Merge branch 'devel' of github.com:SheffieldML/GPy into devel

GPy/core/model.py

@@ -66,7 +66,7 @@ class model(parameterised):
 
 
         # check constraints are okay
-        if isinstance(what, (priors.gamma, priors.log_Gaussian)):
+        if isinstance(what, (priors.gamma, priors.inverse_gamma, priors.log_Gaussian)):
             constrained_positive_indices = [i for i, t in zip(self.constrained_indices, self.constraints) if t.domain == 'positive']
             if len(constrained_positive_indices):
                 constrained_positive_indices = np.hstack(constrained_positive_indices)

GPy/core/parameterised.py

@@ -251,7 +251,18 @@ class parameterised(object):
 
     def _set_params_transformed(self, x):
         """ takes the vector x, which is then modified (by untying, reparameterising or inserting fixed values), and then call self._set_params"""
+        self._set_params(self._untransform_params(x))
 
+    def _untransform_params(self,x):
+        """
+        The transformation required for _set_params_transformed.
+
+        This moves the vector x seen by the optimiser (unconstrained) to the
+        valid parameter vector seen by the model
+
+        Note:
+          - This function is separate from _set_params_transformed for downstream flexibility
+        """
         # work out how many places are fixed, and where they are. tricky logic!
         fix_places = self.fixed_indices + [t[1:] for t in self.tied_indices]
         if len(fix_places):
@@ -272,7 +283,8 @@ class parameterised(object):
         [np.put(xx,i,t.f(xx[i])) for i,t in zip(self.constrained_indices, self.constraints)]
         if hasattr(self,'debug'):
             stop
-        self._set_params(xx)
+
+        return xx
 
     def _get_param_names_transformed(self):
         """

GPy/core/priors.py

@@ -26,7 +26,6 @@ class Gaussian(prior):
     :param mu: mean
     :param sigma: standard deviation
 
-
     .. Note:: Bishop 2006 notation is used throughout the code
 
     """
@@ -144,7 +143,6 @@ def gamma_from_EV(E,V):
     b = E/V
     return gamma(a,b)
 
-
 class gamma(prior):
     """
     Implementation of the Gamma probability function, coupled with random variables.
@@ -155,7 +153,6 @@ class gamma(prior):
     .. Note:: Bishop 2006 notation is used throughout the code
 
     """
-    
     def __init__(self,a,b):
         self.a = float(a)
         self.b = float(b)
@@ -183,3 +180,30 @@ class gamma(prior):
 
     def rvs(self,n):
         return np.random.gamma(scale=1./self.b,shape=self.a,size=n)
+
+class inverse_gamma(prior):
+    """
+    Implementation of the inverse-Gamma probability function, coupled with random variables.
+
+    :param a: shape parameter
+    :param b: rate parameter (warning: it's the *inverse* of the scale)
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    def __init__(self,a,b):
+        self.a = float(a)
+        self.b = float(b)
+        self.constant = -gammaln(self.a) + a*np.log(b)
+
+    def __str__(self):
+        return "iGa("+str(np.round(self.a))+', '+str(np.round(self.b))+')'
+
+    def lnpdf(self,x):
+        return self.constant - (self.a+1)*np.log(x) - self.b/x
+
+    def lnpdf_grad(self,x):
+        return -(self.a+1.)/x + self.b/x**2
+
+    def rvs(self,n):
+        return 1./np.random.gamma(scale=1./self.b,shape=self.a,size=n)

GPy/core/transformations.py

@@ -39,8 +39,8 @@ class logexp(transformation):
         return '(+ve)'
 
 class logexp_clipped(transformation):
-    max_bound = 1e300
+    max_bound = 1e250
-    min_bound = 1e-10
+    min_bound = 1e-9
     log_max_bound = np.log(max_bound)
     log_min_bound = np.log(min_bound)
     def __init__(self, lower=1e-6):
@@ -49,11 +49,13 @@ class logexp_clipped(transformation):
     def f(self, x):
         exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound))
         f = np.log(1. + exp)
+        if np.isnan(f).any():
+            import ipdb;ipdb.set_trace()
         return f
     def finv(self, f):
         return np.log(np.exp(np.clip(f, self.min_bound, self.max_bound)) - 1.)
     def gradfactor(self, f):
-        ef = np.exp(f)
+        ef = np.exp(f) # np.clip(f, self.min_bound, self.max_bound))
         gf = (ef - 1.) / ef
         return np.where(f < self.lower, 0, gf)
     def initialize(self, f):

GPy/examples/classification.py

@@ -9,8 +9,8 @@ import pylab as pb
 import numpy as np
 import GPy
 
-default_seed=10000
+default_seed = 10000
-def crescent_data(seed=default_seed): #FIXME
+def crescent_data(seed=default_seed): # FIXME
     """Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
 
     :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
@@ -27,10 +27,10 @@ def crescent_data(seed=default_seed): #FIXME
 
     # Likelihood object
     distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(data['Y'],distribution)
+    likelihood = GPy.likelihoods.EP(data['Y'], distribution)
 
 
-    m = GPy.models.GP(data['X'],likelihood,kernel)
+    m = GPy.models.GP(data['X'], likelihood, kernel)
     m.ensure_default_constraints()
 
     m.update_likelihood_approximation()
@@ -54,10 +54,10 @@ def oil():
 
     # Likelihood object
     distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(data['Y'][:, 0:1],distribution)
+    likelihood = GPy.likelihoods.EP(data['Y'][:, 0:1], distribution)
 
     # Create GP model
-    m = GPy.models.GP(data['X'],likelihood=likelihood,kernel=kernel)
+    m = GPy.models.GP(data['X'], likelihood=likelihood, kernel=kernel)
 
     # Contrain all parameters to be positive
     m.constrain_positive('')
@@ -85,17 +85,17 @@ def toy_linear_1d_classification(seed=default_seed):
 
     # Likelihood object
     distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(Y,distribution)
+    likelihood = GPy.likelihoods.EP(Y, distribution)
 
     # Model definition
-    m = GPy.models.GP(data['X'],likelihood=likelihood,kernel=kernel)
+    m = GPy.models.GP(data['X'], likelihood=likelihood, kernel=kernel)
     m.ensure_default_constraints()
 
     # Optimize
     m.update_likelihood_approximation()
     # Parameters optimization:
     m.optimize()
-    #m.pseudo_EM() #FIXME
+    # m.pseudo_EM() #FIXME
 
     # Plot
     pb.subplot(211)
@@ -121,20 +121,20 @@ def sparse_toy_linear_1d_classification(seed=default_seed):
 
     # Likelihood object
     distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(Y,distribution)
+    likelihood = GPy.likelihoods.EP(Y, distribution)
 
-    Z = np.random.uniform(data['X'].min(),data['X'].max(),(10,1))
+    Z = np.random.uniform(data['X'].min(), data['X'].max(), (10, 1))
 
     # Model definition
-    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z,normalize_X=False)
+    m = GPy.models.sparse_GP(data['X'], likelihood=likelihood, kernel=kernel, Z=Z, normalize_X=False)
-    m.set('len',2.)
+    m.set('len', 2.)
 
