rate=1e-6, max_iter=1000, cv=3, verbose=True) #important to have v slow learning_rate
glm.fit(X, Y)
# %% direct simulation
yhat = simulate_glm('binomial', glm.beta0_, glm.beta_, X) #simulate spike rate given the firring results
plt.figure()
plt.plot(Y*1.) #ground truth
plt.plot(yhat,'--')
# %%reconstruct kernel
theta = glm.beta_
dc_ = theta[0]
theta_ = theta[1:]
if couple == 1:
theta_ = theta_.reshape(nbasis,N+1) #nbasis times (stimulus + N neurons)
allKs = np.array([theta_[:,kk] @ Ks for kk in range(N+1)])
elif couple == 0:
gl_glm = GLMCV(distr="binomial", tol=1e-3,
group=group_idxs, score_metric="pseudo_R2",
alpha=1.0, cv=3)
# set up the lasso model
glm = GLMCV(distr="binomial", tol=1e-3,
score_metric="pseudo_R2", alpha=1.0, cv=3)
print("gl_glm: ", gl_glm)
print("glm: ", glm)
##########################################################
# Fit models
gl_glm.fit(Xtrain, ytrain)
glm.fit(Xtrain, ytrain)
##########################################################
# Visualize model scores on test set
plt.figure()
plt.semilogx(gl_glm.reg_lambda, gl_glm.scores_, 'go-')
plt.semilogx(glm.reg_lambda, glm.scores_, 'ro--')
plt.legend(['Group Lasso', 'Lasso'], frameon=False,
loc='best')
plt.xlabel('$\lambda$')
plt.ylabel('pseudo-$R^2$')
plt.tick_params(axis='y', right='off')
plt.tick_params(axis='x', top='off')
# Fit models
from sklearn.model_selection import train_test_split
Xtrain, Xtest, Ytrain, Ytest = train_test_split(features,
spike_counts,
test_size=0.2,
random_state=42)
########################################################
from pyglmnet import utils
n_samples = Xtrain.shape[0]
Tau = utils.tikhonov_from_prior(prior_cov, n_samples)
glm = GLMCV(distr='poisson', alpha=0., Tau=Tau, score_metric='pseudo_R2', cv=3)
glm.fit(Xtrain, Ytrain)
print("train score: %f" % glm.score(Xtrain, Ytrain))
print("test score: %f" % glm.score(Xtest, Ytest))
weights = glm.beta_
########################################################
# Visualize
for time_bin_ in range(n_temporal_basis):
RF = strf_model.make_image_from_spatial_basis(
spatial_basis,
weights[range(time_bin_, n_spatial_basis * n_temporal_basis,
n_temporal_basis)])
plt.subplot(1, n_temporal_basis, time_bin_ + 1)
plt.imshow(RF, cmap='Blues', interpolation='none')
n_samples, n_features = X.shape
########################################################
# Split the data into training and test sets
X_train, X_test, y_train, y_test = \
train_test_split(X, y, test_size=0.33, random_state=0)
########################################################
# Fit a gaussian distributed GLM with elastic net regularization
# use the default value for reg_lambda
glm = GLMCV(distr='gaussian', alpha=0.05, score_metric='pseudo_R2')
# fit model
glm.fit(X_train, y_train)
# score the test set prediction
y_test_hat = glm.predict(X_test)
print ("test set pseudo $R^2$ = %f" % glm.score(X_test, y_test))
########################################################
# Plot the true and predicted test set target values
plt.plot(y_test[:50], 'ko-')
plt.plot(y_test_hat[:50], 'ro-')
plt.legend(['true', 'pred'], frameon=False)
plt.xlabel('Counties')
plt.ylabel('Per capita violent crime')
plt.tick_params(axis='y', right='off')
def fit_group_lasso(
X,
knockoffs,
y,
groups,
use_pyglm=True,
y_dist=None,
group_lasso=True,
**kwargs,
):
""" Fits a group lasso model.
:param X: n x p design matrix
:param knockoffs: n x p knockoff matrix
:param groups: p length numpy array of groups
:param use_pyglm: If true, use the pyglmnet grouplasso
Else use the regular one
:param y_dist: Either "gaussian" or "binomial" (for logistic regression)
:param group_lasso: If False, do not use group regularization.
:param kwargs: kwargs for group-lasso GroupLasso class.
In particular includes reg_vals, a list of regularizations
(lambda values) which defaults to [(0.05, 0.05)]. In each
tuple of the list, the first value is the group regularization,
the second value is the individual regularization.
