Pyro

import pyro

import pyro
import pyro.distributions as dist
from pyro.infer import SVI, Trace_ELBO
from pyro.optim import Adam
import torch

import pyro
import pyro.distributions as dist
from pyro.infer import SVI, Trace_ELBO
from pyro.optim import Adam
import torch

# Define a simple Bayesian model
def model(data):
    # Prior on the parameter
    theta = pyro.sample("theta", dist.Beta(1.0, 1.0))
    
    # Likelihood
    with pyro.plate("data", len(data)):
        pyro.sample("obs", dist.Bernoulli(theta), obs=data)

# Define a variational guide (posterior approximation)
def guide(data):
    # Variational parameters
    alpha_q = pyro.param("alpha_q", torch.tensor(1.0), constraint=dist.constraints.positive)
    beta_q = pyro.param("beta_q", torch.tensor(1.0), constraint=dist.constraints.positive)
    
    # Variational distribution
    pyro.sample("theta", dist.Beta(alpha_q, beta_q))

# Generate some data
data = torch.tensor([1.0, 0.0, 1.0, 1.0, 0.0])

# Set up stochastic variational inference
svi = SVI(model, guide, Adam({"lr": 0.01}), loss=Trace_ELBO())

# Training loop
for step in range(1000):
    loss = svi.step(data)
    if step % 100 == 0:
        print(f"Step {step}, Loss: {loss}")

# Get posterior samples
from pyro.infer import Predictive
predictive = Predictive(model, guide=guide, num_samples=1000)
samples = predictive(data)
print(f"Posterior mean of theta: {samples['theta'].mean():.3f}")

def sample(name: str, fn: dist.Distribution, *args, obs=None, obs_mask=None, infer=None, **kwargs):
    """
    Primitive stochastic function for probabilistic programming.
    
    Parameters:
    - name (str): Unique name for the sample site
    - fn (Distribution): Probability distribution to sample from
    - obs (Tensor, optional): Observed data to condition on
    - obs_mask (Tensor, optional): Mask for observed data
    - infer (dict, optional): Inference configuration
    
    Returns:
    Tensor: Sample from the distribution
    """

def param(name: str, init_tensor=None, constraint=None, event_dim=None):
    """
    Declare and retrieve learnable parameters.
    
    Parameters:
    - name (str): Parameter name
    - init_tensor (Tensor, optional): Initial value
    - constraint (Constraint, optional): Parameter constraint
    - event_dim (int, optional): Event dimension
    
    Returns:
    Tensor: Parameter tensor
    """

def plate(name: str, size: int, subsample_size=None, dim=None):
    """
    Independence context manager for vectorized computation.
    
    Parameters:
    - name (str): Plate name
    - size (int): Plate size
    - subsample_size (int, optional): Subsample size for minibatching
    - dim (int, optional): Tensor dimension
    
    Returns:
    PlateMessenger: Context manager
    """

def factor(log_factor):
    """
    Add arbitrary factor to log probability.
    
    Parameters:
    - log_factor (Tensor): Log probability factor
    """

# Core continuous distributions
class Normal(dist.Distribution):
    def __init__(self, loc: torch.Tensor, scale: torch.Tensor): ...

class Beta(dist.Distribution):
    def __init__(self, concentration1: torch.Tensor, concentration0: torch.Tensor): ...

class Gamma(dist.Distribution):
    def __init__(self, concentration: torch.Tensor, rate: torch.Tensor): ...

# Discrete distributions
class Bernoulli(dist.Distribution):
    def __init__(self, probs: torch.Tensor = None, logits: torch.Tensor = None): ...

class Categorical(dist.Distribution):
    def __init__(self, probs: torch.Tensor = None, logits: torch.Tensor = None): ...

