Created
January 15, 2023 15:44
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SMC bug
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| import jax | |
| import jax.numpy as jnp | |
| import matplotlib.pyplot as plt | |
| import numpy as np | |
| from jax.scipy.stats import multivariate_normal | |
| jax.config.update("jax_platform_name", "cpu") | |
| import blackjax | |
| import blackjax.smc.resampling as resampling | |
| key = jax.random.PRNGKey(42) | |
| def V(x): | |
| return 5 * jnp.square(jnp.sum(x**2) - 1) | |
| def prior_log_prob(x): | |
| d = x.shape[0] | |
| return multivariate_normal.logpdf(x, jnp.zeros((d,)), jnp.eye(d)) | |
| def inference_loop(rng_key, mcmc_kernel, initial_state, num_samples): | |
| @jax.jit | |
| def one_step(state, k): | |
| state, _ = mcmc_kernel(k, state) | |
| return state, state | |
| keys = jax.random.split(rng_key, num_samples) | |
| _, states = jax.lax.scan(one_step, initial_state, keys) | |
| return states | |
| def full_logdensity(x): | |
| return -V(x) + prior_log_prob(x) | |
| inv_mass_matrix = jnp.eye(1) | |
| n_samples = 10_000 | |
| hmc_parameters = dict( | |
| step_size=1e-4, inverse_mass_matrix=inv_mass_matrix, num_integration_steps=50 | |
| ) | |
| hmc = blackjax.hmc(full_logdensity, **hmc_parameters) | |
| hmc_state = hmc.init(jnp.ones((1,))) | |
| hmc_samples = inference_loop(key, hmc.step, hmc_state, n_samples) | |
| nuts_parameters = dict(step_size=1e-4, inverse_mass_matrix=inv_mass_matrix) | |
| nuts = blackjax.nuts(full_logdensity, **nuts_parameters) | |
| nuts_state = nuts.init(jnp.ones((1,))) | |
| nuts_samples = inference_loop(key, nuts.step, nuts_state, n_samples) | |
| def smc_inference_loop(rng_key, smc_kernel, initial_state): | |
| """Run the temepered SMC algorithm. | |
| We run the adaptive algorithm until the tempering parameter lambda reaches the value | |
| lambda=1. | |
| """ | |
| def cond(carry): | |
| i, state, _k = carry | |
| return state.lmbda < 1 | |
| def one_step(carry): | |
| i, state, k = carry | |
| k, subk = jax.random.split(k, 2) | |
| state, _ = smc_kernel(subk, state) | |
| return i + 1, state, k | |
| n_iter, final_state, _ = jax.lax.while_loop( | |
| cond, one_step, (0, initial_state, rng_key) | |
| ) | |
| return n_iter, final_state | |
| loglikelihood = lambda x: -V(x) | |
| hmc_parameters = dict( | |
| step_size=1e-4, inverse_mass_matrix=inv_mass_matrix, num_integration_steps=1 | |
| ) | |
| tempered = blackjax.adaptive_tempered_smc( | |
| prior_log_prob, | |
| loglikelihood, | |
| blackjax.hmc, | |
| hmc_parameters, | |
| resampling.systematic, | |
| 0.5, | |
| mcmc_iter=1, | |
| ) | |
| initial_smc_state = jax.random.multivariate_normal( | |
| jax.random.PRNGKey(0), jnp.zeros([1]), jnp.eye(1), (10,) | |
| ) | |
| initial_smc_state_dict = [{"mean1":v[0] , "mean2": v[1]} for v in initial_smc_state] | |
| initial_smc_state = tempered.init(initial_smc_state_dict) | |
| n_iter, smc_samples = smc_inference_loop(key, tempered.step, initial_smc_state) | |
| print("Number of steps in the adaptive algorithm: ", n_iter.item()) |
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