对样本外数据使用贝叶斯 PyMC 线性模型

Question

我正在尝试使用贝叶斯推理技术将线性模型拟合到数据。为此，我想到了使用 PyMC。当然，在训练模型后，我想在新数据上测试其性能，这就是问题发生的地方。我似乎无法设置新的数据集。大家有经验吗

显示错误的示例脚本：

import numpy as np
import pymc as pm
import arviz as az
import matplotlib.pyplot as plt

def run_model():
    # Generate synthetic data
    np.random.seed(42)
    x = np.linspace(0, 10, 100)
    a_true = 2.5  # True slope
    b_true = 1.0  # True intercept
    y_true = a_true * x + b_true
    y = y_true + np.random.normal(0, 1, size=x.size)  # Add some noise

    # Split into training and test sets
    x_train, x_test = x[:80], x[80:]
    y_train, y_test = y[:80], y[80:]

    # Define and fit the model
    with pm.Model() as linear_model:
        # Define x as a pm.Data variable to allow updating with pm.set_data
        x_shared = pm.Data("x", x_train)

        # Priors for slope and intercept
        a = pm.Normal("a", mu=0, sigma=10)
        b = pm.Normal("b", mu=0, sigma=10)
        sigma = pm.HalfNormal("sigma", sigma=1)

        # Expected value of y
        mu = a * x_shared + b

        # Likelihood
        y_obs = pm.Normal("y_obs", mu=mu, sigma=sigma, observed=y_train)

        # Sample from the posterior
        trace = pm.sample(1000, tune=1000, return_inferencedata=True, chains=1)

    # Predict on training data
    with linear_model:
        pm.set_data({"x": x_train})  # Update data to training
        post_pred_train = pm.sample_posterior_predictive(trace)

    # Predict on test data
    with linear_model:
        pm.set_data({"x": x_test})  # Update data to testing
        post_pred_test = pm.sample_posterior_predictive(trace)

    # Plot results
    plt.figure(figsize=(10, 5))

    # Plot training data
    plt.scatter(x_train, y_train, c="blue", label="Training data")
    plt.plot(x_train, y_true[:80], "k--", label="True function")

    # Plot posterior predictive for training data
    plt.plot(
        x_train,
        post_pred_train["y_obs"].mean(axis=0),
        label="Posterior predictive (train)",
        color="red",
    )

    # Plot test data
    plt.scatter(x_test, y_test, c="green", label="Test data")

    # Plot posterior predictive for test data
    plt.plot(
        x_test,
        post_pred_test["y_obs"].mean(axis=0),
        label="Posterior predictive (test)",
        color="orange",
    )

    plt.legend()
    plt.xlabel("x")
    plt.ylabel("y")
    plt.title("Bayesian Linear Regression with PyMC")
    plt.show()

    # Summary of the model parameters
    print(az.summary(trace, var_names=["a", "b", "sigma"]))


# Only execute if run as the main module
if __name__ == '__main__':
    run_model()

ValueError：形状不匹配：对象无法广播到单个形状。 形状 (80,) 的 arg 0 与形状 (20,) 的 arg 1 之间不匹配。 应用导致错误的节点：normal_rv{"(),()->()"}(RNG(), [80], Composite{((i0 * i1) + i2)}.0, ExpandDims{axis= 0}.0) 拓扑排序指数：4 输入类型：[RandomGeneratorType、TensorType(int64, shape=(1,))、TensorType(float64, shape=(None,))、TensorType(float64, shape=(1,))] 输入形状：['无形状', (1,), (20,), (1,)] 输入步幅：['无步幅', (8,), (8,), (8,)] 输入值：[Generator(PCG64) at 0x1F23323B5A0, array([80], dtype=int64), 'not shown', array([0.97974278])] 输出客户端：[[output1], [output0]]

Answer 1

我不知道足够的数学来完全理解你的问题，但这些行似乎很可疑：

    x = np.linspace(0, 10, 100)

    [...]

    x_train, x_test = x[:80], x[80:]
    y_train, y_test = y[:80], y[80:]

这是唯一可能出现尺寸为 20 的错误的地方。