     m.ensure_default_constraints()
     # Optimize
     m.update_likelihood_approximation()
     # Parameters optimization:
     m.optimize()
-    #m.EPEM() #FIXME
+    # m.EPEM() #FIXME
 
     # Plot
     pb.subplot(211)
@@ -162,15 +162,15 @@ def sparse_crescent_data(inducing=10, seed=default_seed):
 
     # Likelihood object
     distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(data['Y'],distribution)
+    likelihood = GPy.likelihoods.EP(data['Y'], distribution)
 
-    sample = np.random.randint(0,data['X'].shape[0],inducing)
+    sample = np.random.randint(0, data['X'].shape[0], inducing)
-    Z = data['X'][sample,:]
+    Z = data['X'][sample, :]
 
     # create sparse GP EP model
-    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+    m = GPy.models.sparse_GP(data['X'], likelihood=likelihood, kernel=kernel, Z=Z)
     m.ensure_default_constraints()
-    m.set('len',10.)
+    m.set('len', 10.)
 
     m.update_likelihood_approximation()
 

GPy/examples/dimensionality_reduction.py

@@ -17,11 +17,11 @@ def BGPLVM(seed=default_seed):
     D = 4
     # generate GPLVM-like data
     X = np.random.rand(N, Q)
-    k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
+    k = GPy.kern.rbf(Q)  + GPy.kern.white(Q, 0.00001)
     K = k.K(X)
     Y = np.random.multivariate_normal(np.zeros(N), K, D).T
 
-    k = GPy.kern.linear(Q, ARD=True) + GPy.kern.white(Q)
+    k = GPy.kern.rbf(Q, ARD=True) + GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True)  + GPy.kern.white(Q)
     # k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
     # k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
     # k = GPy.kern.rbf(Q, ARD = False)  + GPy.kern.white(Q, 0.00001)
@@ -118,9 +118,9 @@ def swiss_roll(optimize=True, N=1000, M=15, Q=4, sigma=.2, plot=False):
     return m
 
 def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k):
+    np.random.seed(0)
     data = GPy.util.datasets.oil()
     from GPy.core.transformations import logexp_clipped
-    np.random.seed(0)
 
     # create simple GP model
     kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
@@ -131,8 +131,7 @@ def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k)
     m = GPy.models.Bayesian_GPLVM(Yn, Q, kernel=kernel, M=M, **k)
     m.data_labels = data['Y'][:N].argmax(axis=1)
 
-#     m.constrain('variance', logexp_clipped())
+    m.constrain('variance|leng', logexp_clipped())
-#     m.constrain('length', logexp_clipped())
     m['lengt'] = m.X.var(0).max() / m.X.var(0)
     m['noise'] = Yn.var() / 100.
 
@@ -140,10 +139,6 @@ def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k)
 
     # optimize
     if optimize:
-#         m.unconstrain('noise'); m.constrain_fixed('noise')
-#         m.optimize('scg', messages=1, max_f_eval=200)
-#         m.unconstrain('noise')
-#         m.constrain('noise', logexp_clipped())
         m.optimize('scg', messages=1, max_f_eval=max_f_eval)
 
     if plot:
@@ -155,11 +150,6 @@ def BGPLVM_oil(optimize=True, N=100, Q=5, M=25, max_f_eval=4e3, plot=False, **k)
         lvm_visualizer = GPy.util.visualize.lvm_dimselect(m.X[0, :].copy(), m, data_show, latent_axes=latent_axes) # , sense_axes=sense_axes)
         raw_input('Press enter to finish')
         plt.close('all')
-    # # plot
-    # print(m)
-    # m.plot_latent(labels=m.data_labels)
-    # pb.figure()
-    # pb.bar(np.arange(m.kern.D), 1. / m.input_sensitivity())
     return m
 
 def oil_100():
@@ -189,15 +179,6 @@ def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
     s3 = s3(x)
     sS = sS(x)
 
-#     s1 -= s1.mean()
-#     s2 -= s2.mean()
-#     s3 -= s3.mean()
-#     sS -= sS.mean()
-#     s1 /= .5 * (np.abs(s1).max() - np.abs(s1).min())
-#     s2 /= .5 * (np.abs(s2).max() - np.abs(s2).min())
-#     s3 /= .5 * (np.abs(s3).max() - np.abs(s3).min())
-#     sS /= .5 * (np.abs(sS).max() - np.abs(sS).min())
-
     S1 = np.hstack([s1, sS])
     S2 = np.hstack([s2, sS])
     S3 = np.hstack([s3, sS])
@@ -217,16 +198,17 @@ def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
     Y2 /= Y2.std(0)
     Y3 /= Y3.std(0)
 
-    slist = [s1, s2, s3, sS]
+    slist = [sS, s1, s2, s3]
+    slist_names = ["sS", "s1", "s2", "s3"]
     Ylist = [Y1, Y2, Y3]
 
     if plot_sim:
         import pylab
         import itertools
-        fig = pylab.figure("MRD Simulation", figsize=(8, 6))
+        fig = pylab.figure("MRD Simulation Data", figsize=(8, 6))
         fig.clf()
         ax = fig.add_subplot(2, 1, 1)
-        labls = sorted(filter(lambda x: x.startswith("s"), locals()))
+        labls = slist_names
         for S, lab in itertools.izip(slist, labls):
             ax.plot(S, label=lab)
         ax.legend()
@@ -250,7 +232,6 @@ def bgplvm_simulation_matlab_compare():
     from GPy.models import mrd
     from GPy import kern
     reload(mrd); reload(kern)
-    # k = kern.rbf(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
     k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
     m = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k,
 #                        X=mu,
@@ -260,26 +241,14 @@ def bgplvm_simulation_matlab_compare():
     m.auto_scale_factor = True
     m['noise'] = Y.var() / 100.
     m['linear_variance'] = .01
-
-#     lscstr = 'X_variance'
-#     m[lscstr] = .01
-#     m.unconstrain(lscstr); m.constrain_fixed(lscstr, .1)
-
-#     cstr = 'white'
-#     m.unconstrain(cstr); m.constrain_bounded(cstr, .01, 1.)
-
-#     cstr = 'noise'
-#     m.unconstrain(cstr); m.constrain_bounded(cstr, .01, 1.)
     return m
 
-def bgplvm_simulation(burnin='scg', plot_sim=False,
+def bgplvm_simulation(optimize='scg',
-                      max_burnin=100, true_X=False,
+                      plot=True,
-                      do_opt=True,
+                      max_f_eval=2e4):
-                      max_f_eval=1000):
     from GPy.core.transformations import logexp_clipped
-
+    D1, D2, D3, N, M, Q = 15, 8, 8, 100, 3, 5
-    D1, D2, D3, N, M, Q = 15, 8, 8, 350, 3, 6
+    slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot)
-    slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim)
 
     from GPy.models import mrd
     from GPy import kern
@@ -289,95 +258,23 @@ def bgplvm_simulation(burnin='scg', plot_sim=False,
     Y = Ylist[0]
 
     k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q)
-#     k = kern.white(Q, .00001) + kern.bias(Q)
     m = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k, _debug=True)
-    # m.set('noise',)
+    m.constrain('variance|noise', logexp_clipped())
-    m.constrain('variance', logexp_clipped())
+#     m.ensure_default_constraints()
-
-    m.ensure_default_constraints()
     m['noise'] = Y.var() / 100.
-    m['linear_variance'] = .001
+    m['linear_variance'] = .01
-#     m.auto_scale_factor = True
-#     m.scale_factor = 1.
 