# Multivariate distributions
class MultivariateNormal(dist.Distribution):
    def __init__(self, loc: torch.Tensor, covariance_matrix: torch.Tensor = None, 
                 precision_matrix: torch.Tensor = None, scale_tril: torch.Tensor = None): ...

class SVI:
    """Stochastic Variational Inference."""
    def __init__(self, model, guide, optim, loss):
        """
        Parameters:
        - model: Generative model function
        - guide: Variational guide function  
        - optim: Optimizer instance
        - loss: Loss function (typically ELBO)
        """
    
    def step(self, *args, **kwargs) -> float:
        """Perform one SVI step, returns loss."""

class MCMC:
    """Markov Chain Monte Carlo."""
    def __init__(self, kernel, num_samples: int, warmup_steps: int = None): ...
    
    def run(self, *args, **kwargs): ...

class Predictive:
    """Generate predictions from posterior samples."""
    def __init__(self, model, guide=None, posterior_samples=None, num_samples=None): ...

class PyroModule(torch.nn.Module):
    """Base class for Pyro modules with parameter/sample integration."""
    
class PyroParam:
    """Descriptor for Pyro parameters in modules."""
    def __init__(self, init_tensor, constraint=None, event_dim=None): ...

class PyroSample:
    """Descriptor for Pyro samples in modules."""  
    def __init__(self, prior): ...

class DenseNN(PyroModule):
    """Dense neural network for use in flows and guides."""
    def __init__(self, input_dim: int, hidden_dims: List[int], output_dim: int): ...

# Core transforms
class Transform:
    """Base class for bijective transforms."""
    def __call__(self, x): ...
    def inv(self, y): ...
    def log_abs_det_jacobian(self, x, y): ...

class AffineTransform(Transform):
    def __init__(self, loc: torch.Tensor, scale: torch.Tensor): ...

# Flow-based transforms  
class AffineAutoregressive(Transform):
    def __init__(self, autoregressive_nn, log_scale_min_clip: float = -5.0): ...

# Constraints
class Constraint:
    """Base class for parameter constraints."""
    def check(self, value): ...

positive: Constraint
unit_interval: Constraint  
simplex: Constraint

class Kernel:
    """Base class for GP kernels."""
    def forward(self, X, Z=None, diag: bool = False): ...

class RBF(Kernel):
    """Radial Basis Function kernel."""
    def __init__(self, input_dim: int, lengthscale=None, variance=None): ...

class GPModel:
    """Base Gaussian Process model."""
    def __init__(self, X, y, kernel, likelihood): ...

class PyroOptim:
    """Base wrapper for PyTorch optimizers."""
    def __init__(self, optim_constructor, optim_args, clip_args=None): ...

class ClippedAdam(PyroOptim):
    """Adam optimizer with gradient clipping."""
    def __init__(self, optim_args, clip_args=None): ...

# PyTorch optimizer wrappers
def Adam(optim_args, clip_args=None): ...
def SGD(optim_args, clip_args=None): ...
def RMSprop(optim_args, clip_args=None): ...

from typing import Union, Optional, Dict, Any, Callable, Iterator, Sequence
from torch import Tensor
from pyro.distributions import Distribution, Transform, Constraint
from pyro.distributions.torch_distribution import TorchDistributionMixin
from pyro.params.param_store import ParamStoreDict
from pyro.poutine.runtime import InferDict
from pyro.poutine.plate_messenger import PlateMessenger

# Core types
ModelFunction = Callable[..., None]
GuideFunction = Callable[..., None] 
InitFunction = Callable[[str], Tensor]

# Distribution types
DistributionType = Union[Distribution, type]
ConstraintType = Union[Constraint, type]
TransformType = Union[Transform, type]

# Inference types  
OptimType = Union[torch.optim.Optimizer, pyro.optim.PyroOptim]
LossType = Union[pyro.infer.ELBO, Callable]

# Pyro-specific types
TorchDistributionMixin = pyro.distributions.torch_distribution.TorchDistributionMixin
ParamStoreDict = pyro.params.param_store.ParamStoreDict
InferDict = pyro.poutine.runtime.InferDict
PlateMessenger = pyro.poutine.plate_messenger.PlateMessenger