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04_logistics_bayesian_v4.2.py
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04_logistics_bayesian_v4.2.py
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# ---
# jupyter:
# jupytext:
# formats: ipynb,py:percent
# text_representation:
# extension: .py
# format_name: percent
# format_version: '1.3'
# jupytext_version: 1.14.5
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
# %%
import jax
from jax import random
from jax.scipy.optimize import minimize as jax_minimize
from jax.scipy.special import expit, logit
import jax.numpy as jnp
import numpy as np
import numpyro
from numpyro.infer import MCMC, NUTS, Predictive
from numpyro.infer.initialization import init_to_median
import numpyro.distributions as dist
import pandas as pd
from sklearn.impute import SimpleImputer
from sklearn.metrics import f1_score, recall_score, precision_score
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
numpyro.set_host_device_count(2)
# %%
kaggle_submission = False
# %% [markdown]
# # Bayesian Logistics Regression
#
# With guessing, shrinkage on metric variables' coefficients, interaction terms,
# and quadratic terms.
#
# ## Data
# %%
if kaggle_submission:
train_path = '/kaggle/input/icr-identify-age-related-conditions/train.csv'
test_path = '/kaggle/input/icr-identify-age-related-conditions/test.csv'
else:
train_path = '../data/train.csv'
test_path = '../data/test.csv'
train_df = pd.read_csv(train_path)
train_df.info()
# %%
test_df = pd.read_csv(test_path)
test_df.info()
# %% [markdown]
# ### Data Preprocessing
# %%
preprocessing = Pipeline([
('imputer', SimpleImputer(strategy='median')),
('scaler', StandardScaler()),
])
# %%
X_df = train_df.drop(columns=['Id', 'Class', 'EJ'])
y = train_df['Class']
ej = train_df['EJ'].astype('category')
X_df = pd.DataFrame(
preprocessing.fit_transform(X_df), columns=X_df.columns, index=X_df.index)
y = y.values
# %%
X_df.columns.size
# %%
def create_interaction_terms_between(df: pd.DataFrame, features: list[str]) -> pd.DataFrame:
assert all(f in df.columns for f in features)
interactions = dict()
for i, fst in enumerate(features):
for snd in features[i+1:]:
interactions[f'{fst}*{snd}'] = df[fst] * df[snd]
return pd.DataFrame(interactions)
# These features are taken from the analyzing notebook,
# based on the posterior distributions.
# If the 95% HDI of a feature does not contain 0,
# then it is considered as important features.
# Otherwise, if the CDF of less than or above 0 is <= 10%,
# then it is considered as less important features.
most_important_features = ['BQ', 'CR', 'DI', 'DU']
less_important_features = ['CD ', 'CH', 'DN', 'DL', 'EE', 'EP', 'FI', 'GE', 'GF']
features = most_important_features + less_important_features
X_interactions_df = create_interaction_terms_between(
X_df, most_important_features + less_important_features)
# %%
X2_df = X_df[features].pow(2.)
# %% [markdown]
# ## Model
# %%
def robust_logistic_regression_with_interactions(
*,
X: jax.Array,
X2: jax.Array,
X_interactions: jax.Array,
group: jax.Array,
nb_groups: int,
y: jax.Array | None = None):
nb_obs, nb_features = X.shape
assert nb_obs == group.shape[0] == X_interactions.shape[0]
# Prior for baselines.
a0 = numpyro.sample('_a0', dist.Normal(0., 1.))
# Prior for the coefficients of metric features.
a_sigma = numpyro.sample('_aSigma', dist.Gamma(1., 1.))
a = numpyro.sample(
'_a', dist.StudentT(1., 0., a_sigma).expand((nb_features, )))
# a = numpyro.sample(
# '_a', dist.Normal(0., 1.).expand((nb_features, )))
# Prior for the coefficients of the interactions between metric features.
nb_interactions = X_interactions.shape[1]
a_interaction_sigma = numpyro.sample('_aInteractionSigma', dist.Gamma(1., 1.))
a_interaction = numpyro.sample(
'_aInteraction', dist.StudentT(1., 0., a_interaction_sigma).expand((nb_interactions, )))
# Prior of the coefficients of the quadratic terms.
nb_quad_terms = X2.shape[1]
a_quad_sigma = numpyro.sample('_aQuadSigma', dist.Gamma(1., 1.))
a_quad = numpyro.sample(
'_aQuad', dist.StudentT(1., 0., a_quad_sigma).expand((nb_quad_terms, ))
)
# Prior for the group feature.
aG = numpyro.sample('_aG', dist.Normal(0., 1.).expand((nb_groups, )))
# Prior for guess term.
guess = numpyro.sample('guess', dist.Beta(1., 1.))