-
+    if optimize:
-    if burnin:
+        print "Optimizing model:"
-        print "initializing beta"
+        m.optimize('scg', max_iters=max_f_eval, max_f_eval=max_f_eval, messages=True)
-        cstr = "noise"
+    if plot:
-        m.unconstrain(cstr); m.constrain_fixed(cstr, Y.var() / 70.)
+        import pylab
-        m.optimize(burnin, messages=1, max_f_eval=max_burnin)
+        m.plot_X_1d()
-
+        pylab.figure(); pylab.axis(); m.kern.plot_ARD()
-        print "releasing beta"
-        cstr = "noise"
-        m.unconstrain(cstr);  m.constrain_positive(cstr)
-
-    if true_X:
-        true_X = np.hstack((slist[0], slist[3], 0. * np.ones((N, Q - 2))))
-        m.set('X_\d', true_X)
-        m.constrain_fixed("X_\d")
-
-        cstr = 'X_variance'
-#         m.unconstrain(cstr), m.constrain_fixed(cstr, .0001)
-        m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-7, .1)
-
-#     cstr = 'X_variance'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-3, 1.)
-
-    # m['X_var'] = np.ones(N * Q) * .5 + np.random.randn(N * Q) * .01
-
-#     cstr = "iip"
-#     m.unconstrain(cstr); m.constrain_fixed(cstr)
-
-#     cstr = 'variance'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 1.)
-#     cstr = 'X_\d'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, -10., 10.)
-#
-#     cstr = 'noise'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-5, 1.)
-#
-#     cstr = 'white'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-6, 1.)
-#
-#     cstr = 'linear_variance'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 10.)
-
-#     cstr = 'variance'
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 10.)
-
-#     np.seterr(all='call')
-#     def ipdbonerr(errtype, flags):
-#         import ipdb; ipdb.set_trace()
-#     np.seterrcall(ipdbonerr)
-
-    if do_opt and burnin:
-        try:
-            m.optimize(burnin, messages=1, max_f_eval=max_f_eval)
-        except:
-            pass
-        finally:
-            return m
     return m
 
-def mrd_simulation(plot_sim=False):
+def mrd_simulation(optimize=True, plot_sim=False):
-    # num = 2
+    D1, D2, D3, N, M, Q = 150, 250, 30, 300, 3, 7
-#     ard1 = np.array([1., 1, 0, 0], dtype=float)
-#     ard2 = np.array([0., 1, 1, 0], dtype=float)
-#     ard1[ard1 == 0] = 1E-10
-#     ard2[ard2 == 0] = 1E-10
-
-#     ard1i = 1. / ard1
-#     ard2i = 1. / ard2
-
-#     k = GPy.kern.rbf(Q, ARD=True, lengthscale=ard1i) + GPy.kern.bias(Q, 0) + GPy.kern.white(Q, 0.0001)
-#     Y1 = np.random.multivariate_normal(np.zeros(N), k.K(X), D1).T
-#     Y1 -= Y1.mean(0)
-#
-#     k = GPy.kern.rbf(Q, ARD=True, lengthscale=ard2i) + GPy.kern.bias(Q, 0) + GPy.kern.white(Q, 0.0001)
-#     Y2 = np.random.multivariate_normal(np.zeros(N), k.K(X), D2).T
-#     Y2 -= Y2.mean(0)
-#     make_params = lambda ard: np.hstack([[1], ard, [1, .3]])
-    D1, D2, D3, N, M, Q = 150, 250, 300, 700, 3, 7
     slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim)
 
     from GPy.models import mrd
@@ -386,50 +283,23 @@ def mrd_simulation(plot_sim=False):
 
     reload(mrd); reload(kern)
 
-#    k = kern.rbf(2, ARD=True) + kern.bias(2) + kern.white(2)
-#     Y1 = np.random.multivariate_normal(np.zeros(N), k.K(S1), D1).T
-#     Y2 = np.random.multivariate_normal(np.zeros(N), k.K(S2), D2).T
-#     Y3 = np.random.multivariate_normal(np.zeros(N), k.K(S3), D3).T
-
-#     Ylist = Ylist[0:2]
-
-    # k = kern.rbf(Q, ARD=True) + kern.bias(Q) + kern.white(Q)
-
     k = kern.linear(Q, [0.01] * Q, True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
-    m = mrd.MRD(*Ylist, Q=Q, M=M, kernel=k, initx="concat", initz='permute', _debug=False)
+    m = mrd.MRD(*Ylist, Q=Q, M=M, kernel=k, initx="concat", initz='permute')
 
     for i, Y in enumerate(Ylist):
         m['{}_noise'.format(i + 1)] = Y.var() / 100.
 
-    m.constrain('variance', logexp_clipped())
+    m.constrain('variance|noise', logexp_clipped())
     m.ensure_default_constraints()
-#     m.auto_scale_factor = True
 
-#     cstr = 'variance'
+    # DEBUG
-#     m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-12, 1.)
+    np.seterr("raise")
-#
-#     cstr = 'linear_variance'
-#     m.unconstrain(cstr), m.constrain_positive(cstr)
 
-    print "initializing beta"
+    if optimize:
-    cstr = "noise"
+        print "Optimizing Model:"
-    m.unconstrain(cstr); m.constrain_fixed(cstr)
+        m.optimize('scg', messages=1, max_iters=3e3)
-    m.optimize('scg', messages=1, max_f_eval=2e3, gtol=100)
 
-    print "releasing beta"
+    return m
-    cstr = "noise"
-    m.unconstrain(cstr);  m.constrain(cstr, logexp_clipped())
-
-#     np.seterr(all='call')
-#     def ipdbonerr(errtype, flags):
-#         import ipdb; ipdb.set_trace()
-#     np.seterrcall(ipdbonerr)
-
-    return m # , mtest
-
-def mrd_silhouette():
-
-    pass
 
 def brendan_faces():
     from GPy import kern

GPy/inference/SCG.py

@@ -36,8 +36,14 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
     Returns
     x the optimal value for x
     flog : a list of all the objective values
-
+    function_eval number of fn evaluations
+    status: string describing convergence status
     """
+    
+    if display:
+        print "  SCG"
+        print ' {0:{mi}s}   {1:11s}    {2:11s}    {3:11s}'.format("I", "F", "Scale", "|g|", mi=len(str(maxiters)))
+
     if xtol is None:
         xtol = 1e-6
     if ftol is None:
@@ -45,18 +51,18 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
     if gtol is None:
         gtol = 1e-5
     sigma0 = 1.0e-4
-    fold = f(x, *optargs)  # Initial function value.
+    fold = f(x, *optargs) # Initial function value.
     function_eval = 1
     fnow = fold
-    gradnew = gradf(x, *optargs)  # Initial gradient.
+    gradnew = gradf(x, *optargs) # Initial gradient.
     current_grad = np.dot(gradnew, gradnew)
     gradold = gradnew.copy()
-    d = -gradnew  # Initial search direction.
+    d = -gradnew # Initial search direction.
-    success = True  # Force calculation of directional derivs.
+    success = True # Force calculation of directional derivs.
-    nsuccess = 0  # nsuccess counts number of successes.
+    nsuccess = 0 # nsuccess counts number of successes.
-    beta = 1.0  # Initial scale parameter.
+    beta = 1.0 # Initial scale parameter.
-    betamin = 1.0e-15  # Lower bound on scale.
+    betamin = 1.0e-15 # Lower bound on scale.
-    betamax = 1.0e100  # Upper bound on scale.
+    betamax = 1.0e100 # Upper bound on scale.
     status = "Not converged"
 
     flog = [fold]
@@ -106,12 +112,12 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
             fnow = fold
 
