param_dict = {
    "eta":                      ["float", {"low": 1e-5,   "high": 1,     "log": True}],
    "max_depth":                ["int",   {"low": 1,      "high": 10,    "log": False}],
    "num_leaves":               ["int",   {"low": 255,    "high": 255,   "log": False}],  # set to constant for this example
    "min_data_in_leaf":         ["int",   {"low": 20,     "high": 20,    "log": False}],  # set to constant for this example
    "min_gain_to_split":        ["float", {"low": 1e-8,   "high": 40,    "log": False}],
    "min_sum_hessian_in_leaf":  ["float", {"low": 1e-8,   "high": 500,   "log": True}],
    "subsample":                ["float", {"low": 0.2,    "high": 1.0,   "log": False}],
    "feature_fraction":         ["float", {"low": 0.2,    "high": 1.0,   "log": False}],
    "boosting":                 ["categorical", ["gbdt"]],
}

np.random.seed(123)
opt_param = lgblss.hyper_opt(param_dict,
                             dtrain,
                             num_boost_round=100,        # Number of boosting iterations.
                             nfold=5,                    # Number of cv-folds.
                             early_stopping_rounds=20,   # Number of early-stopping rounds
                             max_minutes=10,             # Time budget in minutes, i.e., stop study after the given number of minutes.
                             n_trials=30 ,               # The number of trials. If this argument is set to None, there is no limitation on the number of trials.
                             silence=True,               # Controls the verbosity of the trail, i.e., user can silence the outputs of the trail.
                             seed=123,                   # Seed used to generate cv-folds.
                             hp_seed=123                 # Seed for random number generator used in the Bayesian hyperparameter search.
                            )

pred_samples.head()

pred_quantiles.head()

pred_params.head()

# Partial Dependence Plot of how x_true acts on variance
lgblss.plot(X_test,
            parameter="scale",
            feature="x_true",
            plot_type="Partial_Dependence")

# Feature Importance of scale parameter
lgblss.plot(X_test,
            parameter="scale",
            plot_type="Feature_Importance")

np.random.seed(123)

###
# Actual Quantiles
###
q1 = norm.ppf(quant_sel[0], loc = 10, scale = 1 + 4*((0.3 < test["x_true"].values) & (test["x_true"].values < 0.5)) + 2*(test["x_true"].values > 0.7))
q2 = norm.ppf(quant_sel[1], loc = 10, scale = 1 + 4*((0.3 < test["x_true"].values) & (test["x_true"].values < 0.5)) + 2*(test["x_true"].values > 0.7))
test["quant"] = np.where(test["y"].values < q1, 0, np.where(test["y"].values < q2, 1, 2))
test["alpha"] = np.where(test["y"].values <= q1, 1, np.where(test["y"].values >= q2, 1, 0))
df_quantiles = test[test["alpha"] == 1]

# Lower Bound
yl = list(set(q1))
yl.sort()
yl = [yl[2],yl[0],yl[2],yl[1],yl[1]]
sfunl = pd.DataFrame({"x_true":[0, 0.3, 0.5, 0.7, 1], "y":yl})

# Upper Bound
yu = list(set(q2))
yu.sort()
yu = [yu[0],yu[2],yu[0],yu[1],yu[1]]
sfunu = pd.DataFrame({"x_true":[0, 0.3, 0.5, 0.7, 1], "y":yu})