# Observations.
with numpyro.plate('obs', nb_obs) as idx:
prob = numpyro.deterministic(
'prob', expit(a0
+ jnp.dot(X[idx], a)
+ jnp.dot(X_interactions[idx], a_interaction)
+ jnp.dot(X2[idx], a_quad)
+ aG[group[idx]]))
guess_prob = numpyro.deterministic(
'prob_w_guess', guess * 0.5 + (1 - guess) * prob)
if y is not None:
numpyro.sample('y', dist.Bernoulli(guess_prob), obs=y[idx])
else:
numpyro.sample('y', dist.Bernoulli(guess_prob))
kernel = NUTS(robust_logistic_regression_with_interactions,
init_strategy=init_to_median)
mcmc = MCMC(kernel, num_warmup=1000, num_samples=10000, num_chains=2)
mcmc.run(
random.PRNGKey(0),
X=jnp.array(X_df.values),
X2=jnp.array(X2_df.values),
X_interactions=jnp.array(X_interactions_df.values),
y=jnp.array(y),
nb_groups=ej.cat.categories.size,
group=jnp.array(ej.cat.codes.values)
)
mcmc.print_summary()
# %%
# Make the prediction on the traininig data.
predictive = Predictive(robust_logistic_regression_with_interactions,
mcmc.get_samples(),
return_sites=['y', 'prob', 'prob_w_guess'])
predictions = predictive(
random.PRNGKey(1),
X=jnp.array(X_df.values),
X2=jnp.array(X2_df.values),
X_interactions=jnp.array(X_interactions_df.values),
nb_groups=ej.cat.categories.size,
group=jnp.array(ej.cat.codes.values)
)
# %%
y_probs = predictions['prob']
y_prob = jnp.median(y_probs, axis=0)
y_pred = np.asarray(jnp.where(y_prob > 0.5, 1, 0))
# Compute the scores.
f1 = f1_score(y, y_pred)
recall = recall_score(y, y_pred)
precision = precision_score(y, y_pred)
print(f'{f1=}, {recall=}, {precision=}')
# %%
def balanced_log_loss_jax(y_true):
y_true = jnp.asarray(y_true)
def log_loss_jax(logit):
prob = expit(logit)
nb_class_1 = jnp.sum(y_true, axis=1) + 1e-10
nb_class_0 = jnp.sum(1 - y_true, axis=1) + 1e-10
prob_0 = jnp.clip(1. - prob, 1e-8, 1. - 1e-8)[None, ...]
prob_1 = jnp.clip(prob, 1e-8, 1. - 1e-8)[None, ...]
return jnp.mean((-jnp.sum((1 - y_true) * jnp.log(prob_0), axis=1) / nb_class_0 -
jnp.sum(y_true * jnp.log(prob_1), axis=1) / nb_class_1) / 2.)
return log_loss_jax
def calculate_best_prob_prediction(y_preds: np.ndarray):
"""
Calculate the best probability prediction based on the above formula.
y_preds: numpy array of shape (nb_draws, nb_data_points).
"""
assert y_preds.ndim == 2, "Only accept 2d numpy array as input."
_, nb_data = y_preds.shape
print(y_preds.shape)
# Calculate number of classes for each draw.
nb_class_0 = np.sum(1 - y_preds, axis=1)
print(nb_class_0.shape)
nb_class_1 = np.sum(y_preds, axis=1)
best_probs = []
eps = 1e-15
for j in range(nb_data):
cj = np.sum(y_preds[:, j] / (nb_class_1 + eps))
cj_1 = np.sum((1 - y_preds[:, j]) / (nb_class_0 + eps))
prob = cj / (cj + cj_1)
best_probs.append(prob)
return np.asarray(best_probs)
# Using our own derivation.
best_probs = calculate_best_prob_prediction(predictions['y'])
our_log_loss = balanced_log_loss_jax(predictions['y'])(logit(best_probs))
print(f'{our_log_loss=}')
# results = jax_minimize(
# balanced_log_loss_jax(predictions['y']),
# logit(y_prob),
# method='BFGS',
# options=dict(maxiter=10000))
# %%
# print(f'{results.success=}, {results.fun=}, {results.status=}')
# %% [markdown]
# ## Submission
# %%
# Preprocess test data.
X_test_df = test_df.drop(columns=['Id', 'EJ'])
ej_test = test_df['EJ'].astype(ej.dtype)
X_test_df = pd.DataFrame(
preprocessing.transform(X_test_df),
columns=X_test_df.columns,
index=X_test_df.index)
X2_test_df = X_test_df[features].pow(2.)
# Interaction terms.
X_test_interactions_df = create_interaction_terms_between(
X_test_df, most_important_features + less_important_features)
# %%
# Make predictions.
predictions = predictive(
random.PRNGKey(1),
X=jnp.array(X_test_df.values),
X2=jnp.array(X2_test_df.values),
X_interactions=jnp.array(X_test_interactions_df.values),
nb_groups=ej.cat.categories.size,
group=jnp.array(ej_test.cat.codes.values)
)
# %%
# Instead of using median as our predictions,
# we're going to optimize the prediction probability
# such that it minimizes the balanced log loss.
# y_probs = predictions['prob']
# y_prob = np.asarray(jnp.median(y_probs, axis=0))
# results = jax_minimize(
# balanced_log_loss_jax(predictions['y']),
# logit(jnp.median(predictions['prob'], axis=0)),
# method='BFGS',
# options=dict(maxiter=100000))
# print(f'{results.success=}, {results.fun=}, {results.status=}')
# Optimimal y_prob.
# y_prob_optim = expit(results.x)
y_prob_optim = calculate_best_prob_prediction(predictions['y'])
our_log_loss = balanced_log_loss_jax(predictions['y'])(logit(y_prob_optim))
print(f'{our_log_loss=}')
# %%
# Create .csv submission file.
submission = pd.DataFrame({
'Id': test_df['Id'],
'class_0': 1. - y_prob_optim,
'class_1': y_prob_optim,
})
submission.to_csv('submission.csv', index=False)