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matrix_layers.py
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matrix_layers.py
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import theano
import theano.tensor as T
import theano.tensor.nlinalg as Tn
import numpy as np
import nn_utils as nnu
from layers import Layer, sample_gauss, sample_mult_noise, eps_ind, c1, c2, c3
class MatrixGaussDiagLayerFF(Layer):
def __init__(self, dim_in, dim_out, name, priors=(0., 0., 0.), N=1, nonlin='relu', type_init='he2', n_inducing=50,
noise_lvl=0.01):
sigma_in = 0.01
params = [nnu.randmat(dim_in, dim_out, 'mu_' + name, type_init=type_init, type_dist='normal'),
nnu.randvector(dim_in, 'sigma_row_mgauss_' + name, sigma=sigma_in),
nnu.randvector(dim_out, 'sigma_col_mgauss_' + name, sigma=sigma_in),
nnu.randmat2(n_inducing, dim_in, 'inducing_x_' + name, sigma=sigma_in, type_dist='uniform'),
nnu.randmat2(n_inducing, dim_out, 'inducing_y_' + name, sigma=sigma_in, type_dist='uniform'),
nnu.multvector(dim_in, np.log(np.sqrt(noise_lvl)), name='dropout_alpha_ffdrop_x_' + name),
nnu.multvector(dim_out, np.log(np.sqrt(noise_lvl)), name='dropout_alpha_ffdrop_y_' + name),
nnu.multvector(n_inducing, np.log(np.sqrt(noise_lvl)), name='dropout_alpha_ffdrop_pd_' + name)]
self.dim_in = dim_in
self.dim_out = dim_out
self.name = name
self.type_init = type_init
self.n_inducing = n_inducing
self.noise_lvl = noise_lvl
super(MatrixGaussDiagLayerFF, self).__init__(params, N=N, nonlin=nonlin, priors=priors)
def __str__(self):
return 'inducing m_gauss ffdrop layer ' + self.name
def _get_stds(self):
dx, dy, dpp = T.exp(self.params[-3]), T.exp(self.params[-2]), T.exp(self.params[-1])
stdx, stdy = T.outer(dpp, dx), T.outer(dpp, dy)
return stdx, stdy
def f(self, x, sampling=True, **kwargs):
x /= np.cast[theano.config.floatX](np.sqrt(self.dim_in))
indx, indy = self.params[3], self.params[4]
indx /= np.cast[theano.config.floatX](np.sqrt(self.dim_in))
if sampling:
stdx, stdy = self._get_stds()
noisex, noisey = sample_mult_noise(stdx, indx.shape), sample_mult_noise(stdy, indy.shape)
indy *= noisey; indx *= noisex
Rr, Rc = T.exp(self.params[1]), T.exp(self.params[2])
U = T.sqr(Rr)
sigma11 = T.dot(indx * U.dimshuffle('x', 0), indx.T) + eps_ind * T.eye(self.n_inducing)
sigma22 = T.dot(x * U.dimshuffle('x', 0), x.T)
sigma12 = T.dot(indx * U.dimshuffle('x', 0), x.T)
mu_ind = T.dot(indx, self.params[0])
inv_sigma11 = Tn.matrix_inverse(sigma11)
mu_x = T.dot(x, self.params[0]) + T.dot(sigma12.T, inv_sigma11).dot(indy - mu_ind)
if not sampling:
return mu_x
sigma_x = Tn.extract_diag(sigma22 - T.dot(sigma12.T, inv_sigma11).dot(sigma12))
std = T.outer(T.sqrt(sigma_x), Rc)
out_sample = sample_gauss(mu_x, std)
return out_sample
def get_reg_ind(self):
nsl = self.noise_lvl**2
constant = .5 * np.log(nsl) + c1 * nsl + c2 * (nsl**2) + c3 * (nsl**3)
stdx, stdy = self._get_stds()
drop_ax, drop_ay = T.pow(stdx, 2), T.pow(stdy, 2)
reg_indx = .5 * T.log(drop_ax) + c1 * drop_ax + c2 * T.pow(drop_ax, 2) + c3 * T.pow(drop_ax, 3) - constant