         # Store relevant variables
-        flog.append(fnow)  # Current function value
+        flog.append(fnow) # Current function value
 
         iteration += 1
         if display:
             print '\r',
-            print 'Iter: {0:>0{mi}g}  Obj:{1:> 12e}  Scale:{2:> 12e}  |g|:{3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len(str(maxiters))),
+            print '{0:>0{mi}g}  {1:> 12e}  {2:> 12e}  {3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len(str(maxiters))),
             # print 'Iteration:', iteration, ' Objective:', fnow, '  Scale:', beta, '\r',
             sys.stdout.flush()
 
@@ -153,5 +159,6 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
         # iterations.
         status = "maxiter exceeded"
 
-    print ""
+    if display:
+        print ""
     return x, flog, function_eval, status

GPy/inference/SGD.py

@@ -18,7 +18,7 @@ class opt_SGD(Optimizer):
 
     """
 
-    def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, **kwargs):
+    def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, learning_rate_adaptation=None, **kwargs):
         self.opt_name = "Stochastic Gradient Descent"
 
         self.model = model
@@ -33,6 +33,13 @@ class opt_SGD(Optimizer):
         self.center = center
         self.param_traces = [('noise',[])]
         self.iteration_file = iteration_file
+        self.learning_rate_adaptation = learning_rate_adaptation
+        if self.learning_rate_adaptation != None:
+            if self.learning_rate_adaptation == 'annealing':
+                self.learning_rate_0 = self.learning_rate
+            else:
+                self.learning_rate_0 = self.learning_rate.mean()
+
         # if len([p for p in self.model.kern.parts if p.name == 'bias']) == 1:
         #     self.param_traces.append(('bias',[]))
         # if len([p for p in self.model.kern.parts if p.name == 'linear']) == 1:
@@ -204,6 +211,7 @@ class opt_SGD(Optimizer):
 
         ci = self.shift_constraints(j)
         f, fp = f_fp(self.x_opt[j])
+
         step[j] = self.momentum * step[j] + self.learning_rate[j] * fp
         self.x_opt[j] -= step[j]
         self.restore_constraints(ci)
@@ -216,9 +224,53 @@ class opt_SGD(Optimizer):
 
         return f, step, self.model.N
 
+    def adapt_learning_rate(self, t):
+        if self.learning_rate_adaptation == 'adagrad':
+            if t > 5:
+                g = np.array(self.grads)
+                l2_g = np.sqrt(np.square(g).sum(0))
+                self.learning_rate = 0.001/l2_g
+            else:
+                self.learning_rate = np.zeros_like(self.learning_rate)
+        elif self.learning_rate_adaptation == 'annealing':
+            self.learning_rate = self.learning_rate_0/(1+float(t+1)/10)
+        elif self.learning_rate_adaptation == 'semi_pesky':
+            if self.model.__class__.__name__ == 'Bayesian_GPLVM':
+                if t == 0:
+                    N = self.model.N
+                    Q = self.model.Q
+                    M = self.model.M
+
+                    iip_pos = np.arange(2*N*Q,2*N*Q+M*Q)
+                    mu_pos = np.arange(0,N*Q)
+                    S_pos = np.arange(N*Q,2*N*Q)
+                    self.vbparam_dict = {'iip': [iip_pos],
+                                         'mu': [mu_pos],
+                                         'S': [S_pos]}
+
+                    for k in self.vbparam_dict.keys():
+                        hbar_t = 0.0
+                        tau_t = 1000.0
+                        gbar_t = 0.0
+                        self.vbparam_dict[k].append(hbar_t)
+                        self.vbparam_dict[k].append(tau_t)
+                        self.vbparam_dict[k].append(gbar_t)
+                        
+            g_t = self.model.grads
+
+            for k in self.vbparam_dict.keys():
+                pos, hbar_t, tau_t, gbar_t = self.vbparam_dict[k]
+
+                gbar_t = (1-1/tau_t)*gbar_t + 1/tau_t * g_t[pos]
+                hbar_t = (1-1/tau_t)*hbar_t + 1/tau_t * np.dot(g_t[pos].T, g_t[pos])
+                self.learning_rate[pos] = np.dot(gbar_t.T, gbar_t) / hbar_t
+                tau_t = tau_t*(1-self.learning_rate[pos]) + 1
+                self.vbparam_dict[k] = [pos, hbar_t, tau_t, gbar_t]
+
+
     def opt(self, f_fp=None, f=None, fp=None):
         self.x_opt = self.model._get_params_transformed()
-        self.model.grads = np.zeros_like(self.x_opt)
+        self.grads = []
 
         X, Y = self.model.X.copy(), self.model.likelihood.Y.copy()
 
@@ -235,6 +287,7 @@ class opt_SGD(Optimizer):
 
         step = np.zeros_like(num_params)
         for it in range(self.iterations):
+            self.model.grads = np.zeros_like(self.x_opt) # TODO this is ugly
 
             if it == 0 or self.self_paced is False:
                 features = np.random.permutation(Y.shape[1])
@@ -272,16 +325,17 @@ class opt_SGD(Optimizer):
                     sys.stdout.write(status)
                     sys.stdout.flush()
                     self.param_traces['noise'].append(noise)
-                NLL.append(f)
 
-                self.fopt_trace.append(f)
+                NLL.append(f)
+                self.fopt_trace.append(NLL[-1])
                 # fig = plt.figure('traces')
                 # plt.clf()
                 # plt.plot(self.param_traces['noise'])
 
                 # for k in self.param_traces.keys():
                 #     self.param_traces[k].append(self.model.get(k)[0])
-
+            self.grads.append(self.model.grads.tolist())
+            self.adapt_learning_rate(it)
             # should really be a sum(), but earlier samples in the iteration will have a very crappy ll
             self.f_opt = np.mean(NLL)
             self.model.N = N
@@ -293,7 +347,7 @@ class opt_SGD(Optimizer):
             sigma = self.model.likelihood._variance
             self.model.likelihood._variance = None # invalidate cache
             self.model.likelihood._set_params(sigma)
-            
+
             self.trace.append(self.f_opt)
             if self.iteration_file is not None:
                 f = open(self.iteration_file + "iteration%d.pickle" % it, 'w')
@@ -303,6 +357,6 @@ class opt_SGD(Optimizer):
 
             if self.messages != 0:
                 sys.stdout.write('\r' + ' '*len(status)*2 + '  \r')
-                status = "SGD Iteration: {0: 3d}/{1: 3d}  f: {2: 2.3f}\n".format(it+1, self.iterations, self.f_opt)
+                status = "SGD Iteration: {0: 3d}/{1: 3d}  f: {2: 2.3f}   max eta: {3: 1.5f}\n".format(it+1, self.iterations, self.f_opt, self.learning_rate.max())
                 sys.stdout.write(status)
                 sys.stdout.flush()

