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 run_expt(config, loss_opt=0):
ttl = config_to_str(config)
print '\nstarting experiment {}'.format(ttl)
print config
Xtrain, Ytrain, params_true, true_fun, fun_name = \
demo.make_data_linreg_1d(config['N'], config['fun_type'])
data_dim = Xtrain.shape[1]
N = Xtrain.shape[0]
Xtrain, Ytrain = opt.shuffle_data(Xtrain, Ytrain)
model_type = config['model_type']
if model_type == 'linear':
model = LinregModel(data_dim, add_ones=True)
params, loss = model.ols_fit(Xtrain, Ytrain)
elif model_type[0:3] == 'mlp':
_, layer_sizes = model_type.split(':')
layer_sizes = [int(n) for n in layer_sizes.split('-')]
model = MLP(layer_sizes, 'regression', L2_reg=0.001)
else:
raise ValueError('unknown model type {}'.format(model_type))
initial_params = model.init_params()
param_dim = len(initial_params)
plot_data = (data_dim == 1)
plot_params = (param_dim == 2)
nplots = 1
if plot_data:
nplots += 1
if plot_params:
nplots += 1
plot_rows, plot_cols = util.nsubplots(nplots)
if config['optimizer'] == 'BFGS':
obj_fun = lambda params: model.PNLL(params, Xtrain, Ytrain)
grad_fun = autograd.grad(obj_fun)
logger = opt.OptimLogger(lambda params: obj_fun(params), eval_freq=1,
store_freq=1, print_freq=1)
params, obj = opt.bfgs(obj_fun, grad_fun, initial_params, config['num_epochs'],
logger.callback)
if config['optimizer'] == 'SGD':
B = config['batch_size']
M = N / B # num_minibatches_per_epoch (num iter per epoch)
max_iters = config['num_epochs'] * M
grad_fun_with_iter = opt.build_batched_grad(model.gradient, config['batch_size'], Xtrain, Ytrain)
#obj_fun = opt.build_batched_grad(model.PNLL, config['batch_size'], Xtrain, Ytrain)
obj_fun = lambda params: model.PNLL(params, Xtrain, Ytrain)
sf = config.get('store_freq', M)
logger = opt.OptimLogger(obj_fun, eval_freq=sf, store_freq=sf, print_freq=0)
sgd_fun = config['sgd_fun']
if config['lr_tune']==True:
eval_fun = lambda params: model.PNLL(params, Xtrain, Ytrain)
lr, lrs, scores = opt.lr_tuner(eval_fun, 'grid', sgd_fun, grad_fun_with_iter,
initial_params, int(np.ceil(max_iters*0.1)))
print 'lr tuner chose lr {:0.3f}'.format(lr)
print lrs
print scores
config['lr_init'] = lr
lr_fun = lambda iter: opt.lr_exp_decay(iter, config['lr_init'],
config['lr_decay'], config['lr_step'])
params, obj = sgd_fun(obj_fun, grad_fun_with_iter, initial_params,
max_iters, logger.callback, lr_fun)
training_loss = model.PNLL(params, Xtrain, Ytrain)
print 'finished fitting, training loss {:0.3g}, {} obj calls, {} grad calls'.\
format(training_loss, model.num_obj_fun_calls, model.num_grad_fun_calls)
fig = plt.figure()
ax = fig.add_subplot(plot_rows, plot_cols, 1)
opt.plot_loss_trace(logger.eval_trace, loss_opt, ax)
ax.set_title('final objective {:0.3g}'.format(training_loss))
ax.set_xlabel('epochs')
if plot_data:
ax = fig.add_subplot(plot_rows, plot_cols, 2)
predict_fun = lambda X: model.predictions(params, X)
demo.plot_data_and_predictions_1d(Xtrain, Ytrain, true_fun, predict_fun, ax)
if plot_params:
ax = fig.add_subplot(plot_rows, plot_cols, 3)
loss_fun = lambda w0, w1: model.PNLL(np.array([w0, w1]), Xtrain, Ytrain)
demo.plot_error_surface_2d(loss_fun, params, params_true, config['fun_type'], ax)
demo.plot_param_trace_2d(logger.param_trace, ax)
ttl = config_to_str(config) # recompute in case lr has been estimated
fig.suptitle(ttl)
folder = 'figures/linreg-sgd'
fname = os.path.join(folder, 'linreg_1d_sgd_{}.png'.format(ttl))
plt.savefig(fname)
return training_loss