###
# Predicted Quantiles
###
test["lb"] = pred_quantiles.iloc[:,0]
test["ub"] = pred_quantiles.iloc[:,1]

###
# Plot
###
(ggplot(test,
        aes("x_true",
            "y")) + 
 geom_point(alpha = 0.2, color = "black", size = 2) + 
 theme_bw(base_size=15) +
 theme(legend_position="none",
       plot_title = element_text(hjust = 0.5),
       plot_subtitle = element_text(hjust = 0.5)) +
 labs(title = "LightGBMLSS Regression - Simulated Data Example",
      subtitle = "Comparison of Actual (black) vs. Predicted Quantiles (blue)",
      x="x")  + 
 geom_line(aes("x_true",
               "ub"),
           size = 1,
           color = "blue", 
           alpha = 0.7) + 
 geom_line(aes("x_true",
               "lb"),
           size = 1,
           color = "blue", 
           alpha = 0.7) + 
 geom_point(df_quantiles,
            aes("x_true",
                "y"), 
            color = "red", 
            alpha = 0.7,
            size = 2) + 
 geom_step(sfunl,
           aes("x_true",
               "y"), 
           size = 1, 
           linetype = "dashed")  + 
 geom_step(sfunu,
           aes("x_true",
               "y"), 
           size = 1, 
           linetype = "dashed") 
)

pred_params["x_true"] = X_test["x_true"].values
dist_params = list(lgblss.dist.param_dict.keys())

# Data with actual values
plot_df_actual = pd.melt(test[["x_true"] + dist_params],
                         id_vars="x_true",
                         value_vars=dist_params)
plot_df_actual["type"] = "TRUE"

# Data with predicted values
plot_df_predt = pd.melt(pred_params[["x_true"] + dist_params],
                        id_vars="x_true",
                        value_vars=dist_params)
plot_df_predt["type"] = "PREDICT"

plot_df = pd.concat([plot_df_predt, plot_df_actual])

plot_df["variable"] = plot_df.variable.str.upper()
plot_df["type"] = pd.Categorical(plot_df["type"], categories = ["PREDICT", "TRUE"])

(ggplot(plot_df,
        aes(x="x_true",
            y="value",
            color="type")) +
 geom_line(size=1.1) + 
 facet_wrap("variable",
            scales="free") + 
 labs(title="Parameters of univariate Gaussian predicted with LightGBMLSS",
      x="",
      y="") + 
 theme_bw(base_size=15) + 
 theme(legend_position="bottom",
       plot_title = element_text(hjust = 0.5),
       legend_title = element_blank())
)

y_pred = []

n_examples = 9

for i in range(n_examples):    
    y_samples = pd.DataFrame(pred_samples.values[i,:].reshape(-1,1), columns=["PREDICT_DENSITY"])
    y_samples["PREDICT_POINT"] = y_samples["PREDICT_DENSITY"].mean()
    y_samples["PREDICT_Q05"] = y_samples["PREDICT_DENSITY"].quantile(q=quant_sel[0])
    y_samples["PREDICT_Q95"] = y_samples["PREDICT_DENSITY"].quantile(q=quant_sel[1])
    y_samples["ACTUAL"] = y_test[i]
    y_samples["obs"]= f"Obervation {i+1}"
    y_pred.append(y_samples)
    
pred_df = pd.melt(pd.concat(y_pred, axis=0), id_vars="obs")
pred_df["obs"] = pd.Categorical(pred_df["obs"], categories=[f"Obervation {i+1}" for i in range(n_examples)])
df_actual, df_pred_dens, df_pred_point, df_q05, df_q95 = [x for _, x in pred_df.groupby("variable")]

plot_pred = (
    ggplot(pred_df,
           aes(color="variable")) + 
    stat_density(df_pred_dens,
                 aes(x="value"),
                 size=1.1) + 
    geom_point(df_pred_point,
               aes(x="value",
                   y=0),
               size=1.4) + 
    geom_point(df_actual,
               aes(x="value",
                   y=0),
               size=1.4) + 
    geom_vline(df_q05, 
               aes(xintercept="value",
                   fill="variable",
                   color="variable"),
               linetype="dashed",
               size=1.1) + 
    geom_vline(df_q95, 
               aes(xintercept="value",
                   fill="variable",
                   color="variable"),
               linetype="dashed",
               size=1.1) + 
    facet_wrap("obs",
               scales="free",
               ncol=3) + 
    labs(title="Predicted vs. Actual \n",
         x = "") + 
    theme_bw(base_size=15) +
    scale_fill_brewer(type="qual", palette="Dark2") + 
    theme(legend_position="bottom",
          plot_title = element_text(hjust = 0.5),
          legend_title = element_blank()
         )
)

print(plot_pred)