I am creating my first pyro program.

The task is I have a couple of categorical data and want to estimate the distribution on them.

There are four categories A, B, C, D. I assume the categorical distribution with the prior distribution:

P(A) = 0.25, P(B) =0.25, P(C ) = 0.25, P(D) = 0.25.

I define the model as:

```
def data_model(prior_prob):
obs = np.array([0 if random.random() >0.2 else 1 for i in range(1000)]) # This is the synthesized data for test purpose
obs = torch.from_numpy(obs)
data = pyro.sample("data",dist.Categorical(probs=prior_prob),obs=obs)
return data
```

I define the guide function:

```
def param_guide(prior_prob):
posterior = pyro.param("probs", torch.tensor(prior_prob),constraint=constraints.positive)
data = pyro.sample("data", dist.Categorical(posterior))
return data
```

And I use SVI to inference the posterior probability distribution:

```
prior_prob = np.array([0.25, 0.25,0.25,0.25])
prior_prob = torch.from_numpy(prior_prob)
pyro.clear_param_store()
svi = pyro.infer.SVI(model=data_model,
guide=param_guide,
optim=pyro.optim.SGD({"lr": 0.001, "momentum":0.1}),
loss=pyro.infer.Trace_ELBO())
losses, probs = [], []
num_steps = 2500
for t in range(num_steps):
losses.append(svi.step(prior_prob))
probs.append(pyro.param("probs"))
```

Finally, I found my probs = [7.5012e-03, 3.6106e-02, 1.0009e-02, 1.4410e+03]

Two problems here:

- The sum of the probabilities is larger than 1.
- I generate the data by the probabilities [0.8, 0.2, 0, 0], why do not the estimated value approach it?