python概率

```python import torch import pyro import pyro.distributions as dist # Define a probabilistic model using Pyro def model(data): # Define priors mean = pyro.sample("mean", dist.Normal(0, 1)) std = pyro.sample("std", dist.Exponential(1)) # Define likelihood with pyro.plate("data", len(data)): pyro.sample("obs", dist.Normal(mean, std), obs=data) # Generate some synthetic data data = torch.randn(100) # Run inference using Pyro's stochastic variational inference (SVI) from pyro.infer import SVI, Trace_ELBO from pyro.optim import Adam # Define a guide (variational distribution) for SVI def guide(data): mean_loc = pyro.param("mean_loc", torch.tensor(0.)) mean_scale = pyro.param("mean_scale", torch.tensor(1.), constraint=dist.constraints.positive) std_rate = pyro.param("std_rate", torch.tensor(1.), constraint=dist.constraints.positive) pyro.sample("mean", dist.Normal(mean_loc, mean_scale)) pyro.sample("std", dist.Exponential(std_rate)) # Setup SVI pyro.clear_param_store() svi = SVI(model, guide, Adam({"lr": 0.01}), loss=Trace_ELBO()) # Run SVI num_iterations = 1000 for i in range(num_iterations): loss = svi.step(data) if i % 100 == 0: print("Iteration {}: loss = {:.2f}".format(i, loss)) # Extract learned parameters mean_loc = pyro.param("mean_loc").item() mean_scale = pyro.param("mean_scale").item() std_rate = pyro.param("std_rate").item() print("\nLearned parameters:") print("Mean: {:.2f} - {:.2f}".format(mean_loc, mean_scale)) print("Standard deviation: {:.2f}".format(1 / std_rate)) ``` This code demonstrates how to use Pyro, a probabilistic programming library built on top of PyTorch, to define a simple probabilistic model, perform inference using stochastic variational inference (SVI), and extract learned parameters. The model assumes a normal distribution for the data with unknown mean and standard deviation, and the goal is to infer these parameters from the observed data.

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