monotonicity for multidimensional case

[benkour]

Hello all,
i have a project with multiple input dimensions and their corresponding monotonicity. I.e. we know that increasing the first input should decrease the output and increasing the second input should increase the output.

I have modified this example

      def fd(x):
          return -np.ones((x.shape[0],1))
      def test_multioutput_model_with_ep():
              f = lambda x: np.sin(x)+0.1*(x-2.)**2-0.005*x**3
              N=10
              sigma=0.05
              #x = np.random.random((3, 2))
              x = np.array([np.linspace(1,10,N)]).T
              y = f(x) 
              print(y)
              M=15
      
              xd = x
              yd = fd(x)
     
              # squared exponential kernel:
              se = GPy.kern.RBF(input_dim = 1, lengthscale=1.5, variance=0.2)
      
              # We need to generate separate kernel for the derivative observations and give the created kernel as an input:
              se_der = GPy.kern.DiffKern(se, 0)
    
              #Then 
              gauss = GPy.likelihoods.Gaussian(variance=sigma**2)
              probit = GPy.likelihoods.Binomial(gp_link = GPy.likelihoods.link_functions.ScaledProbit(nu=100))
              # Then create the model, we give everything in lists
              inference = GPy.inference.latent_function_inference.expectation_propagation.EP(ep_mode = 'nested')
              # inference = GPy.inference.latent_function_inference.Laplace()
              m = GPy.models.MultioutputGP(X_list=[x, xd], Y_list=[y, yd], kernel_list=[se, se_der], likelihood_list = [gauss, probit], inference_method=inference)
              m.optimize(messages=0, ipython_notebook=False)
              return m

to take in a joint classification problem (dummy one)
However, when i try to increase the dimensionality of the problem, i.e. x = np.random.random((3, 2)), EP throws the error that it is only an 1D method. Laplace on the other hand gives me the following error

        TypeError                                 Traceback (most recent call last)
        <ipython-input-1-032a3ffad658> in <module>
              3 
              4 from regression_2 import *
        ----> 5 model = test_multioutput_model_with_ep()
              6 xpred = np.array([np.linspace(0,11,4)]).T
              7 
        
        ~/Desktop/phd/manuel_BO/GPY_MONOTONICITY/examples/regression_2.py in test_multioutput_model_with_ep()
            106         # inference = GPy.inference.latent_function_inference.FITC()
            107         # inference = GPy.inference.latent_function_inference.PEP(alpha = 0.5)
        --> 108         m = GPy.models.MultioutputGP(X_list=[x, xd], Y_list=[y, yd], kernel_list=[se, se_der], likelihood_list = [gauss, probit], inference_method=inference)
            109         m.optimize(messages=0, ipython_notebook=False)
            110         return m
        
        ~/anaconda3/envs/ml_torch/lib/python3.7/site-packages/paramz/parameterized.py in __call__(self, *args, **kw)
             56         self._model_initialized_ = False
             57         if initialize:
        ---> 58             self.initialize_parameter()
             59         else:
             60             import warnings
        
        ~/anaconda3/envs/ml_torch/lib/python3.7/site-packages/paramz/core/parameter_core.py in initialize_parameter(self)
            335         self._highest_parent_._connect_parameters() #logger.debug("calling parameters changed")
        ...
        --> 124         N = Y_metadata['trials']
            125         np.testing.assert_array_equal(N.shape, y.shape)
            126         Ny = N-y
        
        TypeError: 'NoneType' object is not subscriptable

Any help is greatly appreciated. PS, I am not fixated in any of the above code/methods. I welcome any suggestion on how to include monotonicity of inputs with respect to the outputs so long as 1) i can make predictions about the output 3) it is multidimensional and 3) i dont need the exact gradient values but their sign as specification