add hmc.py

GPy/inference/optimization/hmc.py

@@ -0,0 +1,63 @@
+"""HMC implementation"""
+
+import numpy as np
+
+
+class HMC:
+    def __init__(self,model,M=None,stepsize=1e-1):
+        self.model = model
+        self.stepsize = stepsize
+        self.p = np.empty_like(model.optimizer_array.copy())
+        if M is None:
+            self.M = np.eye(self.p.size)
+        else:
+            self.M = M
+        self.Minv = np.linalg.inv(self.M)
+
+    def sample(self, m_iters=1000, hmc_iters=20):
+        thetas = np.empty((m_iters,self.p.size))
+        ps = np.empty((m_iters,self.p.size))
+        for i in xrange(m_iters):
+            #Gibbs
+            self.p[:] = np.random.multivariate_normal(np.ones(self.p.size),self.M)
+            H_old = self._computeH()
+            p_old = self.p.copy()
+            theta_old = self.model.optimizer_array.copy()
+            #Matropolis
+            self._update(hmc_iters)
+            H_new = self._computeH()
+
+            k = np.exp(H_old-H_new)
+            print k
+            if np.random.rand()<k:
+                thetas[i] = self.model.optimizer_array
+                ps[i] = self.p
+            else:
+                thetas[i] = theta_old
+                ps[i] = p_old
+                self.model.optimizer_array = theta_old
+        return thetas, ps
+
+    def _update(self, hmc_iters):
+        for i in xrange(hmc_iters):
+            g = self.p.copy()
+            g[:] = 1e-2
+#            self.p[:] += self.stepsize/2.*self.model.grad()[:,0]#*-self.model._transform_gradients(self.model.objective_function_gradients())
+            self.p[:] += self.stepsize/2.*-self.model._transform_gradients(self.model.objective_function_gradients())
+            self.model.optimizer_array[:] = self.model.optimizer_array[:] + self.stepsize*np.dot(self.Minv, self.p[:,None])[:,0]
+            self.p[:] += self.stepsize/2.*-self.model._transform_gradients(self.model.objective_function_gradients())
+            #self.model.optimizer_array = self.model.optimizer_array - self.stepsize*self.model._transform_gradients(self.model.objective_function_gradients())
+
+    def _computeH(self,):
+        return self.model.objective_function()+self.p.size*np.log(2*np.pi)/2.+np.log(np.linalg.det(self.M))/2.+np.dot(self.p, np.dot(self.Minv,self.p[:,None]))/2.
+
+class Gmodel:
+    def __init__(self,):
+        self.cov = np.array([[1., 0.99],[0.99, 1.]])
+        self.optimizer_array = np.random.rand(2)
+
+    def grad(self,):
+        return -np.dot(np.linalg.inv(self.cov),self.optimizer_array[:,None])
+
+    def objective_function(self,):
+        return np.dot(self.optimizer_array, np.dot(np.linalg.inv(self.cov),self.optimizer_array[:,None]))/2.