GPy/kern/bias.py

@@ -55,8 +55,9 @@ class bias(kernpart):
         target += self.variance
 
     def psi1(self, Z, mu, S, target):
-        target += self.variance
+        self._psi1 = self.variance
-
+        target += self._psi1
+        
     def psi2(self, Z, mu, S, target):
         target += self.variance**2
 

GPy/kern/kern.py

@@ -315,31 +315,20 @@ class kern(parameterised):
 
         # compute the "cross" terms
         # TODO: input_slices needed
+        crossterms = 0
+
         for p1, p2 in itertools.combinations(self.parts, 2):
-            # white doesn;t combine with anything
+
-            if p1.name == 'white' or p2.name == 'white':
+            # TODO psi1 this must be faster/better/precached/more nice
-                pass
+            tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
-            # rbf X bias
+            p1.psi1(Z, mu, S, tmp1)
-            elif p1.name == 'bias' and p2.name == 'rbf':
+            tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
-                target += p1.variance * (p2._psi1[:, :, None] + p2._psi1[:, None, :])
+            p2.psi1(Z, mu, S, tmp2)
-            elif p2.name == 'bias' and p1.name == 'rbf':
+
-                target += p2.variance * (p1._psi1[:, :, None] + p1._psi1[:, None, :])
+            prod = np.multiply(tmp1, tmp2)
-            # linear X bias
+            crossterms += prod[:,:,None] + prod[:, None, :]
-            elif p1.name == 'bias' and p2.name == 'linear':
+            
-                tmp = np.zeros((mu.shape[0], Z.shape[0]))
+        target += crossterms
-                p2.psi1(Z, mu, S, tmp)
-                target += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
-            elif p2.name == 'bias' and p1.name == 'linear':
-                tmp = np.zeros((mu.shape[0], Z.shape[0]))
-                p1.psi1(Z, mu, S, tmp)
-                target += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
-            # rbf X linear
-            elif p1.name == 'linear' and p2.name == 'rbf':
-                raise NotImplementedError # TODO
-            elif p2.name == 'linear' and p1.name == 'rbf':
-                raise NotImplementedError # TODO
-            else:
-                raise NotImplementedError, "psi2 cannot be computed for this kernel"
         return target
 
     def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
@@ -348,71 +337,34 @@ class kern(parameterised):
 
         # compute the "cross" terms
         # TODO: better looping, input_slices
-        for i1, i2 in itertools.combinations(range(len(self.parts)), 2):
+        for i1, i2 in itertools.permutations(range(len(self.parts)), 2):
             p1, p2 = self.parts[i1], self.parts[i2]
 #             ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
             ps1, ps2 = self.param_slices[i1], self.param_slices[i2]
 
-            # white doesn;t combine with anything
+            tmp = np.zeros((mu.shape[0], Z.shape[0]))
-            if p1.name == 'white' or p2.name == 'white':
+            p1.psi1(Z, mu, S, tmp)
-                pass
+            p2.dpsi1_dtheta((tmp[:,None,:]*dL_dpsi2).sum(1)*2., Z, mu, S, target[ps2])
-            # rbf X bias
-            elif p1.name == 'bias' and p2.name == 'rbf':
-                p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2])
-                p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2._psi1 * 2., Z, mu, S, target[ps1])
-            elif p2.name == 'bias' and p1.name == 'rbf':
-                p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
-                p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1._psi1 * 2., Z, mu, S, target[ps2])
-            # linear X bias
-            elif p1.name == 'bias' and p2.name == 'linear':
-                p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) # [ps1])
-                psi1 = np.zeros((mu.shape[0], Z.shape[0]))
-                p2.psi1(Z, mu, S, psi1)
-                p1.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps1])
-            elif p2.name == 'bias' and p1.name == 'linear':
-                p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
-                psi1 = np.zeros((mu.shape[0], Z.shape[0]))
-                p1.psi1(Z, mu, S, psi1)
-                p2.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps2])
-            # rbf X linear
-            elif p1.name == 'linear' and p2.name == 'rbf':
-                raise NotImplementedError # TODO
-            elif p2.name == 'linear' and p1.name == 'rbf':
-                raise NotImplementedError # TODO
-            else:
-                raise NotImplementedError, "psi2 cannot be computed for this kernel"
 
         return self._transform_gradients(target)
 
     def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
         target = np.zeros_like(Z)
         [p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
+        #target *= 2
 
         # compute the "cross" terms
         # TODO: we need input_slices here.
-        for p1, p2 in itertools.combinations(self.parts, 2):
+        for p1, p2 in itertools.permutations(self.parts, 2):
-            # white doesn;t combine with anything
+            if p1.name == 'linear' and p2.name == 'linear':
-            if p1.name == 'white' or p2.name == 'white':
+                raise NotImplementedError("We don't handle linear/linear cross-terms")
-                pass
+            tmp = np.zeros((mu.shape[0], Z.shape[0]))
-            # rbf X bias
+            p1.psi1(Z, mu, S, tmp)
-            elif p1.name == 'bias' and p2.name == 'rbf':
+            tmp2 = np.zeros_like(target)
-                p2.dpsi1_dX(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
+            p2.dpsi1_dZ((tmp[:,None,:]*dL_dpsi2).sum(1).T, Z, mu, S, tmp2)
-            elif p2.name == 'bias' and p1.name == 'rbf':
+            target += tmp2
-                p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
-            # linear X bias
-            elif p1.name == 'bias' and p2.name == 'linear':
-                p2.dpsi1_dZ(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
-            elif p2.name == 'bias' and p1.name == 'linear':
-                p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
-            # rbf X linear
-            elif p1.name == 'linear' and p2.name == 'rbf':
-                raise NotImplementedError # TODO
-            elif p2.name == 'linear' and p1.name == 'rbf':
-                raise NotImplementedError # TODO
-            else:
-                raise NotImplementedError, "psi2 cannot be computed for this kernel"
 
-        return target * 2.
+        return target * 2
 
     def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S):
         target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
@@ -420,27 +372,13 @@ class kern(parameterised):
 
