Adding example; adding explicit lower bound computation; optionally monitoring...

Adding example; adding explicit lower bound computation; optionally monitoring convergence; full and tied work, somehow spherical and diag diverge.

doc/dp-derivation.rst

@@ -128,13 +128,10 @@ distribution.
   \begin{array}{rcl}
   && E_q[\log P(z)] - E_q[\log Q(z)] \\
   &=&
-  \sum_{k} \left( \left(\sum_{j=k+1}^K
-  \nu_{z_{i,j}}\right)(\Psi(\gamma{k,1})-\Psi(\gamma{k,1}+\gamma_{k,2})) 
-  +
-  \nu_{z_{i,k}}(\Psi(\gamma_{k,1})-\Psi(\gamma_{k,1}+\gamma_{k,2}))\right)
-  \\ &&
-  - \sum_k
-  \nu_{z_{i,k}} \log \nu_{z_{i,k}} \\
+  \sum_{k} \left( 
+       \left(\sum_{j=k+1}^K  \nu_{z_{i,j}}\right)(\Psi(\gamma{k,1})-\Psi(\gamma{k,1}+\gamma_{k,2})) 
+   +  \nu_{z_{i,k}}(\Psi(\gamma_{k,1})-\Psi(\gamma_{k,1}+\gamma_{k,2}))
+   - \log \nu_{z_{i,k}} \right)
   \end{array}
 
 

examples/mixture/plot_dpgmm.py

+"""
+=================================
+DP Mixture Model Ellipsoids
+=================================
+
+Plot the confidence ellipsoids of a mixture of two gaussians.
+"""
+
+import numpy as np
+from scikits.learn import mixture
+import itertools
+
+import pylab as pl
+import matplotlib as mpl
+
+n, m = 300, 2
+
+# generate random sample, two components
+np.random.seed(0)
+C = np.array([[0., -0.7], [3.5, .7]])
+X = np.r_[np.dot(np.random.randn(n, 2), C),
+          np.random.randn(n, 2) + np.array([3, 3])]
+
+for p,alpha in enumerate([0.01, 1., 100.]):
+    clf = mixture.DPGMM(n_states=10, cvtype='full', alpha=alpha)
+    clf.fit(X)
+
+    splot = pl.subplot(310+p+1, aspect='equal')
+    color_iter = itertools.cycle (['r', 'g', 'b', 'c'])
+
+    Y_ = clf.predict(X)
+
+    for i, (mean, covar, color) in enumerate(zip(clf.means, clf.covars, color_iter)):
+        v, w = np.linalg.eigh(covar)
+        u = w[0] / np.linalg.norm(w[0])
+        if sum(Y_ == i) > 1:
+            pl.scatter(X[Y_==i, 0], X[Y_==i, 1], .8, color=color)
+        else:
+            continue
+        angle = np.arctan(u[1]/u[0])
+        angle = 180 * angle / np.pi # convert to degrees
+        ell = mpl.patches.Ellipse (mean, v[0], v[1], 180 + angle, color=color)
+        ell.set_clip_box(splot.bbox)
+        ell.set_alpha(0.5)
+        splot.add_artist(ell)
+
+pl.show()
+

scikits/learn/mixture/__init__.py

@@ -4,4 +4,4 @@ Mixture modeling algorithms
 
 from .gmm import logsum, normalize, sample_gaussian, lmvnpdf
 from .gmm import GMM
-from .dpgmm import DPGMM, VBGMM
+from .dpgmm import DPGMM