import numpy as np
from sklearn.gaussian_process.kernels import Matern, RBF

import plotly

from docs.mse_estimator import ErrorComparer
from docs.data_generation import gen_rbf_X, gen_matern_X, gen_cov_mat
from docs.plotting_utils import gen_model_barplots
from spe.estimators import kfoldcv, kmeanscv, new_y_est, cp_smoother
from spe.smoothers import LinearRegression, BSplineRegressor

np.random.seed(1)

Linear Smoothers

Here we demonstrate the effectiveness of spe.estimators.cp_smoother to estimate MSE on simulated data.

## number of realizations to run
niter = 100

## data generation parameters
gsize=10
n=10**2
p=5
s=5
delta = 0.75
snr = 0.4
tr_frac = .25

noise_kernel = 'matern'
noise_length_scale = 1.
noise_nu = .5

X_kernel = 'matern'
X_length_scale = 5.
X_nu = 2.5

## ErrorComparer parameters
nboot = 100
k = 5
models = [LinearRegression(fit_intercept=False), BSplineRegressor()]
ests = [
    new_y_est,
    cp_smoother,
    kfoldcv,
    kmeanscv
]
est_kwargs = [
    {},
    {},
    {'k': k},
    {'k': k}
]

## plot parameters
model_names = ["Linear Regression", "Spline Regression"]
est_names = ["GenCp", "KFCV", "SPCV"]

err_cmp = ErrorComparer()

nx = ny = int(np.sqrt(n))
xs = np.linspace(0, gsize, nx)
ys = np.linspace(0, gsize, ny)
c_x, c_y = np.meshgrid(xs, ys)
c_x = c_x.flatten()
c_y = c_y.flatten()
coord = np.stack([c_x, c_y]).T

if noise_kernel == 'rbf':
    Sigma_t = gen_cov_mat(c_x, c_y, RBF(length_scale=noise_length_scale))
elif noise_kernel == 'matern':
    Sigma_t = gen_cov_mat(c_x, c_y, Matern(length_scale=noise_length_scale, nu=noise_nu))
else:
    Sigma_t = np.eye(n)

Cov_y_ystar = delta*Sigma_t
Sigma_t = delta*Sigma_t + (1-delta)*np.eye(n)

if noise_kernel == 'rbf' or noise_kernel == 'matern':
    Chol_y = np.linalg.cholesky(Sigma_t)
else:
    Chol_y = np.eye(n)

if X_kernel == 'rbf':
    X = gen_rbf_X(c_x, c_y, p)
elif X_kernel == 'matern':
    X = gen_matern_X(c_x, c_y, p, length_scale=X_length_scale, nu=X_nu)
else:
    X = np.random.randn(n,p)

beta = np.zeros(p)
idx = np.random.choice(p,size=s,replace=False)
beta[idx] = np.random.uniform(-1,1,size=s)

tr_idx = np.ones(n, dtype=bool)

Simulate \(Y, Y^* \overset{iid}{\sim} \mathcal{N}(\mu, \Sigma_Y)\)

model_errs = []

for model in models:
    errs = err_cmp.compare(
        model,
        ests,
        est_kwargs,
        niter=niter,
        n=n,
        p=p,
        s=s,
        snr=snr,
        X=X,
        beta=beta,
        coord=coord,
        Chol_y=Chol_y,
        Chol_ystar=None,
        Cov_y_ystar=None,
        tr_idx=tr_idx,
        fair=False,
        est_sigma=False,
    )
    model_errs.append(errs)

  0%|          | 0/100 [00:00<?, ?it/s]

100%|██████████| 100/100 [00:03<00:00, 27.73it/s]
100%|██████████| 100/100 [00:06<00:00, 15.32it/s]

plotly.offline.init_notebook_mode()
fig = gen_model_barplots(
    model_errs,
    model_names,
    est_names,
    title="Linear Smoothers: No Shared Noise"
)
fig.show()

Simulate \(\begin{pmatrix} Y \\ Y^* \end{pmatrix} \sim \mathcal{N}\left(\begin{pmatrix} \mu \\ \mu \end{pmatrix}, \begin{pmatrix}\Sigma_Y & \Sigma_{Y, Y^*} \\ \Sigma_{Y^*, Y} & \Sigma_{Y} \end{pmatrix}\right)\)

corr_model_errs = []

for model in models:
    errs = err_cmp.compare(
        model,
        ests,
        est_kwargs,
        niter=niter,
        n=n,
        p=p,
        s=s,
        snr=snr,
        X=X,
        beta=beta,
        coord=coord,
        Chol_y=Chol_y,
        Chol_ystar=Chol_y,
        Cov_y_ystar=Cov_y_ystar,
        tr_idx=tr_idx,
        fair=False,
        est_sigma=False,
    )
    corr_model_errs.append(errs)

100%|██████████| 100/100 [00:08<00:00, 12.37it/s]
100%|██████████| 100/100 [00:11<00:00,  8.99it/s]

corr_fig = gen_model_barplots(
    corr_model_errs,
    model_names,
    est_names,
    title="Linear Smoothers: Shared Structured Noise"
)
corr_fig.show()