emission.py

import pymc
import numpy as np
import logging

log = logging.getLogger('emissions') 


log_2_pi = np.log(2*np.pi)
invwishart = lambda nu, L: pymc.InverseWishart("invwishart", nu, L).random()
mvnormal = lambda mu, tau: pymc.MvNormal('mvnormal', mu, tau).random()
#invwishart_like = lambda x, nu, L: pymc.inverse_wishart_like(x,nu,L)

class Gaussian:
    
    def __init__(self, nu, Lambda, mu_0, kappa, mu, tau):
        self.nu = nu
        self.Lambda = Lambda
        self.mu_0 = mu_0 # mu_0 is the mean of the prior on the mean
        self.kappa = float(kappa)
        
        self.mu = mu # mu is the current value of the mean for each state
        self.tau = tau # tau is the current precision matrix for each state
                
        self.states = range(len(mu))
        self.K = len(self.states)
        
        
    def likelihood(self, state, obs):
        assert state in self.states, (state, self.states)
        return pymc.mv_normal_like(obs, self.mu[state], self.tau[state])
    
    def sample_obs(self,state):
        assert state in self.states, (state, self.states)
        return mvnormal(self.mu[state], self.tau[state])
    
    def sample_mean_prec(self, Zs, Ys):
        
        n = dict([(i,[]) for i in self.states])
        
        for Z,Y in zip(Zs,Ys):
            X = [z[0] for z in Z]
            for t,s in enumerate(X):
                n[s].append(np.array([Y[t]]))
        
        for i in self.states:
            n[i] = np.array(n[i]).T
            n[i] = np.squeeze(n[i])
        
        #print n[i]
        #for i in self.states:
            #log.debug("state: %s"%i)
            #log.debug("observations: %s"%n[i].round(2))
        
        taus, mus = [], []
        for i in self.states:
            
            if len(n[i]) > 0:
                try:
                    ybar = np.mean(n[i],1)
                except ValueError:
                    ybar = np.mean(n[i])
                
                ybar = ybar.flatten()
                
                S = np.sum([
                    np.outer((yi - ybar),(yi - ybar)) 
                    for yi in n[i].T
                ], 0)
            else:
                #wtf? we don't have any of these observations...
                # fall back on the prior mean and we won't updated
                # the precision
                ybar = np.array(self.mu_0[i])        
                S = 0
                
                
            #assert not np.isnan(S), S
            #assert not np.isinf(S), S
            
            #log.debug("ybar[%s]: %s"%(i,ybar))
            mu_n = (
                (
                    (self.kappa/(self.kappa + len(n[i]))) * self.mu_0[i]
                ) + 
                (
                    (len(n[i])/(self.kappa + len(n[i]))) * ybar
                )
            )
            #log.debug("mu_n[%s]: %s"%(i,mu_n))
            kappa_n = self.kappa + len(n[i])
            nu_n = self.nu + len(n[i])
            Lambda_n = (
                self.Lambda + 
                S + 
                (
                    (self.kappa * len(n[i]))/(self.kappa + len(n[i])) *
                    (ybar - self.mu_0[i])*(ybar-self.mu_0[i]).T
                )
            )
            
            if (np.isnan(Lambda_n)).any():
                Lambda_n = self.Lambda
            if np.isnan(nu_n):
                nu_n - self.nu
                        
            try:
                sigma = invwishart(nu_n, np.linalg.inv(Lambda_n))
            except np.linalg.LinAlgError:
                try:
                    sigma = invwishart(nu_n, 1.0/Lambda_n)
                except:
                    print "Lambda_n: %s"%Lambda_n
                    print "S: %s"%S
                    print "nu_n: %s"%nu_n
                    raise
            except:
                print Lambda_n
                raise
            # form precion matrix
            tau = np.linalg.inv(sigma)
            #log.debug("tau[%s]: %s"%(i,tau))
            try:
                tau_scaled = np.linalg.inv(sigma/kappa_n)
            except np.linalg.LingAlgError:
                tau_scaled = 1.0 / (sigma/kappa_n)
            #log.debug("tau_scaled[%s]: %s"%(i,tau_scaled))
            try:
                mu = mvnormal(mu_n, tau_scaled)
            except ValueError:
                mu = self.mu_0[i]
                log.debug('fell back onto the prior mu_0 probably due to lack of observations in this state')
            taus.append(tau)
            mus.append(mu)
            log.debug('sampled obs mean for state %s: %s'%(i,mus[-1]))
            log.debug('sampled obs prec for state %s: %s'%(i,taus[-1]))
            
        return mus, taus
    
    def update(self, Z, Y):
        mu, tau = self.sample_mean_prec(Z, Y)
        self.mu = mu
        self.tau = tau
    

if __name__ == "__main__":    
    import pylab as pb
    Z = np.load('Z.npy')
    Y = np.load('Y.npy')
    O = Gaussian(
        nu = 1,
        Lambda = np.array([1]), 
        mu_0 = [0, 0, 0], 
        kappa = 0.01, 
        mu = [-3, 0, 3], 
        tau = [
            np.array([[1]]),
            np.array([[1]]),
            np.array([[1]])
        ]
    )
    #x = np.linspace(-4,4,100)
    #for i in range(3):
    #    pb.plot(x,[pb.exp(O.likelihood(i,xi)) for xi in x])
    #pb.show()
    #mus, sigmas = O.sample_mean_prec(Z,Y)
    pb.figure()
    for j in range(3):
        mus = np.array([O.sample_mean_prec([Z],[Y])[0][j] for i in range(100)]).flatten()
        pb.hist(mus,alpha=0.5)
        
    pb.figure()
    for j in range(3):
        taus = np.array([O.sample_mean_prec([Z],[Y])[1][j] for i in range(100)]).flatten()
        pb.hist(taus,alpha=0.5)
    pb.show()