Is MQBoost suitable for health insurance medical loss prediction? Tips for heavy-tailed claim data?

[vvvviii]

Hi @RektPunk,

I'm using MQBoost for health insurance medical loss prediction. Is this library suitable for this task? Also, could you share some tips for applying it to heavy-tailed medical claim data?

Thank you for your help!

[RektPunk]

Hi @vvvviii,

Thank you for your interest in MQBoost! I believe it is suitable for medical loss prediction.

While my primary background is in data science and financial analysis, MQBoost’s core mechanism—using an objective function with constraints to prevent quantile crossing—is a universal solution for maintaining logical consistency in uncertainty estimation. Even for volatile medical claims, the predicted quantiles will remain perfectly ordered. Careful hyper parameter tuning is essential though, especially for heavy-tailed data where finding the right balance between bias and variance is key.

Also, I’m excited to share that the formal paper detailing the MQBoost methodology is published in the Machine Learning journal: Monotone Composite Quantile Regression via Second-Order Gradient Boosting Framework. It will provide more in-depth technical details on the constrained optimization approach. Hope this helps! Let me know if you have any further questions.

Here is a minimal example tailored to your use case:

Click to expand the example code

import matplotlib.pyplot as plt
import numpy as np
from mqboost import MQDataset, MQRegressor

np.random.seed(42)
n_samples = 100
x = np.linspace(0, 10, n_samples)
y = np.exp(np.random.normal(0, 1, n_samples))

alphas = [0.01, 0.05, 0.1, 0.5, 0.9, 0.95, 0.99]
lgb_params = {
    "max_depth": 10,
    "num_leaves": 50,
    "learning_rate": 0.3,
    "boosting_type": "gbdt",
}
mq_regressor = MQRegressor(params=lgb_params, objective="approx", model="lightgbm")
train_dataset = MQDataset(
    data=x.reshape(-1, 1), label=y, alphas=alphas, model="lightgbm"
)
mq_regressor.fit(dataset=train_dataset)

preds = mq_regressor.predict(train_dataset)

plt.figure(figsize=(10, 6))
plt.scatter(x, y, color="black", s=15, alpha=0.5, label="Actual Claims")
colors = plt.cm.Blues(np.linspace(0.4, 1, len(alphas)))
for i, alpha in enumerate(alphas):
    plt.plot(
        x,
        preds[i, :],
        color=colors[i],
        label=f"q_{alpha}",
        linewidth=2 if alpha == 0.5 else 1,
    )
plt.fill_between(x, preds[0, :], preds[-1, :], color="blue", alpha=0.1)
plt.title("MQBoost: Medical Loss Prediction")
plt.legend(loc="upper left", bbox_to_anchor=(1, 1))
plt.grid(True, which="both", alpha=0.3)
plt.tight_layout()
plt.show()