n,
rate=0.1,
loc=[-3, -2],
yloc=[50, 30])
x, y = torch.Tensor(trX), torch.Tensor(trY)
gaussian = Gaussian()
laplace = Laplace()
adaptive = Adaptive()
# # 2-D linear regression
lr2 = PolyRegression(2)
fit2 = train_regular(lr2,
x,
y,
gaussian,
epoch=1000,
learning_rate=1e-2,
verbose=False)
# # 2-D linear regression + laplace
robust_lr2 = PolyRegression(2)
robust_fit2 = train_regular(robust_lr2,
x,
y,
laplace,
epoch=1000,
learning_rate=1e-2,
verbose=False)
# 2-D linear regression + adaptive
def run_experiment(trX, trY, teX, teY, degree=2):
x, y = torch.Tensor(trX), torch.Tensor(trY)
tx, ty = torch.Tensor(teX), torch.Tensor(teY)
sortedx, idxX = torch.sort(x)
sortedy = y[idxX]
gaussian = Gaussian()
laplace = Laplace()
adaptive = Adaptive()
# linear regression
stats = []
lr = PolyRegression(degree)
fit = train_regular(lr,
x,
y,
gaussian,
epoch=1000,
learning_rate=1e-2,
verbose=False)
res1 = fit(sortedx).detach().numpy().flatten() - sortedy.numpy().flatten()
data = dict()
data['model'] = 'LR+' + str(degree)
data['likelihood'] = gaussian.loglikelihood(res1)
stats.append(data)
# robust linear regression
lr = PolyRegression(degree)
fit = train_regular(lr,
x,
y,
laplace,
epoch=1000,
learning_rate=1e-2,
verbose=False)
res1 = fit(sortedx).detach().numpy().flatten() - sortedy.numpy().flatten()
data = dict()
data['model'] = 'RobustLR+' + str(degree)
data['likelihood'] = laplace.loglikelihood(res1)
stats.append(data)
# adaptive linear regression
lr = PolyRegression(degree)
fit, alpha, scale = train_adaptive(lr,
x,
y,
epoch=1000,
learning_rate=1e-2,
verbose=False)
res = fit(sortedx).view(-1) - sortedy
data = dict()
data['model'] = 'Adaptive+' + str(degree)
data['likelihood'] = adaptive.loglikelihood(res, alpha, scale)
stats.append(data)
# locally adaptive linear regression
lr = PolyRegression(degree)
alpha_model = PolyRegression(2, init_zeros=True)
scale_model = PolyRegression(2, init_zeros=True)
fit, alpha_reg, scale_reg = train_locally_adaptive(lr,
alpha_model,
scale_model,
x,
y,
epoch=1000,
learning_rate=1e-2,
verbose=False)
res = fit(sortedx).view(-1) - sortedy
alphas = torch.exp(alpha_reg(sortedx).view(-1))
scales = torch.exp(scale_reg(sortedx).view(-1))
data = dict()
data['model'] = 'LocalAdaptive+' + str(degree)
data['likelihood'] = adaptive.loglikelihood(res, alphas, scales)
stats.append(data)
# gaussian process regression
likelihood = gpytorch.likelihoods.GaussianLikelihood()
model = ExactGPModel(x, y, likelihood)
model.train()
likelihood.train()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)
mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
training_iter = 100
for _ in tqdm(range(training_iter)):
optimizer.zero_grad()
output = model(x)
loss = -mll(output, y)
loss.backward()
optimizer.step()
model.eval()
likelihood.eval()
with torch.no_grad(), gpytorch.settings.fast_pred_var():
observed_pred = likelihood(model(sortedx))
# the source code divides mll by the size of input -> reconstruct mll
data = dict()
data['model'] = 'GPR'
data['likelihood'] = (mll(observed_pred, sortedy) *
len(sortedy)).detach().numpy()
stats.append(data)
return pd.DataFrame(stats)
def run_experiment(trX,trY, teX, teY, degree=2):
x, y = torch.Tensor(trX), torch.Tensor(trY)
tx, ty = torch.Tensor(teX), torch.Tensor(teY)
sortedx, idxX = torch.sort(tx)
sortedy = ty[idxX]
gaussian = Gaussian()
laplace = Laplace()
adaptive = Adaptive()
# linear regression
stats = []
lr = PolyRegression(degree)
fit = train_regular(lr, x, y, gaussian, epoch=100, learning_rate=1e-2, verbose=False)
data = dict()
data['model'] = 'LR+' + str(degree)
param = fit.beta.weight.data.numpy().flatten()
bias = fit.beta.bias.data.numpy().flatten()
data['param0'] = param[0]
data['param1'] = param[1]
data['param2'] = bias[0]
stats.append(data)
# robust linear regression
lr = PolyRegression(degree)
fit = train_regular(lr, x, y, laplace, epoch=100, learning_rate=1e-2, verbose=False)
data = dict()
data['model'] = 'RobustLR+' + str(degree)
param = fit.beta.weight.data.numpy().flatten()
bias = fit.beta.bias.data.numpy().flatten()
data['param0'] = param[0]
data['param1'] = param[1]
data['param2'] = bias[0]
stats.append(data)
# adaptive linear regression
lr = PolyRegression(degree)
fit, alpha, scale = train_adaptive(lr, x, y, epoch=100, learning_rate=1e-2, verbose=False)
data = dict()
data['model'] = 'Adaptive+' + str(degree)
param = fit.beta.weight.data.numpy().flatten()
bias = fit.beta.bias.data.numpy().flatten()
data['param0'] = param[0]
data['param1'] = param[1]
data['param2'] = bias[0]
stats.append(data)
# locally adaptive linear regression
lr = PolyRegression(degree)
alpha_model = PolyRegression(2, init_zeros=True)
scale_model = PolyRegression(2, init_zeros=True)
fit, alpha_reg, scale_reg = train_locally_adaptive(lr, alpha_model, scale_model, x, y,
epoch=500, learning_rate=1e-2, verbose=False)
data = dict()
data['model'] = 'LocalAdaptive+' + str(degree)
param = fit.beta.weight.data.numpy().flatten()
bias = fit.beta.bias.data.numpy().flatten()
data['param0'] = param[0]
data['param1'] = param[1]
data['param2'] = bias[0]
stats.append(data)
# modal regression
ml = ModalLinearRegression(kernel="gaussian", poly=degree, bandwidth=1)
ml.fit(x.numpy().reshape(len(x), -1), y.numpy().reshape(-1))
yml = ml.predict(sortedx.detach().numpy().reshape(len(sortedx), -1))
data = dict()
data['model'] = 'Modal'
param = ml.coef_.flatten()
bias = ml.intercept_.flatten()
data['param0'] = param[0]
data['param1'] = param[1]
data['param2'] = bias[0]
stats.append(data)
return pd.DataFrame(stats)