#!/usr/bin/env python
# coding: utf-8

# # Parametrising a distribution with a neural network
# 
# Parametrization of a [PyTorch](https://pytorch.org/) distribution with a neural network, for the purpose of uncertainty quantification.
# 
# We'll consider the [OLS Regression Challenge](https://data.world/nrippner/ols-regression-challenge), which aims at predicting cancer mortality rates for US counties.
# 
# ## Data Dictionary
# 
# * **TARGET_deathRate**: Dependent variable. Mean per capita (100,000) cancer mortalities (a)
# * **avgAnnCount**: Mean number of reported cases of cancer diagnosed annually (a)
# * **avgDeathsPerYear**: Mean number of reported mortalities due to cancer (a)
# * **incidenceRate**: Mean per capita (100,000) cancer diagoses (a)
# * **medianIncome**: Median income per county (b)
# * **popEst2015**: Population of county (b)
# * **povertyPercent**: Percent of populace in poverty (b)
# * **studyPerCap**: Per capita number of cancer-related clinical trials per county (a)
# * **binnedInc**: Median income per capita binned by decile (b)
# * **MedianAge**: Median age of county residents (b)
# * **MedianAgeMale**: Median age of male county residents (b)
# * **MedianAgeFemale**: Median age of female county residents (b)
# * **Geography**: County name (b)
# * **AvgHouseholdSize**: Mean household size of county (b)
# * **PercentMarried**: Percent of county residents who are married (b)
# * **PctNoHS18_24**: Percent of county residents ages 18-24 highest education attained: less than high school (b)
# * **PctHS18_24**: Percent of county residents ages 18-24 highest education attained: high school diploma (b)
# * **PctSomeCol18_24**: Percent of county residents ages 18-24 highest education attained: some college (b)
# * **PctBachDeg18_24**: Percent of county residents ages 18-24 highest education attained: bachelor's degree (b)
# * **PctHS25_Over**: Percent of county residents ages 25 and over highest education attained: high school diploma (b)
# * **PctBachDeg25_Over**: Percent of county residents ages 25 and over highest education attained: bachelor's degree (b)
# * **PctEmployed16_Over**: Percent of county residents ages 16 and over employed (b)
# * **PctUnemployed16_Over**: Percent of county residents ages 16 and over unemployed (b)
# * **PctPrivateCoverage**: Percent of county residents with private health coverage (b)
# * **PctPrivateCoverageAlone**: Percent of county residents with private health coverage alone (no public assistance) (b)
# * **PctEmpPrivCoverage**: Percent of county residents with employee-provided private health coverage (b)
# * **PctPublicCoverage**: Percent of county residents with government-provided health coverage (b)
# * **PctPubliceCoverageAlone**: Percent of county residents with government-provided health coverage alone (b)
# * **PctWhite**: Percent of county residents who identify as White (b)
# * **PctBlack**: Percent of county residents who identify as Black (b)
# * **PctAsian**: Percent of county residents who identify as Asian (b)
# * **PctOtherRace**: Percent of county residents who identify in a category which is not White, Black, or Asian (b)
# * **PctMarriedHouseholds**: Percent of married households (b)
# * **BirthRate**: Number of live births relative to number of women in county (b)
# 
# Notes:
# * (a): years 2010-2016
# * (b): 2013 Census Estimates

# In[94]:


import os
from os.path import join

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import torch
import torch.nn.functional as F
from sklearn.metrics import r2_score
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from scipy.stats import binned_statistic
import statsmodels.api as sm

cwd = os.getcwd()
if cwd.endswith('notebook'):
    os.chdir('..')
    cwd = os.getcwd()


# In[267]:


sns.set(palette='colorblind', font_scale=1.3)
palette = sns.color_palette()


# In[3]:


seed = 456
np.random.seed(seed);
torch.manual_seed(seed);
torch.set_default_dtype(torch.float64)


# ## Dataset

# In[4]:


df = pd.read_csv(join(cwd, 'data/cancer_reg.csv'))
df.head()


# In[5]:


df.describe()