"""
warnings.filterwarnings("ignore")
# Parse some kwargs/defaults
if "max_iter" in kwargs:
max_iter = kwargs.pop("max_iter")
else:
max_iter = 100
if "tol" in kwargs:
tol = kwargs.pop("tol")
else:
tol = 1e-2
if "cv" in kwargs:
cv = kwargs.pop("cv")
else:
cv = 5
if "learning_rate" in kwargs:
learning_rate = kwargs.pop("learning_rate")
else:
learning_rate = 2
if y_dist is None:
y_dist = parse_y_dist(y)
# Bind data
n = X.shape[0]
p = X.shape[1]
features = np.concatenate([X, knockoffs], axis=1)
# By default, all variables are their own group
if groups is None:
groups = np.arange(1, p + 1, 1)
m = np.unique(groups).shape[0]
# If m == p, meaning each variable is their own group,
# just fit a regular lasso
if m == p or not group_lasso:
return fit_lasso(X, knockoffs, y, y_dist, **kwargs)
# Make sure variables and their knockoffs are in the same group
# This is necessary for antisymmetry
doubled_groups = np.concatenate([groups, groups], axis=0)
# Randomize coordinates to make sure everything is symmetric
inds, rev_inds = random_permutation_inds(2 * p)
features = features[:, inds]
doubled_groups = doubled_groups[inds]
# Standardize - important for pyglmnet performance,
# highly detrimental for group_lasso performance
if use_pyglm:
features = (features - features.mean()) / features.std()
if y_dist == "gaussian":
y = (y - y.mean()) / y.std()
# Get regularizations
if "reg_vals" in kwargs:
reg_vals = kwargs.pop("reg_vals")
else:
reg_vals = [(x, x) for x in DEFAULT_REG_VALS]
# Fit pyglm model using warm starts
if use_pyglm:
l1_regs = [x[0] for x in reg_vals]
gl = GLMCV(
distr=y_dist,
tol=tol,
group=doubled_groups,
alpha=1.0,
learning_rate=learning_rate,
max_iter=max_iter,
reg_lambda=l1_regs,
cv=cv,
solver="cdfast",
)
gl.fit(features, y)
# Pull score, rename
best_score = -1 * calc_mse(gl, features, y)
best_gl = gl
# Fit model
if not use_pyglm:
best_gl = None
best_score = -1 * np.inf
for group_reg, l1_reg in reg_vals:
# Fit logistic/gaussian group lasso
if not use_pyglm:
if y_dist.lower() == "gaussian":
gl = GroupLasso(
groups=doubled_groups,
tol=tol,
group_reg=group_reg,
l1_reg=l1_reg,
**kwargs,
)
elif y_dist.lower() == "binomial":
gl = LogisticGroupLasso(
groups=doubled_groups,
tol=tol,
group_reg=group_reg,
l1_reg=l1_reg,
**kwargs,
)
else:
raise ValueError(
f"y_dist must be one of gaussian, binomial, not {y_dist}"
)
gl.fit(features, y.reshape(n, 1))
score = -1 * calc_mse(gl, features, y.reshape(n, 1))
# Score, possibly select
if score > best_score:
best_score = score
best_gl = gl
warnings.resetwarnings()
return best_gl, inds, rev_inds
def fit(self, X, Y, get_history_terms=True):
"""
Fits the model to the data in X to predict the response Y.
Imports models and creates model instance as well.
Parameters
----------
X: float, n_samples x n_features, features of interest
Y: float, n_samples x 1, population activity
get_history_terms = Boolean. Whether to compute the temporal features.
Note that if spike_history and cov_history are False,
no history will be computed anyways and the flag does nothing.
"""
if self.default_params:
warnings.warn(
'\n Using default hyperparameters. Consider optimizing on' +
' a held-out dataset using, e.g. hyperopt or random search')
# make the covariate matrix. Include spike or covariate history?
# The different methods here are to satisfy the needs of recurrent keras
# models
if get_history_terms:
if self.tunemodel == 'lstm':
X, Y = self.get_all_with_history_keras(X, Y)
else:
X, Y = self.get_all_with_history(X, Y)
if self.tunemodel == 'glm':
model = GLMCV(**self.params)
model.fit(X, Y)
# we want the last of the regularization path
# self.model = model[-1]
self.GLMCV = model
self.model = model.glm_
elif self.tunemodel == 'feedforward_nn':
if np.ndim(X) == 1:
X = np.transpose(np.atleast_2d(X))
params = self.params
model = Sequential()
model.add(
Dense(params['n1'],
input_dim=np.shape(X)[1],
kernel_initializer='glorot_normal',
activation='relu',
kernel_regularizer=l2(params['l2'])))
model.add(Dropout(params['dropout']))
model.add(BatchNormalization())
model.add(
Dense(params['n2'],
kernel_initializer='glorot_normal',
activation='relu',
kernel_regularizer=l2(params['l2'])))
model.add(BatchNormalization())
model.add(Dense(1, activation='softplus'))
optim = adam(lr=params['lr'],
clipnorm=params['clipnorm'],
decay=params['decay'],
beta_1=1 - params['b1'],
beta_2=1 - params['b2'])
model.compile(
loss='poisson',
optimizer=optim,
)
hist = model.fit(X,
Y,
batch_size=128,
epochs=30,
verbose=self.verbose)
self.model = model
elif self.tunemodel == 'xgboost':
dtrain = xgb.DMatrix(X, label=Y)
num_round = 200
self.model = xgb.train(self.params, dtrain, num_round)
elif self.tunemodel == 'random_forest':
