# Having trouble setting up basic HMC model

**URL:** <https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149>\
**Category:** General\
**Created:** [May 26, 2017, 5:25am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149 "2017-05-26T05:25:47Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![paktor132](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@paktor132](https://discourse.edwardlib.org/u/paktor132)\
**Post date:** [May 26, 2017, 5:25am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149/1 "2017-05-26T05:25:47Z")

</div>

Hey all–my apologies for the newbie question, but I’m having some trouble setting up even a pretty basic model using HMC. Here’s the code I’m having trouble with:

```auto
import numpy as np
import tensorflow as tf
from edward.models import Normal, Empirical
import edward as ed

X_train = np.array([[0.87024415, 0.65901989],
       [0.09892046, 0.92157853],
       [0.34324086, 0.7804544],
       [0.19976632, 0.90515983],
       [0.75492591, 0.50158632],
       [0.41315702, 0.63009453],
       [0.40734398, 0.74817169],
       [0.85471708, 0.69424045],
       [0.14578448, 0.95430565],
       [0.51036876, 0.63925266]], dtype=np.float32)

y_train = np.array([[-0.1065],
       [-0.005],
       [0.0488],
       [0.0714],
       [-0.0192],
       [0.0944],
       [0.],
       [-0.0888],
       [0.0392],
       [-0.73610002]], dtype=np.float32)

layer_1_size = 10

W_0 = Normal(loc = tf.zeros([2,layer_1_size]), scale = tf.ones([2,layer_1_size]))
W_1 = Normal(loc = tf.zeros([layer_1_size,1]), scale = tf.ones([layer_1_size,1]))
b_0 = Normal(loc = tf.zeros(layer_1_size), scale = tf.ones(layer_1_size))
b_1 = Normal(loc = tf.zeros(1), scale = tf.ones(1))

x = tf.placeholder(dtype=np.float32)

y = Normal(loc = tf.matmul(tf.tanh(tf.matmul(x, W_0) + b_0), W_1) + b_1,
           scale = 0.1)

T = 10000
ydata = tf.constant(np.repeat([y_train],T,axis=0))

qy = Empirical(params = ydata)
inference = ed.HMC({y: qy}, data = {x: X_train})
inference.run(n_iter=10000)

```

When I run that, I get:

```auto
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
<ipython-input-122-8793699b40bc> in <module>()
----> 1 inference.run(n_iter=10000)

/home/matthew/anaconda3/envs/edward/lib/python3.6/site-packages/edward/inferences/inference.py in run(self, variables, use_coordinator, *args, **kwargs)
    114 Passed into ``initialize``.
    115 """
--> 116 self.initialize(*args, **kwargs)
    117 
    118 if variables is None:

/home/matthew/anaconda3/envs/edward/lib/python3.6/site-packages/edward/inferences/hmc.py in initialize(self, step_size, n_steps, *args, **kwargs)
     62 self.n_steps = n_steps
     63 self.scope_iter = 0 # a convenient counter for log joint calculations
---> 64 return super(HMC, self).initialize(*args, **kwargs)
     65 
     66 def build_update(self):

/home/matthew/anaconda3/envs/edward/lib/python3.6/site-packages/edward/inferences/monte_carlo.py in initialize(self, *args, **kwargs)
     96 self.n_accept = tf.Variable(0, trainable=False, name="n_accept")
     97 self.n_accept_over_t = self.n_accept / self.t
---> 98 self.train = self.build_update()
     99 
    100 def update(self, feed_dict=None):

/home/matthew/anaconda3/envs/edward/lib/python3.6/site-packages/edward/inferences/hmc.py in build_update(self)
    113 assign_ops = []
    114 for z, qz in six.iteritems(self.latent_vars):
--> 115 variable = qz.get_variables()[0]
    116 assign_ops.append(tf.scatter_update(variable, self.t, sample[z]))
    117 

IndexError: list index out of range

```

I have no idea what list is even being accessed here. All the dimensions seem right but maybe I’ve got something wrong:

```auto
ydata
<tf.Tensor 'Const_112:0' shape=(10000, 10, 1) dtype=float32>

qy
<ed.RandomVariable 'Empirical_74/' shape=(10, 1) dtype=float32>

```

Incidentally, is my understanding of `Empirical` correct that I should be setting up a `tf.constant` tensor with the number of desired samples as the first dimension, with the target data repeated for each one?

Thanks very much for any assistance you can provide!

Matt

---

<div class="post-metadata">

**Author:** ![dustin](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.edwardlib.org/dustin/32/134_2.png) [@dustin](https://discourse.edwardlib.org/u/dustin)\
**Post date:** [May 29, 2017, 1:14am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149/2 "2017-05-29T01:14:53Z")

</div>

Before delving into code, it’s useful to reason about what your model is and what it means to infer hidden structure from your model via a posterior distribution.

In your example, you wrote a Bayesian neural network with likelihood `y` given `x`, and with weight and bias parameters `W_0,W_1,b_0,b_1`. You then set up data `xdata` and `ydata`.

To perform inference means to calculate a distribution over the weights and biases given the data. In particular, with something like HMC, you should set up `Empirical` distributions that each approximate `W_0,W_1,b_0,b_1` respectively. For more background, I recommend the pages linked to in [http://edwardlib.org/tutorials/](http://edwardlib.org/tutorials/).

---

<div class="post-metadata">

**Author:** ![paktor132](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@paktor132](https://discourse.edwardlib.org/u/paktor132)\
**Post date:** [May 29, 2017, 2:18am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149/3 "2017-05-29T02:18:18Z")

</div>

So I guess based on your answer that I’m having some sort of fundamental misunderstanding about what the function of the `Empirical` distributions is in your examples. I’m coming from a PyMC background so I may be making some unfounded assumptions about how the syntax works. Here, I was attempting to place standard normal priors on `W_0`, `W_1`, `b_0`, and `b_1`, and then draw inference given `x` and `y`. I had assumed that `y: qy` (with `qy` filled with the observed values) was the way to get edward to treat `y` as a likelihood rather than as a prior, like setting the `observed=True` flag in PyMC (and then putting the observed values of `y` in `qy`). But it sounds like instead the `Empirical`s are used for holding the HMC samples from the posterior for the unknown parameters?

---

<div class="post-metadata">

**Author:** ![dustin](https://yyz1.discourse-cdn.com/flex035/user_avatar/discourse.edwardlib.org/dustin/32/134_2.png) [@dustin](https://discourse.edwardlib.org/u/dustin)\
**Post date:** [May 29, 2017, 2:23am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149/4 "2017-05-29T02:23:39Z")

</div>

Yes.

To treat `y` as data, you simply pass it into the corresponding argument during inference:

```python
inference = ed.HMC({W_0: qW_0, b_0: qb_0,
                    W_1: qW_1, b_1: qb_1,
                    W_2: qW_2, b_2: qb_2}, data={X: X_train, y: y_train})

```

where `q*` are all the Empirical approximations. See the [inference API](http://edwardlib.org/api/inference) for more details. For this example, a useful reference is the [`examples/bayesian_nn.py`](https://github.com/blei-lab/edward/blob/master/examples/bayesian_nn.py) script in the Github repository.

---

<div class="post-metadata">

**Author:** ![paktor132](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@paktor132](https://discourse.edwardlib.org/u/paktor132)\
**Post date:** [May 29, 2017, 2:26am UTC](https://discourse.edwardlib.org/t/having-trouble-setting-up-basic-hmc-model/149/5 "2017-05-29T02:26:13Z")

</div>

Ah, excellent, thank you!