def main():
np.random.seed(1)
Xtrain, ytrain, params_true, true_fun, ttl = make_data_linreg_1d(21, 'linear')
model = LinregModel(1, True)
params_init = model.init_params()
print model
# Check that OLS and BFGS give same result
params_ols, loss_ols = model.ols_fit(Xtrain, ytrain)
obj_fun = lambda params: model.objective(params, Xtrain, ytrain)
grad_fun = lambda params: model.gradient(params, Xtrain, ytrain)
params_bfgs, loss_bfgs = bfgs(obj_fun, grad_fun, params_init)
assert(np.allclose(params_bfgs, params_ols))
assert(np.allclose(loss_bfgs, loss_ols))
# Check that analytic gradient and automatic gradient give same result
# when evaluated on training data
grad_fun = autograd.grad(obj_fun)
grad_auto = grad_fun(params_init)
grad_finite_diff = autograd.util.nd(lambda p : obj_fun(p), params_init)[0]
grad_analytic = model.gradient(params_init, Xtrain, ytrain)
assert(np.allclose(grad_auto, grad_finite_diff))
assert(np.allclose(grad_auto, grad_analytic))
params_autograd, loss_autograd = bfgs(obj_fun, grad_fun, params_init)
assert(np.allclose(params_bfgs, params_autograd))
assert(np.allclose(loss_bfgs, loss_autograd))
print "All assertions passed"
def main():
np.random.seed(1)
Xtrain, ytrain, params_true, true_fun, ttl = make_data_linreg_1d(
21, 'linear')
model = LinregModel(1, True)
params_init = model.init_params()
print(model)
# Check that OLS and BFGS give same result
params_ols, loss_ols = model.ols_fit(Xtrain, ytrain)
obj_fun = lambda params: model.objective(params, Xtrain, ytrain)
grad_fun = lambda params: model.gradient(params, Xtrain, ytrain)
params_bfgs, loss_bfgs = bfgs(obj_fun, grad_fun, params_init)
assert (np.allclose(params_bfgs, params_ols))
assert (np.allclose(loss_bfgs, loss_ols))
# Check that analytic gradient and automatic gradient give same result
# when evaluated on training data
grad_fun = autograd.grad(obj_fun)
grad_auto = grad_fun(params_init)
grad_finite_diff = autograd.util.nd(lambda p: obj_fun(p), params_init)[0]
grad_analytic = model.gradient(params_init, Xtrain, ytrain)
assert (np.allclose(grad_auto, grad_finite_diff))
assert (np.allclose(grad_auto, grad_analytic))
params_autograd, loss_autograd = bfgs(obj_fun, grad_fun, params_init)
assert (np.allclose(params_bfgs, params_autograd))
assert (np.allclose(loss_bfgs, loss_autograd))
print("All assertions passed")
def main():
np.random.seed(1)
xtrain, ytrain, params_true = make_data_linreg_1d()
N = xtrain.shape[0]
D = 2
Xtrain = np.c_[np.ones(N), xtrain] # add column of 1s
params_init = np.zeros(D)
logger = MinimizeLogger(LinregModel.objective, (Xtrain, ytrain),
print_freq=10)
# Check that OLS and BFGS give same result
params_ols, loss_ols = LinregModel.ols_fit(Xtrain, ytrain)
obj_fun = LinregModel.objective
grad_fun = LinregModel.gradient
params_bfgs, loss_bfgs, logger = bfgs_fit(params_init, obj_fun, grad_fun,
(Xtrain, ytrain), logger)
assert (np.allclose(params_bfgs, params_ols))
assert (np.allclose(loss_bfgs, loss_ols))
# Check that analytic gradient and automatic gradient give same result
grad_fun = autograd.grad(obj_fun)
grad_auto = grad_fun(params_init, Xtrain, ytrain)
grad_finite_diff = autograd.util.nd(lambda p: obj_fun(p, Xtrain, ytrain),
params_init)[0]
grad_analytic = LinregModel.gradient(params_init, Xtrain, ytrain)
assert (np.allclose(grad_auto, grad_finite_diff))
assert (np.allclose(grad_auto, grad_analytic))
params_autograd, loss_autograd = bfgs_fit(params_init, obj_fun, grad_fun,
(Xtrain, ytrain))
assert (np.allclose(params_bfgs, params_autograd))
assert (np.allclose(loss_bfgs, loss_autograd))
print "All assertions passed"
# Plot loss vs time
print logger.obj_trace
ax = plot_loss_trace(logger.obj_trace, loss_ols)
ax.set_title('BFGS')
# Plot 2d trajectory of parameter values over time
loss_fun = lambda w0, w1: LinregModel.objective([w0, w1], xtrain, ytrain)
ax = plot_error_surface(loss_fun, params_true)
plot_param_trace(logger.param_trace, ax)
ax.set_title('BFGS')
plt.show()
def main():
np.random.seed(1)
xtrain, ytrain, params_true = make_data_linreg_1d()
N = xtrain.shape[0]
D = 2
Xtrain = np.c_[np.ones(N), xtrain] # add column of 1s
params_init = np.zeros(D)
logger = MinimizeLogger(LinregModel.objective, (Xtrain, ytrain), print_freq=10)
# Check that OLS and BFGS give same result
params_ols, loss_ols = LinregModel.ols_fit(Xtrain, ytrain)
obj_fun = LinregModel.objective
grad_fun = LinregModel.gradient
params_bfgs, loss_bfgs, logger = bfgs_fit(params_init, obj_fun, grad_fun, (Xtrain, ytrain), logger)
assert(np.allclose(params_bfgs, params_ols))
assert(np.allclose(loss_bfgs, loss_ols))
# Check that analytic gradient and automatic gradient give same result
grad_fun = autograd.grad(obj_fun)
grad_auto = grad_fun(params_init, Xtrain, ytrain)
grad_finite_diff = autograd.util.nd(lambda p : obj_fun(p, Xtrain, ytrain), params_init)[0]
grad_analytic = LinregModel.gradient(params_init, Xtrain, ytrain)
assert(np.allclose(grad_auto, grad_finite_diff))
assert(np.allclose(grad_auto, grad_analytic))
params_autograd, loss_autograd = bfgs_fit(params_init, obj_fun, grad_fun, (Xtrain, ytrain))
assert(np.allclose(params_bfgs, params_autograd))
assert(np.allclose(loss_bfgs, loss_autograd))
print "All assertions passed"
# Plot loss vs time
print logger.obj_trace
ax = plot_loss_trace(logger.obj_trace, loss_ols)
ax.set_title('BFGS')
# Plot 2d trajectory of parameter values over time
loss_fun = lambda w0, w1: LinregModel.objective([w0, w1], xtrain, ytrain)
ax = plot_error_surface(loss_fun, params_true)
plot_param_trace(logger.param_trace, ax)
ax.set_title('BFGS')
plt.show()