reg_indy = .5 * T.log(drop_ay) + c1 * drop_ay + c2 * T.pow(drop_ay, 2) + c3 * T.pow(drop_ay, 3) - constant
reg_ind = T.sum(reg_indx) + T.sum(reg_indy)
return reg_ind
def get_reg(self):
amount_reg = 1. / self.N
reg_ind = self.get_reg_ind()
reg = [amount_reg * self.kldiv_m(self.params[0], T.exp(self.params[1]), T.exp(self.params[2])),
amount_reg * reg_ind]
return reg
def get_priors(self):
pstdr = T.exp(self.priors[1])
pstdc = T.exp(self.priors[2])
return self.priors[0], pstdr, pstdc
def kldiv_m(self, mu, std_r, std_c):
pmu, pstdr, pstdc = self.get_priors()
var_r, var_c = T.sqr(std_r), T.sqr(std_c)
# first kl term
fa = T.sum((1./(pstdc**2)) * var_c)*T.sum((1./(pstdr**2))*var_r)
# second kl term
prior_sigma = T.outer(T.ones((mu.shape[0],))*(pstdr**2), T.ones((mu.shape[1],))*(pstdc**2))
fb = T.sum(T.sqr(mu - pmu) / prior_sigma)
# third kl term
fc = mu.shape[1]*(mu.shape[0]*T.log(pstdr**2) - T.sum(T.log(var_r))) + \
mu.shape[0]*(mu.shape[1]*T.log(pstdc**2) - T.sum(T.log(var_c)))
return - 0.5 * (fa + fb - T.prod(mu.shape) + fc)
def __copy__(self):
cpl = MatrixGaussDiagLayerFF(self.dim_in, self.dim_out, self.name, priors=self.priors, N=self.N,
nonlin=self.nonlin, type_init=self.type_init, n_inducing=self.n_inducing,
noise_lvl=self.noise_lvl)
return cpl
class MatrixGaussDiagLayerLearnP(Layer):
def __init__(self, dim_in, dim_out, name, priors=(0., 1., 1.), N=1, nonlin='relu', type_init='he2', n_inducing=50,
noise_lvl=0.01):
sigma_in = 0.01
self.a0, self.b0 = 1., .5
params = [nnu.randmat(dim_in, dim_out, 'mu_' + name, type_init=type_init),
nnu.randvector(dim_in, 'sigma_row_mgauss_' + name, sigma=sigma_in),
nnu.randvector(dim_out, 'sigma_col_mgauss_' + name, sigma=sigma_in),
nnu.randmat2(n_inducing, dim_in, 'inducing_x_' + name, sigma=sigma_in, type_dist='uniform'),
nnu.randmat2(n_inducing, dim_out, 'inducing_y_' + name, sigma=sigma_in, type_dist='uniform'),
nnu.multvector(1, np.log(self.a0), 'row_a_' + name), nnu.multvector(1, np.log(self.b0), 'row_b_' + name),
nnu.multvector(1, np.log(self.a0), 'col_a_' + name), nnu.multvector(1, np.log(self.b0), 'col_b_' + name),
nnu.tscalar(np.log(np.sqrt(noise_lvl)), 'scalar_dropout_alpha_x_' + name),
nnu.tscalar(np.log(np.sqrt(noise_lvl)), 'scalar_dropout_alpha_y_' + name)]
self.dim_in = dim_in
self.dim_out = dim_out
self.name = name
self.type_init = type_init
self.n_inducing = n_inducing
self.noise_lvl = noise_lvl
super(MatrixGaussDiagLayerLearnP, self).__init__(params, N=N, nonlin=nonlin, priors=priors)
def __str__(self):
return 'inducing m_gauss learn_p layer'
def f(self, x, sampling=True, **kwargs):
x /= np.cast[theano.config.floatX](np.sqrt(self.dim_in))
indx, indy = self.params[3], self.params[4]
indx /= np.cast[theano.config.floatX](np.sqrt(self.dim_in))
if sampling:
noisex = sample_mult_noise(T.exp(self.params[-2]), indx.shape)
noisey = sample_mult_noise(T.exp(self.params[-1]), indy.shape)
indy *= noisey; indx *= noisex
