In [2]:

    

%matplotlib inline
from matplotlib import pyplot as plt
import pandas as pd, numpy as np, seaborn as sns


    

In [3]:

    

import GPy


    

In [4]:

    

class GPTwoSample(GPy.core.Model):
    def __init__(self, Xlist, Ylist, kernel):
        super(GPTwoSample, self).__init__(name='gptwosample')
        self.shared = GPy.models.GPRegression(np.concatenate(Xlist), np.concatenate(Ylist), kernel=kernel.copy())
        self.shared.name = "shared"
        X_ind = np.concatenate(Xlist)
        X_ind = np.c_[X_ind, np.zeros(X_ind.shape[0])]
        curr = 0
        for i, X in enumerate(Xlist):
            X_ind[curr:curr+X.shape[0],-1] = i
            curr += X.shape[0]
        independent_kernel = GPy.kern.IndependentOutputs(kernel.copy())
        self.independent = GPy.models.GPRegression(X_ind, np.concatenate(Ylist), kernel=independent_kernel.copy())
        self.independent.name = "independent"
        
        self.link_parameters(self.shared, self.independent) 
        
    def log_likelihood(self):
        return self.shared.log_likelihood() + self.independent.log_likelihood()


    

In [5]:

    

Xlist = [np.random.uniform(-2,2,np.random.randint(30,60))[:,None] for i in range(2)]
Ylist = [np.sin(X) + np.random.normal(0,.05,(X.shape[0],1)) for X in Xlist]

Ylist2 = [np.sin(X) + np.random.normal(0,.05,(X.shape[0],1)) for X in Xlist]
Ylist2[1][Ylist2[1] > 0] = -Ylist2[1][Ylist2[1] > 0]


    

In [6]:

    

plt.scatter(Xlist[0],Ylist[0])
plt.scatter(Xlist[1],Ylist[1])


    

    
Out[6]:





<matplotlib.collections.PathCollection at 0x1a1bf57e10>






    

In [7]:

    

plt.scatter(Xlist[0],Ylist2[0])
plt.scatter(Xlist[1],Ylist2[1])


    

    
Out[7]:





<matplotlib.collections.PathCollection at 0x1a1c05b748>






    

In [8]:

    

m = GPTwoSample(Xlist, Ylist2, GPy.kern.RBF(1))


    

In [9]:

    

m.optimize(messages=1)


    

    






 
 










    
Out[9]:





<paramz.optimization.optimization.opt_lbfgsb at 0x1a1bf0af28>

In [10]:

    

fig, ax = plt.subplots(1,1)
m.shared.plot_mean(ax=ax, color='r', label=False)
m.shared.plot_density(ax=ax, color='r', label="Shared")
m.independent.plot_mean(visible_dims=[0], ax=ax, fixed_inputs=[[1,0]], color='b', label=False)
m.independent.plot_density(visible_dims=[0], ax=ax, fixed_inputs=[[1,0]], color='b', label="Independent")
m.independent.plot_mean(visible_dims=[0], ax=ax, fixed_inputs=[[1,1]], color='b', label=False)
m.independent.plot_density(visible_dims=[0], ax=ax, fixed_inputs=[[1,1]], color='b', label=False)


    

    
Out[10]:





<matplotlib.axes._subplots.AxesSubplot at 0x1a1de69e10>






    

In [11]:

    

m.shared.log_likelihood() - m.independent.log_likelihood()


    

    
Out[11]:





-154.4096787201422

In [12]:

    

m2 = GPTwoSample(Xlist, Ylist, GPy.kern.RBF(1))
m2.optimize()
m2.shared.log_likelihood() - m2.independent.log_likelihood()


    

    
Out[12]:





15.656860185296239

In [13]:

    

fig, ax = plt.subplots(1,1)
m2.shared.plot_mean(ax=ax, color='r', label=False)
m2.shared.plot_density(ax=ax, color='r', label="Shared")
m2.independent.plot_mean(visible_dims=[0], ax=ax, fixed_inputs=[[1,0]], color='b', label=False)
m2.independent.plot_density(visible_dims=[0], ax=ax, fixed_inputs=[[1,0]], color='b', label="Independent")
m2.independent.plot_mean(visible_dims=[0], ax=ax, fixed_inputs=[[1,1]], color='b', label=False)
m2.independent.plot_density(visible_dims=[0], ax=ax, fixed_inputs=[[1,1]], color='b', label=False)


    

    
Out[13]:





<matplotlib.axes._subplots.AxesSubplot at 0x1a1f10dcc0>






    

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