# ### Plot distribution of target variable

# In[6]:


_, ax = plt.subplots(1, 1, figsize=(10, 5))
df['TARGET_deathRate'].hist(bins=50, ax=ax);
ax.set_title('Distribution of cancer death rate per 100,000 people');
ax.set_xlabel('Cancer death rate in county (per 100,000 people)');
ax.set_ylabel('Count');


# ### Define feature & target variables

# In[7]:


target = 'TARGET_deathRate'
features = [
    col for col in df.columns
    if col not in [
        target, 
        'Geography',                # Label describing the county - each row has a different one
        'binnedInc',                # Redundant with median income?
        'PctSomeCol18_24',          # contains null values - ignoring for now
        'PctEmployed16_Over',       # contains null values - ignoring for now
        'PctPrivateCoverageAlone',  # contains null values - ignoring for now
    ]
]
print(len(features), 'features')


# In[8]:


x = df[features].values
y = df[[target]].values
print(x.shape, y.shape)


# ## Define model

# In[9]:


class DeepNormalModel(torch.nn.Module):
    def __init__(
        self, 
        n_inputs,
        n_hidden,
        x_scaler, 
        y_scaler,
    ):
        super().__init__()
        
        self.x_scaler = x_scaler
        self.y_scaler = y_scaler
        self.jitter = 1e-6
        
        self.shared = torch.nn.Linear(n_inputs, n_hidden)
        
        self.mean_hidden = torch.nn.Linear(n_hidden, n_hidden)
        self.mean_linear = torch.nn.Linear(n_hidden, 1)
        
        self.std_hidden = torch.nn.Linear(n_hidden, n_hidden)
        self.std_linear = torch.nn.Linear(n_hidden, 1)
        
        self.dropout = torch.nn.Dropout()
        
    def forward(self, x):
        # Normalization
        shared = self.x_scaler(x)
        
        # Shared layer
        shared = self.shared(shared)
        shared = F.relu(shared)
        shared = self.dropout(shared)
        
        # Parametrization of the mean
        mean_hidden = self.mean_hidden(shared)
        mean_hidden = F.relu(mean_hidden)
        mean_hidden = self.dropout(mean_hidden)
        mean = self.mean_linear(mean_hidden)
        
        # Parametrization fo the standard deviation
        std_hidden = self.std_hidden(shared)
        std_hidden = F.relu(std_hidden)
        std_hidden = self.dropout(std_hidden)
        std = F.softplus(self.std_linear(std_hidden)) + self.jitter
        
        return torch.distributions.Normal(mean, std)


# In[10]:


def compute_loss(model, x, y, kl_reg=0.1):
    y_scaled = model.y_scaler(y)
    y_hat = model(x)
    neg_log_likelihood = -y_hat.log_prob(y_scaled)
    return torch.mean(neg_log_likelihood)


def compute_rmse(model, x_test, y_test):
    model.eval()
    y_hat = model(x_test)
    pred = model.y_scaler.inverse_transform(y_hat.mean)
    return torch.sqrt(torch.mean((pred - y_test)**2))


def train_one_step(model, optimizer, x_batch, y_batch):
    model.train()
    optimizer.zero_grad()
    loss = compute_loss(model, x_batch, y_batch)
    loss.backward()
    optimizer.step()
    return loss


# In[11]:


def train(model, optimizer, x_train, x_val, y_train, y_val, n_epochs, batch_size, scheduler=None, print_every=10):
    train_losses, val_losses = [], []
    for epoch in range(n_epochs):
        batch_indices = sample_batch_indices(x_train, y_train, batch_size)
        
        batch_losses_t, batch_losses_v, batch_rmse_v = [], [], []
        for batch_ix in batch_indices:
            b_train_loss = train_one_step(model, optimizer, x_train[batch_ix], y_train[batch_ix])

            model.eval()
            b_val_loss = compute_loss(model, x_val, y_val)
            b_val_rmse = compute_rmse(model, x_val, y_val)

