Upload stream.py

stream.py

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+import numpy as np
+import jax.numpy as jnp
+import matplotlib.pyplot as plt
+import numpyro
+import numpyro.distributions as dist
+from numpyro.infer import MCMC, NUTS
+from sklearn.datasets import make_regression
+from jax import random
+import streamlit as st
+
+
+# Define the model
+def linear_regression(X, y, alpha_prior, beta_prior, sigma_prior):
+    alpha = numpyro.sample('alpha', alpha_prior)
+    beta = numpyro.sample('beta', beta_prior)
+    sigma = numpyro.sample('sigma', sigma_prior)
+    mean = alpha + beta * X
+    numpyro.sample('obs', dist.Normal(mean, sigma), obs=y)
+
+
+def run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior):
+    # Run MCMC
+    rng_key = random.PRNGKey(0)
+    nuts_kernel = NUTS(linear_regression)
+    mcmc = MCMC(nuts_kernel, num_warmup=100, num_samples=600)
+    mcmc.run(rng_key, jnp.array(X), jnp.array(y), alpha_prior=alpha_prior, beta_prior=beta_prior, sigma_prior=sigma_prior)
+
+    mcmc.print_summary()
+
+    # Get posterior samples
+    samples = mcmc.get_samples()
+
+    # Plot the results
+    fig, ax = plt.subplots(figsize=(8, 6))
+    ax.scatter(X, y, color='blue', alpha=0.5, label='data')
+    light_color = (1.0, 0.5, 0.5, 0.7)
+    for i in range(500):
+        alpha_i = samples['alpha'][i]
+        beta_i = samples['beta'][i]
+        ax.plot(X, alpha_i + beta_i * X, color=light_color)
+    ax.plot(X, np.mean(samples['alpha']) + np.mean(samples['beta']) * X, color='red', label='mean')
+    ax.legend(loc='upper left')
+    st.pyplot(fig)
+
+
+# User Input
+st.write("# Bayesian Linear Regression with numpyro")
+alpha_prior_option = st.selectbox("Choose an option for alpha prior:", ["Normal", "Laplace", "Cauchy"])
+beta_prior_option = st.selectbox("Choose an option for beta prior:", ["Normal", "Laplace", "Cauchy"])
+sigma_prior_option = st.selectbox("Choose an option for sigma prior:", ["HalfNormal", "HalfCauchy"])
+
+if st.button("Run Regression"):
+    alpha_prior = None
+    beta_prior = None
+    sigma_prior = None
+    
+    if alpha_prior_option == "Normal":
+        alpha_loc = st.slider("Select a mean value for alpha", -10.0, 10.0, 0.0, 0.1)
+        alpha_scale = st.slider("Select a standard deviation value for alpha", 0.0, 10.0, 1.0, 0.1)
+        alpha_prior = dist.Normal(alpha_loc, alpha_scale)
+    elif alpha_prior_option == "Laplace":
+        alpha_loc = st.slider("Select a mean value for alpha", -10.0, 10.0, 0.0, 0.1)
+        alpha_scale = st.slider("Select a scale value for alpha", 0.0, 10.0, 1.0, 0.1)
+        alpha_prior = dist.Laplace(alpha_loc, alpha_scale)
+    elif alpha_prior_option == "Cauchy":
+        alpha_loc = st.slider("Select a location value for alpha", -10.0, 10.0, 0.0, 0.1)
+        alpha_scale = st.slider("Select a scale value for alpha", 0.0, 10.0, 1.0, 0.1)
+        alpha_prior = dist.Cauchy(alpha_loc, alpha_scale)
+
+    if beta_prior_option == "Normal":
+        beta_loc = st.slider("Select a mean value for beta", -10.0, 10.0, 0.0, 0.1)
+        beta_scale = st.slider("Select a standard deviation value for beta", 0.0, 10.0, 1.0, 0.1)
+        beta_prior = dist.Normal(beta_loc, beta_scale)
+    elif beta_prior_option == "Laplace":
+        beta_loc = st.slider("Select a mean value for beta", -10.0, 10.0, 0.0, 0.1)
+        beta_scale = st.slider("Select a scale value for beta", 0.0, 10.0, 1.0, 0.1)
+        beta_prior = dist.Laplace(beta_loc, beta_scale)
+    elif beta_prior_option == "Cauchy":
+        beta_loc = st.slider("Select a location value for beta", -10.0, 10.0, 0.0, 0.1)
+        beta_scale = st.slider("Select a scale value for beta", 0.0, 10.0, 1.0, 0.1)
+        beta_prior = dist.Cauchy(beta_loc, beta_scale)
+
+    if sigma_prior_option == "HalfNormal":
+        sigma_scale = st.slider("Select a scale value for sigma", 0.0, 10.0, 1.0, 0.1)
+        sigma_prior = dist.HalfNormal(sigma_scale)
+    elif sigma_prior_option == "HalfCauchy":
+        sigma_scale = st.slider("Select a scale value for sigma", 0.0, 10.0, 1.0, 0.1)
+        sigma_prior = dist.HalfCauchy(sigma_scale)
+
+    # Generate data
+    rng_key = random.PRNGKey(0)
+    X, y = make_regression(n_samples=25, n_features=1, noise=10.0, random_state=0)
+    X = X.reshape(25)
+
+    # Run the regression
+    run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior)
+