Rr, Rc = T.exp(self.params[1]), T.exp(self.params[2])
U = T.sqr(Rr)
sigma11 = T.dot(indx * U.dimshuffle('x', 0), indx.T) + eps_ind * T.eye(self.n_inducing)
sigma22 = T.dot(x * U.dimshuffle('x', 0), x.T)
sigma12 = T.dot(indx * U.dimshuffle('x', 0), x.T)
mu_ind = T.dot(indx, self.params[0])
inv_sigma11 = Tn.matrix_inverse(sigma11)
mu_x = T.dot(x, self.params[0]) + T.dot(sigma12.T, inv_sigma11).dot(indy - mu_ind)
if not sampling:
return mu_x
sigma_x = Tn.extract_diag(sigma22 - T.dot(sigma12.T, inv_sigma11).dot(sigma12))
std = T.outer(T.sqrt(sigma_x), Rc)
out_sample = sample_gauss(mu_x, std)
return out_sample
def get_reg_ind(self):
drop_ax, drop_ay = T.pow(T.exp(self.params[-2]), 2), T.pow(T.exp(self.params[-1]), 2)
constant = np.cast[theano.config.floatX](.5 * np.log(self.noise_lvl) + c1 * self.noise_lvl + c2 * (self.noise_lvl**2) + c3 * (self.noise_lvl**3))
reg_indx = .5 * T.log(drop_ax) + c1 * drop_ax + c2 * T.pow(drop_ax, 2) + c3 * T.pow(drop_ax, 3) - constant
reg_indy = .5 * T.log(drop_ay) + c1 * drop_ay + c2 * T.pow(drop_ay, 2) + c3 * T.pow(drop_ay, 3) - constant
reg_ind = T.cast(T.prod(self.params[3].shape), theano.config.floatX) * reg_indx + T.cast(T.prod(self.params[4].shape), theano.config.floatX) * reg_indy
return reg_ind
def get_reg(self, anneal=None):
amount_reg = 1. / self.N
reg_ind = self.get_reg_ind()
reg = [amount_reg * self.kldiv_m(self.params[0], T.exp(self.params[1]), T.exp(self.params[2])),
amount_reg * reg_ind,
amount_reg * (self.kldiv_r(*self._get_row_pl()) + self.kldiv_r(*self._get_col_pl()))]
return reg
def get_priors(self):
pstdr = T.exp(self.priors[1])
pstdc = T.exp(self.priors[2])
return self.priors[0], pstdr, pstdc
def _get_row_pl(self):
return T.exp(self.params[5]), T.exp(self.params[6])
def _get_col_pl(self):
return T.exp(self.params[7]), T.exp(self.params[8])
def kldiv_m(self, mu, std_r, std_c):
ar, br = self._get_row_pl()
ac, bc = self._get_col_pl()
etaur, etauc, elogtaur, elogtauc = (ar/br)[0], (ac/bc)[0], (nnu.Psi()(ar) - T.log(br))[0], (nnu.Psi()(ac) - T.log(bc))[0]
# first kl term
fa = T.sum(etauc * T.sqr(std_c))*T.sum(etaur * T.sqr(std_r))
# second kl term
prior_sigma = etaur * etauc
fb = prior_sigma * T.sum(T.sqr(mu))
# third kl term
fc = T.cast(- mu.shape[1]*(mu.shape[0]*elogtaur + T.sum(T.log(T.sqr(std_r)))) + \
- mu.shape[0]*(mu.shape[1]*elogtauc + T.sum(T.log(T.sqr(std_c)))), theano.config.floatX)
return - np.cast[theano.config.floatX](0.5) * T.cast((fa + fb - T.cast(T.prod(mu.shape), theano.config.floatX) + fc),
theano.config.floatX)
def kldiv_r(self, a1, b1):
return - ((a1 - self.a0)*nnu.Psi()(a1) - T.gammaln(a1) + T.gammaln(self.a0) +
self.a0*(T.log(b1) - T.log(self.b0)) + a1*((self.b0 - b1)/b1))[0]
def __copy__(self):
cpl = MatrixGaussDiagLayerLearnP(self.dim_in, self.dim_out, self.name, priors=self.priors, N=self.N,
nonlin=self.nonlin, type_init=self.type_init, n_inducing=self.n_inducing,
noise_lvl=self.noise_lvl)
return cpl
layers_def = {'mgdl_lp': MatrixGaussDiagLayerLearnP, 'mgdl_ff': MatrixGaussDiagLayerFF}