def linear_regression_mvn(x, lmbda=1.):
sigma <~ dist.Exponential(lmbda)
sigma2 <~ dist.Exponential(lmbda)
rho <~ dist.Uniform(-1, 1)
cov = jnp.array([[sigma**2, rho*sigma*sigma2],[rho*sigma*sigma2, sigma2**2]])
coeffs <~ dist.MvNormal(jnp.ones(x.shape[-1]), cov)
y = jnp.dot(x, coeffs)
predictions <~ dist.Normal(y, sigma)
return predictions
def linear_regression(x, lmbda=1.0):
sigma < ~dist.Exponential(lmbda)
coeffs_init = jnp.ones(x.shape[-1])
coeffs < ~dist.Normal(coeffs_init, sigma)
y = jnp.dot(x, coeffs)
predictions < ~dist.Normal(y, sigma)
return predictions
def naive_bayes(X, num_categories):
num_predictors = np.shape(X)[1]
num_training_samples = np.shape(X)[0]
# Priors
alpha = np.ones(num_categories)
pi <~ dist.Dirichlet(alpha, shape=num_categories)
mu <~ dist.Normal(mu=0, sigma=100, shape=(num_categories, num_predictors))
sigma <~ dist.Exponential(100, shape=(num_categories, num_predictors))
# Assign classes to data points
z <~ dist.Categorical(pi, shape=num_training_samples)
# The components are independent and normally distributed
xi <~ dist.Normal(mu=mu[z], sd=sigma[z])
return z
def linear_regression(x, lmbda=1.0):
sigma < ~dist.Exponential(lmbda)
coeffs < ~dist.Normal(jnp.zeros(x.shape[-1]), 1)
predictions < ~dist.Normal(x * coeffs, sigma)
return predictions