            batch_losses_t.append(b_train_loss.detach().numpy())
            batch_losses_v.append(b_val_loss.detach().numpy())
            batch_rmse_v.append(b_val_rmse.detach().numpy())
            
        if scheduler is not None:
            scheduler.step()
            
        train_loss = np.mean(batch_losses_t)
        val_loss = np.mean(batch_losses_v)
        val_rmse = np.mean(batch_rmse_v)
        
        train_losses.append(train_loss)
        val_losses.append(val_loss)

        if epoch == 0 or (epoch + 1) % print_every == 0:
            print(f'Epoch {epoch+1} | Validation loss = {val_loss:.4f} | Validation RMSE = {val_rmse:.4f}')
        
    _, ax = plt.subplots(1, 1, figsize=(12, 6))
    ax.plot(range(1, n_epochs + 1), train_losses, label='Train loss')
    ax.plot(range(1, n_epochs + 1), val_losses, label='Validation loss')
    ax.set_xlabel('Epoch')
    ax.set_ylabel('Loss')
    ax.set_title('Training Overview')
    ax.legend()
    
    return train_losses, val_losses


def sample_batch_indices(x, y, batch_size, rs=None):
    if rs is None:
        rs = np.random.RandomState()
    
    train_ix = np.arange(len(x))
    rs.shuffle(train_ix)
    
    n_batches = int(np.ceil(len(x) / batch_size))
    
    batch_indices = []
    for i in range(n_batches):
        start = i * batch_size
        end = start + batch_size
        batch_indices.append(
            train_ix[start:end].tolist()
        )

    return batch_indices


# In[12]:


class StandardScaler(object):
    """
    Standardize data by removing the mean and scaling to unit variance.
    """
    def __init__(self):
        self.mean = None
        self.scale = None

    def fit(self, sample):
        self.mean = sample.mean(0, keepdim=True)
        self.scale = sample.std(0, unbiased=False, keepdim=True)
        return self

    def __call__(self, sample):
        return self.transform(sample)
    
    def transform(self, sample):
        return (sample - self.mean) / self.scale

    def inverse_transform(self, sample):
        return sample * self.scale + self.mean


# ## Split between training and validation sets

# In[13]:


def compute_train_test_split(x, y, test_size):
    x_train, x_test, y_train, y_test, train_ix, test_ix = train_test_split(
        x, 
        y, 
        list(range(len(x))),
        test_size=test_size,
    )
    return (
        torch.from_numpy(x_train),
        torch.from_numpy(x_test),
        torch.from_numpy(y_train),
        torch.from_numpy(y_test),
        train_ix,
        test_ix,
    )


# In[14]:


x_train, x_val, y_train, y_val, train_ix, test_ix = compute_train_test_split(x, y, test_size=0.2)

print(x_train.shape, y_train.shape, len(train_ix))
print(x_val.shape, y_val.shape, len(test_ix))


# ## Train model

# In[15]:


x_scaler = StandardScaler().fit(torch.from_numpy(x))
y_scaler = StandardScaler().fit(torch.from_numpy(y))


# In[16]:


get_ipython().run_cell_magic('time', '', "\nlearning_rate = 1e-3\nmomentum = 0.9\nweight_decay = 1e-5\n\nn_epochs = 300\nbatch_size = 64\nprint_every = 50\n\nn_hidden = 100\n\nmodel = DeepNormalModel(\n    n_inputs=x.shape[1],\n    n_hidden=n_hidden,\n    x_scaler=x_scaler, \n    y_scaler=y_scaler,\n)\n\npytorch_total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\nprint(f'{pytorch_total_params:,} trainable parameters')\nprint()\n\noptimizer = torch.optim.SGD(\n    model.parameters(), \n    lr=learning_rate, \n    momentum=momentum, \n    nesterov=True,\n    weight_decay=weight_decay,\n)\nscheduler = None\n\ntrain_losses, val_losses = train(\n    model, \n    optimizer, \n    x_train, \n    x_val, \n    y_train, \n    y_val, \n    n_epochs=n_epochs, \n    batch_size=batch_size, \n    scheduler=scheduler, \n    print_every=print_every,\n)\n")