self.model = RandomForestRegressor(**self.params)
self.model.fit(X, Y)
elif self.tunemodel == 'lstm':
if np.ndim(X) == 1:
X = np.transpose(np.atleast_2d(X))
params = self.params
model = Sequential() #Declare model
#Add recurrent layer
model.add(LSTM(int(params['n_units']),input_shape=(X.shape[1],X.shape[2]),\
dropout_W=params['dropout'],dropout_U=params['dropout']))
#Within recurrent layer, include dropout
model.add(Dropout(params['dropout'])
) #Dropout some units (recurrent layer output units)
#Add dense connections to output layer
model.add(Dense(1, activation='softplus'))
#Fit model (and set fitting parameters)
model.compile(loss='poisson',
optimizer='rmsprop',
metrics=['accuracy'])
model.fit(X,
Y,
epochs=int(params['epochs']),
batch_size=int(params['batch_size']),
verbose=self.verbose) #Fit the model
self.model = model
else: #using predefined model
self.model.fit(X, Y)
#fake spike train output
rate = np.concatenate((input_,-input_,output_)).reshape(3,lt) ### input signal, output, and negative output
nneuron = 0
pad = 100 #window for kernel
nbasis = 7 #number of basis
couple = 1 #wether or not coupling cells considered
Y = np.squeeze(rate[nneuron,:]) #spike train of interest
Ks = (np.fliplr(basis_function1(pad,nbasis).T).T).T #basis function used for kernel approximation
stimulus = input_[:,None] #same stimulus for all neurons
X = build_convolved_matrix(stimulus, rate.T, Ks, couple) #design matrix with features projected onto basis functions
###pyGLMnet function with optimal parameters
distr = "binomial"
glm = GLMCV(distr=distr, tol=1e-5, eta=1.0,
score_metric="deviance",
alpha=0., learning_rate=1e-6, max_iter=1000, cv=3, verbose=True) #important to have v slow learning_rate
glm.fit(X, Y)
# %% direct simulation
yhat = simulate_glm(distr, glm.beta0_, glm.beta_, X) #simulate spike rate given the firring results
plt.figure()
plt.plot(Y*1.,label='input') #ground truth
plt.plot(yhat,'--',label='ouput_est')
plt.plot(-output_,'k',alpha=0.5,label='target')
plt.legend()
# %%
theta = glm.beta_
dc_ = theta[0]
theta_ = theta[1:]
if couple == 1:
theta_ = theta_.reshape(nbasis,N+1) #nbasis times (stimulus + N neurons)
n_samples, n_features = X.shape
########################################################
# Split the data into training and test sets
X_train, X_test, y_train, y_test = \
train_test_split(X, y, test_size=0.33, random_state=0)
########################################################
# Fit a gaussian distributed GLM with elastic net regularization
# use the default value for reg_lambda
glm = GLMCV(distr='gaussian', alpha=0.05, score_metric='pseudo_R2')
# fit model
glm.fit(X_train, y_train)
# score the test set prediction
y_test_hat = glm.predict(X_test)
print ("test set pseudo $R^2$ = %f" % glm.score(X_test, y_test))
########################################################
# Now use plain grid search cv to compare
import numpy as np # noqa
from sklearn.model_selection import GridSearchCV # noqa
from sklearn.cross_validation import StratifiedKFold # noqa
cv = StratifiedKFold(y_train, 3)
reg_lambda = np.logspace(np.log(0.5), np.log(0.01), 10,
# %%
###############################################################################
###############################################################################
# %% test pyGLM
### This is super-easy if we rely on built-in GLM fitting code
glm = GLMCV(distr="binomial",
tol=1e-3,
score_metric="pseudo_R2",
alpha=1.0,
learning_rate=3,
max_iter=100,
cv=3,
verbose=True)
glm.fit(X, np.squeeze(spk))
# %%
plt.figure()
pyglm_infer = glm.beta_
plt.plot(pyglm_infer / np.linalg.norm(pyglm_infer))
plt.plot(K / np.linalg.norm(K), '--')
# %% Two-neuron circuit with pyGLMnet
###############################################################################
###############################################################################
# %% combine basis function here
###convolve with basis first??
N = 2
dt = 0.1 #ms
T = 10000
gl_glm = GLMCV(distr="binomial", tol=1e-2,
group=group_idxs, score_metric="pseudo_R2",
alpha=1.0)
# set up the lasso model
glm = GLMCV(distr="binomial", tol=1e-2,
score_metric="pseudo_R2", alpha=1.0)
print("gl_glm: ", gl_glm)
print("glm: ", glm)
##########################################################
# Fit models
gl_glm.fit(Xtrain, ytrain)
glm.fit(Xtrain, ytrain)
##########################################################
# Visualize model scores on test set
plt.figure()
plt.semilogx(gl_glm.reg_lambda, gl_glm.scores_, 'go-')
plt.semilogx(glm.reg_lambda, glm.scores_, 'ro--')
plt.legend(['Group Lasso', 'Lasso'], frameon=False,
loc='best')
plt.xlabel('$\lambda$')
plt.ylabel('pseudo-$R^2$')
plt.tick_params(axis='y', right='off')
plt.tick_params(axis='x', top='off')