         # compute the "cross" terms
         # TODO: we need input_slices here.
-        for p1, p2 in itertools.combinations(self.parts, 2):
+        for p1, p2 in itertools.permutations(self.parts, 2):
-            # white doesn;t combine with anything
+            if p1.name == 'linear' and p2.name == 'linear':
-            if p1.name == 'white' or p2.name == 'white':
+                raise NotImplementedError("We don't handle linear/linear cross-terms")
-                pass
+
-            # rbf X bias
+            tmp = np.zeros((mu.shape[0], Z.shape[0]))
-            elif p1.name == 'bias' and p2.name == 'rbf':
+            p1.psi1(Z, mu, S, tmp)
-                p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
+            p2.dpsi1_dmuS((tmp[:,None,:]*dL_dpsi2).sum(1).T*2., Z, mu, S, target_mu, target_S)
-            elif p2.name == 'bias' and p1.name == 'rbf':
-                p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
-            # linear X bias
-            elif p1.name == 'bias' and p2.name == 'linear':
-                p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
-            elif p2.name == 'bias' and p1.name == 'linear':
-                p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
-            # rbf X linear
-            elif p1.name == 'linear' and p2.name == 'rbf':
-                raise NotImplementedError # TODO
-            elif p2.name == 'linear' and p1.name == 'rbf':
-                raise NotImplementedError # TODO
-            else:
-                raise NotImplementedError, "psi2 cannot be computed for this kernel"
 
         return target_mu, target_S
 

GPy/kern/kernpart.py

@@ -54,5 +54,3 @@ class kernpart(object):
         raise NotImplementedError
     def dK_dX(self,X,X2,target):
         raise NotImplementedError
-
-

GPy/kern/white.py

@@ -18,7 +18,8 @@ class white(kernpart):
         self.Nparam = 1
         self.name = 'white'
         self._set_params(np.array([variance]).flatten())
-
+        self._psi1 = 0 # TODO: more elegance here
+        
     def _get_params(self):
         return self.variance
 
@@ -81,4 +82,3 @@ class white(kernpart):
 
     def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
         pass
-

GPy/likelihoods/Gaussian.py

@@ -69,6 +69,7 @@ class Gaussian(likelihood):
                 # Note. for D>1, we need to re-normalise all the outputs independently.
                 # This will mess up computations of diag(true_var), below.
                 # note that the upper, lower quantiles should be the same shape as mean
+            # Augment the output variance with the likelihood variance and rescale.
             true_var = (var + np.eye(var.shape[0]) * self._variance) * self._scale ** 2
             _5pc = mean - 2.*np.sqrt(np.diag(true_var))
             _95pc = mean + 2.*np.sqrt(np.diag(true_var))

GPy/models/Bayesian_GPLVM.py

@@ -171,9 +171,6 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
         self.dbound_dZtheta = sparse_GP._log_likelihood_gradients(self)
         return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta))
 
-    def _log_likelihood_normal_gradients(self):
-        Si, _, _, _ = pdinv(self.X_variance)
-
     def plot_latent(self, which_indices=None, *args, **kwargs):
 
         if which_indices is None:
@@ -208,23 +205,25 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
         else:
             colors = iter(colors)
         plots = []
+        x = np.arange(self.X.shape[0])
         for i in range(self.X.shape[1]):
             if axes is None:
                 ax = fig.add_subplot(self.X.shape[1], 1, i + 1)
             else:
                 ax = axes[i]
             ax.plot(self.X, c='k', alpha=.3)
-            plots.extend(ax.plot(self.X.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i)))
+            plots.extend(ax.plot(x, self.X.T[i], c=colors.next(), label=r"$\mathbf{{X_{{{}}}}}$".format(i)))
-            ax.fill_between(np.arange(self.X.shape[0]),
+            ax.fill_between(x,
                             self.X.T[i] - 2 * np.sqrt(self.X_variance.T[i]),
                             self.X.T[i] + 2 * np.sqrt(self.X_variance.T[i]),
                             facecolor=plots[-1].get_color(),
                             alpha=.3)
             ax.legend(borderaxespad=0.)
+            ax.set_xlim(x.min(), x.max())
             if i < self.X.shape[1] - 1:
                 ax.set_xticklabels('')
         pylab.draw()
-        fig.tight_layout(h_pad=.01)  # , rect=(0, 0, 1, .95))
+        fig.tight_layout(h_pad=.01) # , rect=(0, 0, 1, .95))
         return fig
 
     def _debug_filter_params(self, x):
@@ -263,7 +262,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
         kllls = np.array(self._savedklll)
         LL, = ax1.plot(kllls[:, 0], kllls[:, 1] - kllls[:, 2], '-', label=r'$\log p(\mathbf{Y})$', mew=1.5)
         KL, = ax1.plot(kllls[:, 0], kllls[:, 2], '-', label=r'$\mathcal{KL}(p||q)$', mew=1.5)
-        L, = ax1.plot(kllls[:, 0], kllls[:, 1], '-', label=r'$L$', mew=1.5)  # \mathds{E}_{q(\mathbf{X})}[p(\mathbf{Y|X})\frac{p(\mathbf{X})}{q(\mathbf{X})}]
+        L, = ax1.plot(kllls[:, 0], kllls[:, 1], '-', label=r'$L$', mew=1.5) # \mathds{E}_{q(\mathbf{X})}[p(\mathbf{Y|X})\frac{p(\mathbf{X})}{q(\mathbf{X})}]
 
         param_dict = dict(self._savedparams)
         gradient_dict = dict(self._savedgradients)
@@ -411,7 +410,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
 
         # parameter changes
         # ax2 = pylab.subplot2grid((4, 1), (1, 0), 3, 1, projection='3d')
-        button_options = [0, 0]  # [0]: clicked -- [1]: dragged
+        button_options = [0, 0] # [0]: clicked -- [1]: dragged
 
         def update_plots(event):
             if button_options[0] and not button_options[1]:
@@ -483,4 +482,4 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
         cidp = figs[0].canvas.mpl_connect('button_press_event', onclick)
         cidd = figs[0].canvas.mpl_connect('motion_notify_event', motion)
 
-        return ax1, ax2, ax3, ax4, ax5  # , ax6, ax7
+        return ax1, ax2, ax3, ax4, ax5 # , ax6, ax7

GPy/models/sparse_GP.py

@@ -3,7 +3,7 @@
 
 import numpy as np
 import pylab as pb
-from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides
+from ..util.linalg import mdot, jitchol, tdot, symmetrify, backsub_both_sides,chol_inv
 from ..util.plot import gpplot
 from .. import kern
 from GP import GP
@@ -16,9 +16,9 @@ class sparse_GP(GP):
     :param X: inputs
     :type X: np.ndarray (N x Q)
     :param likelihood: a likelihood instance, containing the observed data
-    :type likelihood: GPy.likelihood.(Gaussian | EP)
+    :type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
-    :param kernel : the kernel/covariance function. See link kernels
+    :param kernel : the kernel (covariance function). See link kernels
-    :type kernel: a GPy kernel
+    :type kernel: a GPy.kern.kern instance
     :param X_variance: The uncertainty in the measurements of X (Gaussian variance)
     :type X_variance: np.ndarray (N x Q) | None
     :param Z: inducing inputs (optional, see note)
@@ -30,8 +30,6 @@ class sparse_GP(GP):
     """
 
     def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
-#         self.scale_factor = 100.0  # a scaling factor to help keep the algorithm stable
-#         self.auto_scale_factor = False
         self.Z = Z
         self.M = Z.shape[0]
         self.likelihood = likelihood
@@ -63,49 +61,29 @@ class sparse_GP(GP):
             self.psi2 = None
 
     def _computations(self):
-#         sf = self.scale_factor
-#         sf2 = sf ** 2
 