# ### Validation

# In[17]:


y_dist = model(x_val)
y_hat = model.y_scaler.inverse_transform(y_dist.mean)


# In[18]:


val_rmse = float(compute_rmse(model, x_val, y_val).detach().numpy())
print(f'Validation RMSE = {val_rmse:.2f}')


# In[19]:


val_r2 = r2_score(
    y_val.detach().numpy().flatten(),
    y_hat.detach().numpy().flatten(),
)
print(f'Validation $R^2$ = {val_r2:.2f}')


# In[20]:


def plot_results(y_true, y_pred):
    f, ax = plt.subplots(1, 1, figsize=(7, 7))
    palette = sns.color_palette()
    
    min_value = min(np.amin(y_true), np.amin(y_pred))
    max_value = max(np.amax(y_true), np.amax(y_pred))
    y_mid = np.linspace(min_value, max_value)
    
    ax.plot(y_mid, y_mid, '--', color=palette[1])
    ax.scatter(y_true, y_pred, color=palette[0], alpha=0.5);
    
    return f, ax


# In[21]:


f, ax = plot_results(
    y_val.detach().numpy().flatten(),
    y_hat.detach().numpy().flatten(),
);

ax.text(225, 95, f'$R^2 = {val_r2:.2f}$')
ax.text(225, 80, f'$RMSE = {val_rmse:.2f}$')
    
ax.set_xlabel('Actuals');
ax.set_ylabel('Predictions');
ax.set_title('Regression results on validation set');


# ## Uncertainty

# In[22]:


def make_predictions(model, x):
    dist = model(x)
    
    inv_tr = model.y_scaler.inverse_transform
    y_hat = inv_tr(dist.mean)
    
    # Recover standard deviation's original scale
    std = inv_tr(dist.mean + dist.stddev) - y_hat
    
    return y_hat, std


# In[23]:


y_hat, std = make_predictions(model, x_val)


# In[337]:


f, axes = plt.subplots(1, 2, figsize=(18, 6))
ax1, ax2 = axes

ax1.hist(y_hat.detach().numpy().flatten(), bins=50);
ax2.hist(std.detach().numpy().flatten(), bins=50, color=palette[1]);

ax1.set_xlabel('Cancer mortality rate (mean)');
ax1.set_ylabel('Instance count');
ax1.set_title('Distribution of mean $\mu$ on validation set');

ax2.set_xlabel('Cancer mortality rate (stddev)');
ax2.set_ylabel('Instance count');
ax2.set_title('Distribution of stddev $\sigma$ on validation set');


# In[240]:


low_ix = [i for i, v in enumerate(y_hat.detach().numpy().flatten()) if float(v) < 140][0]
average_ix = [i for i, v in enumerate(y_hat.detach().numpy().flatten()) if 170 < float(v) < 190][0]
high_ix = [i for i, v in enumerate(y_hat.detach().numpy().flatten()) if float(v) > 220][0]


# In[265]:


def plot_normal_distributions(y_hat, std, indices):
    f, ax = plt.subplots(1, 1, figsize=(12, 6))
    
    normal_fn = lambda z, m, s: (1/(s * np.sqrt(2*np.pi))) * np.exp(-0.5*((z - m) / s)**2)
    
    x = np.linspace(80, 300, 300)
    
    for ix in indices:
        mu = y_hat.detach().numpy().flatten()[ix]
        sigma = std.detach().numpy().flatten()[ix]
        
        ax.plot(x, normal_fn(x, mu, sigma), label=rf'$\mu = {mu:.0f}$, $\sigma = {sigma:.1f}$')
    
    ax.set_xlabel('Cancer mortality rate ($y$)');
    ax.set_ylabel(r'$P(y \mid \mu, \sigma)$');
    ax.set_title('PDF of three instances of the validation set');
    ax.legend(loc='upper left');
    
    return f, ax


# In[338]:


f, ax = plot_normal_distributions(y_hat, std, [low_ix, average_ix, high_ix])


