Added new link-function to enable derivative sign values as in Riihimaki & Vehtari (2010) paper

GPy/likelihoods/link_functions.py

@@ -138,6 +138,38 @@ class Probit(GPTransformation):
         input_dict["class"] = "GPy.likelihoods.link_functions.Probit"
         return input_dict
 
+class ScaledProbit(Probit):
+    """
+    .. math::
+        g(f) = \\Phi^{-1} (nu*mu)
+    """
+    def __init__(self, nu=1.):
+        self.nu = float(nu)
+        
+    def transf(self,f):
+        return std_norm_cdf(f*self.nu)
+
+    def dtransf_df(self,f):
+        return std_norm_pdf(f*self.nu)*self.nu
+
+    def d2transf_df2(self,f):
+        return -(f*self.nu) * std_norm_pdf(f*self.nu)*(self.nu**2)
+
+    def d3transf_df3(self,f):
+        return (safe_square(f*self.nu)-1.)*std_norm_pdf(f*self.nu)*(self.nu**3)
+    
+    def to_dict(self):
+        """
+        Convert the object into a json serializable dictionary.
+
+        Note: It uses the private method _save_to_input_dict of the parent.
+
+        :return dict: json serializable dictionary containing the needed information to instantiate the object
+        """
+
+        input_dict = super(ScaledProbit, self)._save_to_input_dict()
+        input_dict["class"] = "GPy.likelihoods.link_functions.ScaledProbit"
+        return input_dict
 
 class Cloglog(GPTransformation):
     """

GPy/testing/link_function_tests.py

@@ -2,11 +2,12 @@ import numpy as np
 import scipy
 from scipy.special import cbrt
 from GPy.models import GradientChecker
+import random
 _lim_val = np.finfo(np.float64).max
 _lim_val_exp = np.log(_lim_val)
 _lim_val_square = np.sqrt(_lim_val)
 _lim_val_cube = cbrt(_lim_val)
-from GPy.likelihoods.link_functions import Identity, Probit, Cloglog, Log, Log_ex_1, Reciprocal, Heaviside
+from GPy.likelihoods.link_functions import Identity, Probit, Cloglog, Log, Log_ex_1, Reciprocal, Heaviside, ScaledProbit
 
 class LinkFunctionTests(np.testing.TestCase):
     def setUp(self):
@@ -124,6 +125,11 @@ class LinkFunctionTests(np.testing.TestCase):
         lim_of_inf = _lim_val
         self.check_gradient(link, lim_of_inf, test_lim=True)
         
+    def test_scaledprobit_gradients(self):
+        link = ScaledProbit(nu=random.random())
+        lim_of_inf = _lim_val
+        self.check_gradient(link, lim_of_inf, test_lim=True)
+
     def test_Cloglog_gradients(self):
         link = Cloglog()
         lim_of_inf = _lim_val_exp