         # factor Kmm
         self.Lm = jitchol(self.Kmm)
 
         # The rather complex computations of self.A
-        if self.likelihood.is_heteroscedastic:
+        if self.has_uncertain_inputs:
-            assert self.likelihood.D == 1  # TODO: what if the likelihood is heterscedatic and there are multiple independent outputs?
+            if self.likelihood.is_heteroscedastic:
-            if self.has_uncertain_inputs:
+                psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
-#                 psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1) / sf2)).sum(0)
-                psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
-                evals, evecs = linalg.eigh(psi2_beta_scaled)
-                clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
-                if not np.allclose(evals, clipped_evals):
-                    print "Warning: clipping posterior eigenvalues"
-                tmp = evecs * np.sqrt(clipped_evals)
-                tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
-                self.A = tdot(tmp)
             else:
-#                 tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)) / sf)
+                psi2_beta = self.psi2.sum(0) * self.likelihood.precision
-                tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
+            evals, evecs = linalg.eigh(psi2_beta)
-                tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
+            clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
-                self.A = tdot(tmp)
+            tmp = evecs * np.sqrt(clipped_evals)
         else:
-            if self.has_uncertain_inputs:
+            if self.likelihood.is_heteroscedastic:
-#                 psi2_beta_scaled = (self.psi2 * (self.likelihood.precision / sf2)).sum(0)
+                tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
-                psi2_beta_scaled = (self.psi2 * (self.likelihood.precision)).sum(0)
-                evals, evecs = linalg.eigh(psi2_beta_scaled)
-                clipped_evals = np.clip(evals, 0., 1e15)  # TODO: make clipping configurable
-                if not np.allclose(evals, clipped_evals):
-                    print "Warning: clipping posterior eigenvalues"
-                tmp = evecs * np.sqrt(clipped_evals)
-                tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
-                self.A = tdot(tmp)
             else:
-                # tmp = self.psi1 * (np.sqrt(self.likelihood.precision) / sf)
                 tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
-                tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
+        tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
-                self.A = tdot(tmp)
+        self.A = tdot(tmp)
+
 
         # factor B
-#         self.B = np.eye(self.M) / sf2 + self.A
         self.B = np.eye(self.M) + self.A
         self.LB = jitchol(self.B)
 
@@ -121,8 +99,6 @@ class sparse_GP(GP):
         # Compute dL_dKmm
         tmp = tdot(self._LBi_Lmi_psi1V)
         self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
-#         tmp = -0.5 * self.DBi_plus_BiPBi / sf2
-#         tmp += -0.5 * self.B * sf2 * self.D
         tmp = -0.5 * self.DBi_plus_BiPBi
         tmp += -0.5 * self.B * self.D
         tmp += self.D * np.eye(self.M)
@@ -132,9 +108,10 @@ class sparse_GP(GP):
         self.dL_dpsi0 = -0.5 * self.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
         self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
         dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
+
         if self.likelihood.is_heteroscedastic:
             if self.has_uncertain_inputs:
-                self.dL_dpsi2 = self.likelihood.precision[:, None, None] * dL_dpsi2_beta[None, :, :]
+                self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
             else:
                 self.dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, self.psi1 * self.likelihood.precision.reshape(1, self.N))
                 self.dL_dpsi2 = None
@@ -158,7 +135,6 @@ class sparse_GP(GP):
         else:
             # likelihood is not heterscedatic
             self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
-            #  self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision * sf2)
             self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
             self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
 
@@ -166,16 +142,12 @@ class sparse_GP(GP):
 
     def log_likelihood(self):
         """ Compute the (lower bound on the) log marginal likelihood """
-#         sf2 = self.scale_factor ** 2
         if self.likelihood.is_heteroscedastic:
             A = -0.5 * self.N * self.D * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
-#             B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
             B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
         else:
             A = -0.5 * self.N * self.D * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
-#             B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
             B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
-#         C = -self.D * (np.sum(np.log(np.diag(self.LB))) + 0.5 * self.M * np.log(sf2))
         C = -self.D * (np.sum(np.log(np.diag(self.LB))))  # + 0.5 * self.M * np.log(sf2))
         D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
         return A + B + C + D
@@ -185,14 +157,6 @@ class sparse_GP(GP):
         self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
         self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
         self._compute_kernel_matrices()
-        # if self.auto_scale_factor:
-        #    self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
-        # if self.auto_scale_factor:
-            # if self.likelihood.is_heteroscedastic:
-                # self.scale_factor = max(100,np.sqrt(self.psi2_beta_scaled.sum(0).mean()))
-            # else:
-                # self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
-#         self.scale_factor = 100.
         self._computations()
 
     def _get_params(self):
@@ -205,11 +169,17 @@ class sparse_GP(GP):
         """
         Approximates a non-gaussian likelihood using Expectation Propagation
 
-        For a Gaussian (or direct: TODO) likelihood, no iteration is required:
+        For a Gaussian likelihood, no iteration is required:
         this function does nothing
         """
         if self.has_uncertain_inputs:
-            raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
+
+            Lmi = chol_inv(self.Lm)
+            Kmmi = tdot(Lmi.T)
+            diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2,Kmmi)])
+
+            self.likelihood.fit_FITC(self.Kmm,self.psi1,diag_tr_psi2Kmmi) #This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
+            #raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
         else:
             self.likelihood.fit_DTC(self.Kmm, self.psi1)
             # self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)

GPy/util/datasets.py

@@ -5,6 +5,8 @@ import GPy
 import scipy.sparse
 import scipy.io
 import cPickle as pickle
+import urllib2 as url
+
 data_path = os.path.join(os.path.dirname(__file__), 'datasets')
 default_seed = 10000
 
@@ -15,6 +17,18 @@ def sample_class(f):
     c = np.where(c, 1, -1)
     return c
 
+def fetch_dataset(resource, file_name, messages = True):
+    if messages:
+        print "Downloading resource: " , resource, " ... "
+    response = url.urlopen(resource)
+    # TODO: Some error checking...
+    html = response.read()
+    response.close()
+    with open(file_name, "w") as text_file:
+        text_file.write("%s"%html)
+    if messages:
+        print "Done!"
+
 def della_gatta_TRP63_gene_expression(gene_number=None):
     mat_data = scipy.io.loadmat(os.path.join(data_path, 'DellaGattadata.mat'))
     X = np.double(mat_data['timepoints'])

GPy/util/linalg.py

@@ -236,7 +236,7 @@ def tdot(*args, **kwargs):
     else:
         return tdot_numpy(*args,**kwargs)
 
-def DSYR(A,x,alpha=1.):
+def DSYR_blas(A,x,alpha=1.):
     """
     Performs a symmetric rank-1 update operation:
     A <- A + alpha * np.dot(x,x.T)
@@ -258,6 +258,26 @@ def DSYR(A,x,alpha=1.):
             x_, byref(INCX), A_, byref(LDA))
     symmetrify(A,upper=True)
 
+def DSYR_numpy(A,x,alpha=1.):
+    """
+    Performs a symmetric rank-1 update operation:
+    A <- A + alpha * np.dot(x,x.T)
+
+    Arguments
+    ---------
+    :param A: Symmetric NxN np.array
+    :param x: Nx1 np.array
+    :param alpha: scalar
+    """
+    A += alpha*np.dot(x[:,None],x[None,:])
+
+
+def DSYR(*args, **kwargs):
+    if _blas_available:
+        return DSYR_blas(*args,**kwargs)
+    else:
+        return DSYR_numpy(*args,**kwargs)
+
 def symmetrify(A,upper=False):
     """
     Take the square matrix A and make it symmetrical by copting elements from the lower half to the upper

GPy/util/mocap_fetch.py

@@ -0,0 +1,13 @@
+import GPy
+import urllib2
+
+# TODO...
+class mocap_fetch(base_url = 'http://mocap.cs.cmu.edu:8080/subjects/', skel_store_dir = './', motion_store_dir = './'):
+    def __init__(self):
+        self.base_url = base_url
+        self.store_dir = store_dir
+        self.motion_dict = []
+    
+    def fetch_motions(self, motion_dict = None):
+        response = urllib2.urlopen(...)
+        html = response.read()

GPy/util/visualize.py

@@ -44,7 +44,7 @@ class vector_show(data_show):
 
 
 class lvm(data_show):
-    def __init__(self, vals, model, data_visualize, latent_axes=None, latent_index=[0,1]):
+    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0,1]):
         """Visualize a latent variable model
 
         :param model: the latent variable model to visualize.
@@ -71,7 +71,7 @@ class lvm(data_show):
         self.data_visualize = data_visualize
         self.model = model
         self.latent_axes = latent_axes
-
+        self.sense_axes = sense_axes
         self.called = False
         self.move_on = False
         self.latent_index = latent_index
@@ -81,10 +81,12 @@ class lvm(data_show):
         self.latent_values = vals
         self.latent_handle = self.latent_axes.plot([0],[0],'rx',mew=2)[0]
         self.modify(vals)
+        self.show_sensitivities()
 
     def modify(self, vals):
         """When latent values are modified update the latent representation and ulso update the output visualization."""
         y = self.model.predict(vals)[0]
+        print y
         self.data_visualize.modify(y)
         self.latent_handle.set_data(vals[self.latent_index[0]], vals[self.latent_index[1]])
         self.axes.figure.canvas.draw()
@@ -99,6 +101,7 @@ class lvm(data_show):
         if event.inaxes!=self.latent_axes: return
         self.move_on = not self.move_on
         self.called = True
+
     def on_move(self, event):
         if event.inaxes!=self.latent_axes: return
         if self.called and self.move_on:
@@ -107,22 +110,54 @@ class lvm(data_show):
             self.latent_values[self.latent_index[1]]=event.ydata
             self.modify(self.latent_values)
 
+    def show_sensitivities(self):
+        # A click in the bar chart axis for selection a dimension.
+        if self.sense_axes != None:
+            self.sense_axes.cla()
+            self.sense_axes.bar(np.arange(self.model.Q),1./self.model.input_sensitivity(),color='b')
+
+            if self.latent_index[1] == self.latent_index[0]:
+                self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='y')
+                self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='y')
+
+            else:
+                self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='g')
+                self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='r')
+
+            self.sense_axes.figure.canvas.draw()
+
+
 class lvm_subplots(lvm):
     """
-    latent_axes is a np array of dimension np.ceil(Q/2) + 1,
+    latent_axes is a np array of dimension np.ceil(Q/2),
-    one for each pair of the axes, and the last one for the sensitiity bar chart
+    one for each pair of the latent dimensions.
     """
-    def __init__(self, vals, model, data_visualize, latent_axes=None, latent_index=[0,1]):
+    def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None):
-        lvm.__init__(self, vals, model,data_visualize,latent_axes,[0,1])
         self.nplots = int(np.ceil(model.Q/2.))+1
-        lvm.__init__(self,model,data_visualize,latent_axes,latent_index)
+        assert len(latent_axes)==self.nplots
-        self.latent_values = np.zeros(2*np.ceil(self.model.Q/2.)) # possibly an extra dimension on this
+        if vals==None:
-        assert latent_axes.size == self.nplots
+            vals = model.X[0, :]
+        self.latent_values = vals 
+
+        for i, axis in enumerate(latent_axes):
+            if i == self.nplots-1:
+                if self.nplots*2!=model.Q:
+                    latent_index = [i*2, i*2]
+                lvm.__init__(self, self.latent_vals, model, data_visualize, axis, sense_axes, latent_index=latent_index)
+            else:
+                latent_index = [i*2, i*2+1]
+                lvm.__init__(self, self.latent_vals, model, data_visualize, axis, latent_index=latent_index)
+
 
 
 class lvm_dimselect(lvm):
     """
     A visualizer for latent variable models which allows selection of the latent dimensions to use by clicking on a bar chart of their length scales.
+
+    For an example of the visualizer's use try:
+    
+    GPy.examples.dimensionality_reduction.BGPVLM_oil()
+
     """
     def __init__(self, vals, model, data_visualize, latent_axes=None, sense_axes=None, latent_index=[0, 1]):
         if latent_axes==None and sense_axes==None:
@@ -133,24 +168,9 @@ class lvm_dimselect(lvm):
         else:
             self.sense_axes = sense_axes
         
-        lvm.__init__(self,vals,model,data_visualize,latent_axes,latent_index)
+        lvm.__init__(self,vals,model,data_visualize,latent_axes,sense_axes,latent_index)
-        self.show_sensitivities()
         print "use left and right mouse butons to select dimensions"
 
-    def show_sensitivities(self):
-        # A click in the bar chart axis for selection a dimension.
-        self.sense_axes.cla()
-        self.sense_axes.bar(np.arange(self.model.Q),1./self.model.input_sensitivity(),color='b')
-
-        if self.latent_index[1] == self.latent_index[0]:
-            self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='y')
-            self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='y')
-            
-        else:
-            self.sense_axes.bar(np.array(self.latent_index[0]),1./self.model.input_sensitivity()[self.latent_index[0]],color='g')
-            self.sense_axes.bar(np.array(self.latent_index[1]),1./self.model.input_sensitivity()[self.latent_index[1]],color='r')
-
-        self.sense_axes.figure.canvas.draw()
 
     def on_click(self, event):
 
@@ -177,12 +197,6 @@ class lvm_dimselect(lvm):
         self.called = True
 
 
-    def on_move(self, event):
-        if event.inaxes!=self.latent_axes: return
-        if self.called and self.move_on:
-            self.latent_values[self.latent_index[0]]=event.xdata
-            self.latent_values[self.latent_index[1]]=event.ydata            
-            self.modify(self.latent_values)
 
     def on_leave(self,event):
         latent_values = self.latent_values.copy()
@@ -333,7 +347,7 @@ class stick_show(mocap_data_show):
 
     def process_values(self, vals):
         self.vals = vals.reshape((3, vals.shape[1]/3)).T.copy()
-    
+
 class skeleton_show(mocap_data_show):
     """data_show class for visualizing motion capture data encoded as a skeleton with angles."""
     def __init__(self, vals, skel, padding=0, axes=None):