# ### Plot absolute error against uncertainty

# In[291]:


def plot_absolute_error_vs_uncertainty(y_val, y_hat, std):
    absolute_errors = 100 * (torch.abs(y_hat - y_val) / y_val).detach().numpy().flatten()
    stds = std.detach().numpy().flatten()
    
    a = absolute_errors
    b = stds
    alpha = 0.5

    f, ax = plt.subplots(1, 1, figsize=(7, 7))
    ax.scatter(a, b, alpha=alpha)
    
    X = a.reshape((-1, 1))
    y = b
    linreg = LinearRegression().fit(X, y)
    r2 = linreg.score(X, y)
    corr = np.corrcoef(a, b)[0, 1]
    print(f'R2: {r2:.2f}')
    print(f'Correlation: {corr:.2f}')
    
    y_fit = linreg.coef_[0] * a + linreg.intercept_
    
    ax.plot(a, y_fit, '-', color=palette[1], alpha=0.5)

    ax.text(56, 7.5, f'Corr  =  {corr:.2f}')
    
    return f, ax


# In[292]:


f, ax = plot_absolute_error_vs_uncertainty(y_val, y_hat, std)

ax.set_title('Error vs uncertainty');
ax.set_xlabel('Absolute error / actual (%)');
ax.set_ylabel('Standard deviation');


# ### Uncertainty on an input not yet seen & very different from the rest of the dataset
# 
# We'll consider an input made of the maximum of all features.

# In[28]:


max_input_np = np.zeros((1, x_val.shape[1]))
for i in range(x_val.shape[1]):
    max_input_np[0, i] = torch.amax(x_val[:, i]) * 2

max_input = torch.from_numpy(max_input_np)
max_input.shape


# In[167]:


r_y_hat, r_first_order_std = make_predictions(model, max_input)

print(f'First order uncertainty: {float((r_first_order_std / r_y_hat).detach().numpy()):.2f}')


# ## Unexpectedness
# 
# An instance's expectedness can be measured by its average feature quantile minus the median 0.5.
# 
# We can then estimate the relation between uncertainty and expectedness.

# In[30]:


def set_feature_quantile(df, features):
    series = []
    quantiles = np.arange(0., 1., 0.01)
    for q in quantiles:
        series.append(df[features].quantile(q))
        
    def apply_quantile(row):
        v = np.zeros((len(features)))
        
        for i, f in enumerate(features):
            value = row[f]
            for j, q in enumerate(quantiles):
                if value <= series[j][f]:
                    v[i] = q
                    break
        
        return v.mean()
    
    df['quantile'] = df.apply(apply_quantile, axis=1)


# In[31]:


set_feature_quantile(df, features)


# In[32]:


df['quantile'].hist(bins=20);


# In[331]:


def plot_expectedness_vs_uncertainty(df, test_ix, y_val, std):
    quantiles = df['quantile'].iloc[test_ix].values
    expectedness = 100 * np.abs(quantiles - 0.5)
    stds = std.detach().numpy().flatten()
    
    f, ax = plt.subplots(1, 1, figsize=(7, 7))
    ax.scatter(expectedness, stds, alpha=0.5)
    
    X = sm.add_constant(expectedness.reshape((-1, 1)))
    y = stds.reshape((-1, 1))
    
    linreg = sm.OLS(y, X).fit()
    y_fit = linreg.predict(X).flatten()
    
    corr = np.corrcoef(expectedness, stds)[0, 1]
    print(f'Correlation: {corr:.2f}')
    
    print(linreg.summary())
    
    ax.plot(expectedness, y_fit, '-', color=palette[1], alpha=0.5)
    
    ax.text(27, 7.5, f'Corr  =  {corr:.2f}')
    
    return f, ax


# In[332]:


f, ax = plot_expectedness_vs_uncertainty(df, test_ix, y_val, std)

ax.set_xlabel('Unexpectedness (%)')
ax.set_ylabel('Standard deviation')
ax.set_title('Unexpectedness vs uncertainty');


# In[ ]: