def mcmc(ll, *frvs): full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, frvs)])) loglik = -full_log_likelihood(full_observations) proposals = free_RVs_prop H = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals])/2. + loglik # -- this should be an inner loop g = [] g.append(tensor.grad(loglik, frvs)) proposals = [(p - epsilon*gg[0]/2.) for p, gg in zip(proposals, g)] rvsp = [(rvs + epsilon*rvp) for rvs,rvp in zip(frvs, proposals)] full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, rvsp)])) new_loglik = -full_log_likelihood(full_observations) gnew = [] gnew.append(tensor.grad(new_loglik, rvsp)) proposals = [(p - epsilon*gn[0]/2.) for p, gn in zip(proposals, gnew)] # -- Hnew = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals])/2. + new_loglik dH = Hnew - H accept = tensor.or_(dH < 0., U < tensor.exp(-dH)) return [tensor.switch(accept, -new_loglik, ll)] + \ [tensor.switch(accept, p, f) for p, f in zip(rvsp, frvs)], \ {}, theano.scan_module.until(accept)
def likelihood_gradient(observations = {}, learning_rate = 0.1): all_vars = ancestors(list(observations.keys())) for o in observations: assert o in all_vars if not is_raw_rv(o): raise TypeError(o) RVs = [v for v in all_vars if is_raw_rv(v)] free_RVs = [v for v in RVs if v not in observations] # Instantiate actual values for the different random variables: params = dict() for v in free_RVs: f = theano.function([], v, mode=theano.Mode(linker='py', optimizer=None)) params[v] = theano.shared(f()) # Compute the full log likelihood: full_observations = dict(observations) full_observations.update(params) log_likelihood = full_log_likelihood(full_observations) # Construct the update equations for learning: updates = dict() for frvs in params.values(): updates[frvs] = frvs + learning_rate * tensor.grad(log_likelihood, frvs) return params, updates, log_likelihood
def test_tt(self): RVs = dict([(self.D, self.D_data)]) lik = full_log_likelihood(RVs) lf = theano.function([self.m1, self.m2, self.C], lik) print lf(1,3,0) print lf(1,3,1)
def test_tt(self): RVs = dict([(self.D, self.D_data)]) lik = full_log_likelihood(RVs) lf = theano.function([self.m1, self.m2, self.C], lik) print lf(1, 3, 0) print lf(1, 3, 1)
def mcmc(ll, *frvs): full_observations = dict(observations) full_observations.update( dict([(rv, s) for rv, s in zip(free_RVs, frvs)])) loglik = -full_log_likelihood(full_observations) proposals = free_RVs_prop H = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals]) / 2. + loglik # -- this should be an inner loop g = [] g.append(tensor.grad(loglik, frvs)) proposals = [(p - epsilon * gg[0] / 2.) for p, gg in zip(proposals, g)] rvsp = [(rvs + epsilon * rvp) for rvs, rvp in zip(frvs, proposals)] full_observations = dict(observations) full_observations.update( dict([(rv, s) for rv, s in zip(free_RVs, rvsp)])) new_loglik = -full_log_likelihood(full_observations) gnew = [] gnew.append(tensor.grad(new_loglik, rvsp)) proposals = [(p - epsilon * gn[0] / 2.) for p, gn in zip(proposals, gnew)] # -- Hnew = tensor.add(*[tensor.sum(tensor.sqr(p)) for p in proposals]) / 2. + new_loglik dH = Hnew - H accept = tensor.or_(dH < 0., U < tensor.exp(-dH)) return [tensor.switch(accept, -new_loglik, ll)] + \ [tensor.switch(accept, p, f) for p, f in zip(rvsp, frvs)], \ {}, theano.scan_module.until(accept)
def mcmc(ll, *frvs): proposals = [s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, frvs)] proposals_rev = [s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, proposals)] full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, proposals)])) new_log_likelihood = full_log_likelihood(full_observations) logratio = new_log_likelihood - ll \ + tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals_rev, frvs)]) \ - tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals, proposals)]) accept = tensor.gt(logratio, tensor.log(U)) return [tensor.switch(accept, new_log_likelihood, ll)] + \ [tensor.switch(accept, p, f) for p, f in zip(proposals, frvs)], \ {}, theano.scan_module.until(accept)
def mcmc(ll, *frvs): proposals = [ s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, frvs) ] proposals_rev = [ s_rng.local_proposal(v, rvs) for v, rvs in zip(free_RVs, proposals) ] full_observations = dict(observations) full_observations.update( dict([(rv, s) for rv, s in zip(free_RVs, proposals)])) new_log_likelihood = full_log_likelihood(full_observations) logratio = new_log_likelihood - ll \ + tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals_rev, frvs)]) \ - tensor.add(*[tensor.sum(lpdf(p, r)) for p, r in zip(proposals, proposals)]) accept = tensor.gt(logratio, tensor.log(U)) return [tensor.switch(accept, new_log_likelihood, ll)] + \ [tensor.switch(accept, p, f) for p, f in zip(proposals, frvs)], \ {}, theano.scan_module.until(accept)
def mh2_sample(s_rng, outputs, observations = {}, givens = {}): all_vars = ancestors(list(observations.keys()) + list(outputs)) for o in observations: assert o in all_vars if not is_raw_rv(o): raise TypeError(o) RVs = [v for v in all_vars if is_raw_rv(v)] free_RVs = [v for v in RVs if v not in observations] free_RVs_state = [] for v in free_RVs: f = theano.function([], v, mode=theano.Mode(linker='py', optimizer=None)) free_RVs_state.append(theano.shared(f())) U = s_rng.uniform(low=0.0, high=1.0) rr = [] for index in range(len(free_RVs)): # TODO: why does the compiler crash when we try to expose the likelihood ? full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)])) log_likelihood = full_log_likelihood(full_observations) proposal = s_rng.local_proposal(free_RVs[index], free_RVs_state[index]) proposal_rev = s_rng.local_proposal(free_RVs[index], proposal) full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)])) full_observations.update(dict([(free_RVs[index], proposal)])) new_log_likelihood = full_log_likelihood(full_observations) bw = tensor.sum(lpdf(proposal_rev, free_RVs_state[index])) fw = tensor.sum(lpdf(proposal, proposal)) lr = new_log_likelihood-log_likelihood+bw-fw accept = tensor.gt(lr, tensor.log(U)) updates = {free_RVs_state[index] : tensor.switch(accept, proposal, free_RVs_state[index])} rr.append(theano.function([], [accept], updates=updates, givens=givens)) # TODO: this exacte amount of samples given back is still wrong def sampler(nr_samples, burnin = 100, lag = 100): data = [[] for o in outputs] for i in range(nr_samples*lag+burnin): accept = False while not accept: index = numpy.random.randint(len(free_RVs)) accept = rr[index]() if accept and i > burnin and (i-burnin) % lag == 0: for d, o in zip(data, outputs): # TODO: this can be optimized if is_raw_rv(o): d.append(free_RVs_state[free_RVs.index(o)].get_value()) else: full_observations = dict(observations) full_observations.update(dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)])) d.append(evaluate(evaluate_with_assignments(o, full_observations), givens=givens)) data = [numpy.asarray(d).squeeze() for d in data] return data return sampler
# Define model w = s_rng.normal(0, 4, draw_shape=(2, )) x = tensor.matrix('x') y = tensor.nnet.sigmoid(tensor.dot(x, w)) t = s_rng.binomial(p=y, draw_shape=(4, )) # Define data X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]], dtype=theano.config.floatX).T Y_data = numpy.asarray([1., 1., 0., 0.], dtype=theano.config.floatX) # Plot full likelihood function RVs = dict([(t, Y_data)]) lik = full_log_likelihood(RVs) givens = dict([(x, X_data)]) lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True) delta = .1 x_range = numpy.arange(-10.0, 10.0, delta) y_range = numpy.arange(-10.0, 10.0, delta) X, Y = numpy.meshgrid(x_range, y_range) response = [] for xl, yl in zip(X.flatten(), Y.flatten()): response.append(lik_func([xl, yl])) pylab.figure(1) pylab.contour(X, Y, numpy.exp(numpy.asarray(response)).reshape(X.shape), 20)
def mh2_sample(s_rng, outputs, observations={}, givens={}): all_vars = ancestors(list(observations.keys()) + list(outputs)) for o in observations: assert o in all_vars if not is_raw_rv(o): raise TypeError(o) RVs = [v for v in all_vars if is_raw_rv(v)] free_RVs = [v for v in RVs if v not in observations] free_RVs_state = [] for v in free_RVs: f = theano.function([], v, mode=theano.Mode(linker='py', optimizer=None)) free_RVs_state.append(theano.shared(f())) U = s_rng.uniform(low=0.0, high=1.0) rr = [] for index in range(len(free_RVs)): # TODO: why does the compiler crash when we try to expose the likelihood ? full_observations = dict(observations) full_observations.update( dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)])) log_likelihood = full_log_likelihood(full_observations) proposal = s_rng.local_proposal(free_RVs[index], free_RVs_state[index]) proposal_rev = s_rng.local_proposal(free_RVs[index], proposal) full_observations = dict(observations) full_observations.update( dict([(rv, s) for rv, s in zip(free_RVs, free_RVs_state)])) full_observations.update(dict([(free_RVs[index], proposal)])) new_log_likelihood = full_log_likelihood(full_observations) bw = tensor.sum(lpdf(proposal_rev, free_RVs_state[index])) fw = tensor.sum(lpdf(proposal, proposal)) lr = new_log_likelihood - log_likelihood + bw - fw accept = tensor.gt(lr, tensor.log(U)) updates = { free_RVs_state[index]: tensor.switch(accept, proposal, free_RVs_state[index]) } rr.append(theano.function([], [accept], updates=updates, givens=givens)) # TODO: this exacte amount of samples given back is still wrong def sampler(nr_samples, burnin=100, lag=100): data = [[] for o in outputs] for i in range(nr_samples * lag + burnin): accept = False while not accept: index = numpy.random.randint(len(free_RVs)) accept = rr[index]() if accept and i > burnin and (i - burnin) % lag == 0: for d, o in zip(data, outputs): # TODO: this can be optimized if is_raw_rv(o): d.append( free_RVs_state[free_RVs.index(o)].get_value()) else: full_observations = dict(observations) full_observations.update( dict([ (rv, s) for rv, s in zip(free_RVs, free_RVs_state) ])) d.append( evaluate(evaluate_with_assignments( o, full_observations), givens=givens)) data = [numpy.asarray(d).squeeze() for d in data] return data return sampler
# Define model w = s_rng.normal(0, 4, draw_shape=(2,)) x = tensor.matrix("x") y = tensor.nnet.sigmoid(tensor.dot(x, w)) t = s_rng.binomial(p=y, draw_shape=(4,)) # Define data X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]], dtype=theano.config.floatX).T Y_data = numpy.asarray([1.0, 1.0, 0.0, 0.0], dtype=theano.config.floatX) # Plot full likelihood function RVs = dict([(t, Y_data)]) lik = full_log_likelihood(RVs) givens = dict([(x, X_data)]) lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True) delta = 0.1 x_range = numpy.arange(-10.0, 10.0, delta) y_range = numpy.arange(-10.0, 10.0, delta) X, Y = numpy.meshgrid(x_range, y_range) response = [] for xl, yl in zip(X.flatten(), Y.flatten()): response.append(lik_func([xl, yl])) pylab.figure(1) pylab.contour(X, Y, numpy.exp(numpy.asarray(response)).reshape(X.shape), 20)