More tests

GPy/testing/ccd_test.py

@@ -35,4 +35,96 @@ ccdpos,ccdres = m2.CCD()
 m2.optimize()
 
 assert np.all(np.isclose(np.sum((ccdpos-np.array([1,2]))**2,1)[1:],1.21,atol=0.01)), "CCD placement error - should be 1.21 from mode"
-s
+
+
+#####CODE TO COMBINE TODO!
+
+import numpy as np
+import matplotlib.pyplot as plt
+import GPy
+%matplotlib inline
+np.set_printoptions(suppress=True, precision=10)
+from paramz.transformations import Logexp
+
+class SimpleModel(GPy.Model):
+    def __init__(self, name, dims, priors=False):
+        super(SimpleModel, self).__init__(name)
+        self.params = []
+        self.peak_loc = range(1,dims+1,1)
+        for i,pos in enumerate(self.peak_loc):
+            if priors:
+                p = GPy.Param('param%d' % i, 1.0, Logexp())
+            else:
+                p = GPy.Param('param%d' % i, 1.0)
+            self.params.append(p)
+            self.link_parameter(p)
+    
+    def log_likelihood(self):
+        like = 0
+        for i,pos in enumerate(self.peak_loc):
+            like -= ((self.params[i])-pos)**2
+        return like[0]
+    
+    def parameters_changed(self):
+        for i,pos in enumerate(self.peak_loc):
+            self.params[i].gradient = -2*((self.params[i])-pos)
+            
+import itertools
+def find_likes(m,stepsize=0.3,rangemin=-2,rangemax=7):
+    """Numerical grid integral over model parameters
+    This function returns an array of all the """
+    params = m.parameter_names_flat()
+    param_ranges = []
+    for param in params:
+        param_ranges.append(np.arange(rangemin,rangemax,stepsize))
+    combs = itertools.product(*param_ranges)
+    llsum = 0
+    for el in combs:
+        llsum+=np.exp(-m._objective(el))
+    return llsum
+
+for dims in range(1,8):
+    m1 = SimpleModel('simple',dims)
+    m1.optimize()
+    assert np.all(np.isclose(m1.numerical_parameter_hessian(),np.eye(dims)*2)), "Numerical approximation to Hessian doesn't match. Error in numerical_parameter_hessian()."
+    peak_loc = range(1,dims+1)
+    for d in range(dims):        
+        assert np.isclose(m1.params[d],d+1,atol=0.01), "Failed to find likelihood maximum of test model's parameter while testing CCD"
+
+    ccdpos,ccdres = m1.CCD()
+    m1.optimize()
+    dists = np.sum((ccdpos-np.array(peak_loc))**2,1)[1:]
+    dists - np.mean(dists)
+    assert np.all(np.isclose(dists,np.mean(dists),atol=0.01)), "CCD placement error - should be 1.21 from mode, for nd symmetrical Quadratic test case"
+    assert np.all(np.isclose(np.sum(ccdres[1:]/ccdres[0]),4.7619,atol=0.1)), "CCD placement error - off-centre locations should have log likelihood ratios to central point summing to 4.76 times the centre, for nd symmetrical Quadratic test case"
+    
+for dims in range(1,5):
+    stepsize=0.3*dims #make step size bigger as dims goes up so this isn't too slow
+    m2 = SimpleModel('simple',dims,True)
+    ls = find_likes(m2,stepsize)
+    numsum = ls*(stepsize**dims)
+    hes = m2.numerical_parameter_hessian()
+    hessum = np.exp(m2.log_likelihood())*1/np.sqrt(np.linalg.det(1/(2*np.pi)*hes))
+    assert np.isclose(hessum,numsum,atol=0.2), "Laplace approximation using numerical_parameter_hessian()=%0.4f not equal to numerical grid sum=%0.4f" % (hessum,numsum)
+
+#Test numerical_parameter_hessian gives us the right integral for a more complex GP model
+#sample data
+X = np.arange(0,40,1)[:,None]
+Y = np.sin(X/5)+np.random.randn(X.shape[0],X.shape[1])*0.1
+k = GPy.kern.RBF(1)
+
+#create model and optimise
+m2 = GPy.models.GPRegression(X,Y,k)
+m2.Gaussian_noise.fix(0.5)
+m2.optimize()
+
+m2.numerical_parameter_hessian()
+
+dims = 2 #equals the number of unfixed parameters
+stepsize=0.2
+ls = find_likes(m2,stepsize,rangemin=0.0001,rangemax=20)
+numsum = ls*(stepsize**dims)
+m2.optimize()
+hes = m2.numerical_parameter_hessian()
+hessum = np.exp(m2.log_likelihood())*1/np.sqrt(np.linalg.det(1/(2*np.pi)*hes))
+assert np.isclose(hessum,numsum,atol=0,rtol=0.1), "Laplace approximation using numerical_parameter_hessian() not equal to numerical grid sum"