# Problem when using shared variable and linear mean function with GP conditional

**URL:** https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350
**Category:** Questions
**Created:** [December 2, 2020, 6:27pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350 "2020-12-02T18:27:44Z")
**Posts on this page:** 11
**Page:** 1

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 2, 2020, 6:27pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/1 "2020-12-02T18:27:44Z")

</div>

Hi,  
Thanks to all devs for creating this wonderful tool!

I run into a problem when trying to do prediction using GP. First, I have no issue when not using shared variable. I can run my model and sample posterior predictive using gp conditionnal for new X. Here’s my model…

```
with pm.Model() as gp_model_1:

#Mean Function
mean_func = pm.gp.mean.Linear(coeffs=-0.2, intercept=0.5)
#mean_func = pm.gp.mean.Constant(0.3)
#custom Mean function
#mean_func = InvLogit(a = -5, x0 = 0.5, c = 0.27, d = 0.3)

#Cov Function
cov_base = pm.gp.cov.WhiteNoise(0.15)
cov_func = pm.gp.cov.ScaledCov(1, scaling_func=logistic, args=(a,x0,c,d), cov_func=cov_base)

# Specify the GP
gp = pm.gp.Latent(mean_func = mean_func, cov_func=cov_func)
# make gp prior
f = gp.prior("f", X=df.x.values.reshape(-1,1), shape= df.x.values.shape)

sigma = pm.HalfNormal('sigma', sd =0.1)
p = pm.Deterministic("p", pm.math.invlogit(f))
y = pm.Beta("y", mu = p, sigma = sigma, observed = df.y_DH.values)
mp = pm.find_MAP()
#gp_trace1 = pm.sample(1000, tune=1000, chains=2)

#set up log-normal parameter on new X for the shared variable
zeta = np.sqrt(np.log(1 + 0.4**2))
lam = np.log(0.4) - (zeta**2)/2
n_pixel = 625

with gp_model_1:
    x_depth = stats.lognorm.rvs(scale = np.exp(lam),s = zeta, loc = 0, size = n_pixel).reshape(-1,1)
    x_tensor = shared(value = x_depth)
    print(x_tensor.get_value().shape)
    f_pred = gp.conditional(f'y_pred', x_tensor, shape = n_pixel)
    
"""
 end GP Model definition
 begin Sampling with shared variable
"""

```

But when I tried with shared variable so I can sample through a for loop and update new Xs, I get this error message in the GP Conditionnal about the mean function. If I use a constant mean function, no problem, but I get the same error if I use the linear mean function or my custom mean function. I was able to use my custom or the Linear mean function just fine before using shared variable… The shape of the Teano tensor is (625,1).

```
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-20-dd75cbc07b09> in <module>
     68 x_tensor = shared(value = x_depth)
     69 print(x_tensor.get_value().shape)
---> 70 f_pred = gp.conditional(f'y_pred', x_tensor, shape = n_pixel)
     71 
     72 """

~/anaconda3/envs/bayes/lib/python3.7/site-packages/pymc3/gp/gp.py in conditional(self, name, Xnew, given, **kwargs)
    218 """
    219 givens = self._get_given_vals(given)
--> 220 mu, cov = self._build_conditional(Xnew, *givens)
    221 shape = infer_shape(Xnew, kwargs.pop("shape", None))
    222 return pm.MvNormal(name, mu=mu, cov=cov, shape=shape, **kwargs)

~/anaconda3/envs/bayes/lib/python3.7/site-packages/pymc3/gp/gp.py in _build_conditional(self, Xnew, X, f, cov_total, mean_total)
    183 A = solve_lower(L, Kxs)
    184 v = solve_lower(L, f - mean_total(X))
--> 185 mu = self.mean_func(Xnew) + tt.dot(tt.transpose(A), v)
    186 Kss = self.cov_func(Xnew)
    187 cov = Kss - tt.dot(tt.transpose(A), A)

~/anaconda3/envs/bayes/lib/python3.7/site-packages/theano/tensor/var.py in __add__ (self, other)
    129 def __add__ (self, other):
    130 try:
--> 131 return theano.tensor.basic.add(self, other)
    132 # We should catch the minimum number of exception here.
    133 # Otherwise this will convert error when Theano flags

~/anaconda3/envs/bayes/lib/python3.7/site-packages/theano/gof/op.py in __call__ (self, *inputs, **kwargs)
    672 thunk.outputs = [storage_map[v] for v in node.outputs]
    673 
--> 674 required = thunk()
    675 assert not required # We provided all inputs
    676 

~/anaconda3/envs/bayes/lib/python3.7/site-packages/theano/gof/op.py in rval()
    860 
    861 def rval():
--> 862 thunk()
    863 for o in node.outputs:
    864 compute_map[o][0] = True

~/anaconda3/envs/bayes/lib/python3.7/site-packages/theano/gof/cc.py in __call__ (self)
   1737 print(self.error_storage, file=sys.stderr)
   1738 raise
-> 1739 reraise(exc_type, exc_value, exc_trace)
   1740 
   1741 

~/anaconda3/envs/bayes/lib/python3.7/site-packages/six.py in reraise(tp, value, tb)
    701 if value. __traceback__ is not tb:
    702 raise value.with_traceback(tb)
--> 703 raise value
    704 finally:
    705 value = None

ValueError: Input dimension mis-match. (input[0].shape[1] = 1, input[1].shape[1] = 625)

```

Is this a bug or I’m simply feeding wrong shape or params into the model?  
Any help would be appreciated.

Versions  
pymc3 - 3.9.3  
theano 1.0.5  
python - 3.7.3  
Ubuntu - 18.04.3

---

<div class="post-metadata">

### Author: ![tirthasheshpatel](https://avatars.discourse-cdn.com/v4/letter/t/ac91a4/32.png) [@tirthasheshpatel](https://discourse.pymc.io/u/tirthasheshpatel)
#### Post date: [December 3, 2020, 3:21am UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/2 "2020-12-03T03:21:59Z")

</div>

I am not entirely sure why is it working for the mean functions other that the `Linear` mean function, but I think the problem is with passing the `shape` parameter in the `gp.prior` and `gp.conditional` method. Does it raise an exception if you don’t pass the `shape` parameter? If not, then can you please remove it and try again?

Other reason could be that your custom mean function doesn’t output a tensor of correct shape. Make sure that the mean function you create or choose outputs a tensor of shape `(X.shape[0], )` (`(625, )` in your case). Shapes other that this may lead to problems…

If none of the above comment resolve your issue, can you please share the code for custom mean functions that you are using?

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 3, 2020, 3:37pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/3 "2020-12-03T15:37:20Z")

</div>

Thanks for the reply,

1. I’ve tried not specifying a shape parameter like you said but the gp.conditional gives an error **(Cannot infer shape)**. The prior doesn’t seem to care but I think I’ve seen in another post you need to specify the shape if you’re using shared variable… So, I do have to pass a shape to the conditional…

2. I’m not sure how I can specify the shape of the mean function like you ask (any hint)… Here’s the code for my custom mean function and I added the code for the linear function. I’ve tried to replicate the linear function output to do mine.

I still don’t understand why it work without shared variable… but I need to sample ppc for a big number of parameters with the x\_depth tensor … So I kind of need shared variable.

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 14, 2020, 8:04pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/4 "2020-12-14T20:04:23Z")

</div>

Could this be link to [issue 3345](https://github.com/pymc-devs/pymc3/issues/3345) and the init of the mean\_func shape?

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 14, 2020, 8:06pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/5 "2020-12-14T20:06:52Z")

</div>

Input data to test code  
[input\_GP\_error.csv](https://discourse.pymc.io/uploads/short-url/eX2olHMysjq4MzXYNoJm68pEVZ0.csv) (10.5 KB)

---

<div class="post-metadata">

### Author: ![luisroque](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@luisroque](https://discourse.pymc.io/u/luisroque)
#### Post date: [December 15, 2020, 10:20am UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/6 "2020-12-15T10:20:58Z")

</div>

I didn’t check in great detail your code or request, please tell me if I missed something. From what I can see, the problem is on the tt.dot inside of the mean function because you are sending it a scalar and asking for it to be broadcasted. I just did the following and it runs for me.

```auto
mean_func = Linear(coeffs=np.array([-0.2]), intercept=np.array([0.5]))

```

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 15, 2020, 2:25pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/7 "2020-12-15T14:25:05Z")

</div>

thanks! It does work for the linear mean function! It doesn’t work for my custom invLogit function but at least it work for the linear. I didn’t want to use the constant function for my application…

I will have a deeper look into my custom function, it’s certainly my bad not the code…

thanks again!

---

<div class="post-metadata">

### Author: ![luisroque](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@luisroque](https://discourse.pymc.io/u/luisroque)
#### Post date: [December 15, 2020, 3:32pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/8 "2020-12-15T15:32:57Z")

</div>

Glad it helped. If you get stuck, feel free to post the new code. Handling the shapes in the custom mean funcs of GPs is tricky.

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 15, 2020, 6:59pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/9 "2020-12-15T18:59:12Z")

</div>

I’m trying to do a mean function that follows an inverse logic based on this scaling function from the GP covariance documentation.

```
d * pm.math.invlogit(a*(x - x0)) + c

```

I’ve define my mean function like this:

```
def __init__ (self, a, x0, c, d):
pm.gp.mean.Mean. __init__ (self)
self.a = a
self.x0 = x0
self.c = c
self.d = d

def __call__ (self, X):
return tt.squeeze(self.d * pm.math.invlogit(self.a*(X - self.x0)) + self.c)

```

and use the input like you said

```
mean_func = InvLogit(a = np.array([-5]), 
                     x0 = np.array([0.5]), 
                     c = np.array([0.27]), 
                     d = np.array([0.3]))

```

I still get the same error

```
ValueError: Input dimension mis-match. (input[0].shape[1] = 1, input[1].shape[1] = 625)

```

I’ve replaced the multiplication of both constant (self.a and self.d) with the pm.math.dot function but it doesn’t work…

---

<div class="post-metadata">

### Author: ![luisroque](https://avatars.discourse-cdn.com/v4/letter/l/7c8e57/32.png) [@luisroque](https://discourse.pymc.io/u/luisroque)
#### Post date: [December 16, 2020, 9:37am UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/10 "2020-12-16T09:37:04Z")

</div>

I can’t understand why, but `tt.squeeze` seems to not be doing what it is supposed to. You can make it work by using another way to remove the second dimension.

```auto
(self.d * pm.math.invlogit(self.a*(X - self.x0)) + self.c).reshape((-1,))

```

---

<div class="post-metadata">

### Author: ![JulienMeloche](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/julienmeloche/32/3382_2.png) [@JulienMeloche](https://discourse.pymc.io/u/JulienMeloche)
#### Post date: [December 16, 2020, 2:14pm UTC](https://discourse.pymc.io/t/problem-when-using-shared-variable-and-linear-mean-function-with-gp-conditional/6350/11 "2020-12-16T14:14:56Z")

</div>

Thanks so much!