app.py

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
import sympy as sp


# 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=50, num_samples=1000)
    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")

st.write(f"### Y = \u03B1 + \u03B2X + \u03C3")
alpha_prior_option = st.selectbox("Choose an option for alpha prior:", ["Normal", "Laplace", "Cauchy"])
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)

beta_prior_option = st.selectbox("Choose an option for beta prior:", ["Normal", "Laplace", "Cauchy"])
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)

sigma_prior_option = st.selectbox("Choose an option for sigma prior:", ["HalfNormal", "HalfCauchy"])
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)

rng_key = random.PRNGKey(0)
X, y = make_regression(n_samples=50, n_features=1, noise=10.0, random_state=0)
X = X.reshape(50)

if alpha_prior and beta_prior and sigma_prior:
    run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior)