Theano自定義操作爲PyMC3

Question

我試圖實現一個自定義操作，我得到「錯誤的輸入參數theano函數」錯誤。這是代碼。我所理解的問題是：如何將PyMC3變量轉換爲可以理解的類型？

import numpy as np 
import theano 
import theano.tensor as t 
from theano import config 
config.compute_test_value = 'off' 

#true_Data = [1,2] 
#values=[] 

class trial_Op(theano.Op): 
    __props__ =() 
    itypes = [t.dmatrix, t.dmatrix, t.dmatrix] 
    otypes = [t.dmatrix] 

    def perform(self,node,inputs,output_storage): 
     x0 = inputs[0] 
     x1 = inputs[1] 
     x2 = inputs[2] 
     z = output_storage[0] 
     z[0] = np.add(x0,x1) 
     z[0] = np.add(z[0],x2) 

    def grad(self,inputs,output_grads): 
     return output_grads[0] 
Trial_Op = trial_Op() 

x1 = t.dmatrix() 
x2 = t.dmatrix() 
x3 = t.dmatrix() 
f = theano.function([x1,x2,x3], trial_Op()(x1,x2,x3)) 

# the Op works for the 
#inp1 = np.random.rand(3,1) # a 2d matrix 
#inp2 = np.random.rand(3,1) # a 2d matrix 
#inp3 = np.array([[-40]])    # a constant 
#print("Op application gives = ", f(inp1,inp2,inp3)) 


import pymc3 as pm 
true_Data = [[1]] 

with pm.Model() as model: 
    x1 = pm.Normal('x1', mu = 0, sd = 0.1) 
    x2 = pm.Normal('x2', mu = 3, sd = 0.5) 
    x3 = np.asarray([[4]], dtype='float64') 
# x1 = x1.reshape(1,1) 
# x2 = x2.reshape(1,1) 
    sum_of_x1_x2_x3 = f(x1,x2,x3) 
    z = pm.Normal('z', sum_of_x1_x2_x3, observed = true_Data) 
    start = {'x1':[[0.1]], 'x2':[[0.1]]} 
    step = pm.Metropolis() 
    trace = pm.sample(100, step, start) 

pm.traceplot(trace) 

Answer 1

我想我可以回答你的問題。

首先，你不應該使用f = theano.function([x1,x2,x3], trial_Op()(x1,x2,x3))。一旦定義，f將數值作爲參數。但是，在pymc3模型中，定義爲Normal的x1和x2不是數字，而是符號。所以它會拋出你剛纔遇到的錯誤。如果您熟悉教程中記錄的@as_op方法，則解決方案很簡單：將sum_of_x1_x2_x3 = f(x1,x2,x3)更改爲sum_of_x1_x2_x3 = Trial_Op(x1,x2,x3);

其次，在您的代碼中，似乎dmatrix類型是沒有必要的。所以我修改後的代碼：

N = 20 #data array length 

class Trial_Op(theano.Op): 
    __props__ =() 
    itypes = [t.dscalar, t.dscalar] 
    otypes = [t.dvector] #if the data has multiple values i.e. data array 

    def perform(self,node,inputs,output_storage): 
     x0 = inputs[0] 
     x1 = inputs[1] 

     f = np.add(x0,x1) 
     out = np.empty(N) 
     out[:] = f 
     z = output_storage[0] 
     z[0] = out 


trial_Op = Trial_Op() 


import pymc3 as pm 
true_Data = np.random.normal(2,1,N) 

with pm.Model() as model: 
    x1 = pm.Normal('x1', mu = 0, sd = 0.1) 
    x2 = pm.Normal('x2', mu = 3, sd = 0.5)  

    mu = trial_Op(x1, x2) 
    z = pm.Normal('z', mu = mu, sd = 1., observed = true_Data) 

    step = pm.Metropolis() 
    trace = pm.sample(10000, step) 

pm.traceplot(trace) 

注意在自定義功能，otypes是dvector滿足mu在z = pm.Normal('z', mu = mu, sd = 1., observed = true_Data)。而且樣本數擴大到10000，結果形象示人：

result

然而，我不知道如何定義自定義theano功能grad()方法。也許稍後有人或我可以解決它，以在模型中啓用NUTS採樣方法:)。