def compute_forward_posterior(self, az, bz, ax, bx):
# estimate x from x = sgn(z)
x_pos = +bz / np.sqrt(az)
x_neg = -bz / np.sqrt(az)
delta = 2 * bx + phi_0(x_pos) - phi_0(x_neg)
rx = np.tanh(delta / 2)
v = 1 - rx**2
vx = np.mean(v)
return rx, vx
def compute_forward_posterior(self, az, bz, ax, bx):
# estimate x from x = relu(z)
a = ax + az
x_pos = (bx + bz) / np.sqrt(a)
x_neg = - bz / np.sqrt(az)
delta = phi_0(x_pos) - phi_0(x_neg) + 0.5 * np.log(az / a)
sigma_pos = sigmoid(+delta)
sigma_neg = sigmoid(-delta)
r_pos = phi_1(x_pos) / np.sqrt(a)
v_pos = phi_2(x_pos) / a
# NB: r_neg = 0 and v_neg = 0
rx = sigma_pos * r_pos
Dx = r_pos**2
v = sigma_pos * sigma_neg * Dx + sigma_pos * v_pos
vx = np.mean(v)
return rx, vx
def compute_backward_posterior(self, az, bz, ax, bx):
# estimate z from x = sgn(z)
x_pos = +bz / np.sqrt(az)
x_neg = -bz / np.sqrt(az)
delta = 2 * bx + phi_0(x_pos) - phi_0(x_neg)
sigma_pos = sigmoid(+delta)
sigma_neg = sigmoid(-delta)
r_pos = +phi_1(x_pos) / np.sqrt(az) # NB: + phi'(x_pos)
r_neg = -phi_1(x_neg) / np.sqrt(az) # NB: + phi'(x_pos)
v_pos = phi_2(x_pos) / az
v_neg = phi_2(x_neg) / az
rz = sigma_pos * r_pos + sigma_neg * r_neg
Dz = (r_pos - r_neg)**2
v = sigma_pos * sigma_neg * Dz + sigma_pos * v_pos + sigma_neg * v_neg
vz = np.mean(v)
return rz, vz
def compute_backward_posterior(self, az, bz, ax, bx):
# estimate z from x = relu(z)
a = ax + az
x_pos = (bx + bz) / np.sqrt(a)
x_neg = - bz / np.sqrt(az)
delta = phi_0(x_pos) - phi_0(x_neg) + 0.5 * np.log(az / a)
sigma_pos = sigmoid(+delta)
sigma_neg = sigmoid(-delta)
r_pos = + phi_1(x_pos) / np.sqrt(a) # NB: + phi'(x_pos)
r_neg = - phi_1(x_neg) / np.sqrt(az) # NB: - phi'(x_pos)
v_pos = phi_2(x_pos) / a
v_neg = phi_2(x_neg) / az
rz = sigma_pos * r_pos + sigma_neg * r_neg
Dz = (r_pos - r_neg)**2
v = sigma_pos * sigma_neg * Dz + sigma_pos * v_pos + sigma_neg * v_neg
vz = np.mean(v)
return rz, vz
def compute_forward_posterior(self, az, bz, ax, bx):
# estimate x from x = abs(z)
a = ax + az
x_pos = (bx + bz) / np.sqrt(a)
x_neg = (bx - bz) / np.sqrt(a)
delta = phi_0(x_pos) - phi_0(x_neg)
sigma_pos = sigmoid(+delta)
sigma_neg = sigmoid(-delta)
r_pos = phi_1(x_pos) / np.sqrt(a)
r_neg = phi_1(x_neg) / np.sqrt(a)
v_pos = phi_2(x_pos) / a
v_neg = phi_2(x_neg) / a
rx = sigma_pos * r_pos + sigma_neg * r_neg
Dx = (r_pos - r_neg)**2
v = sigma_pos * sigma_neg * Dx + sigma_pos * v_pos + sigma_neg * v_neg
vx = np.mean(v)
return rx, vx
def compute_backward_posterior(self, az, bz, ax, bx):
# estimate z from x = leaky_relu(z)
a_pos = az + ax
a_neg = az + (self.slope**2) * ax
b_pos = bz + bx
b_neg = -bz - self.slope * bx
x_pos = b_pos / np.sqrt(a_pos)
x_neg = b_neg / np.sqrt(a_neg)
delta = phi_0(x_pos) - phi_0(x_neg) + 0.5 * np.log(a_neg / a_pos)
sigma_pos = sigmoid(+delta)
sigma_neg = sigmoid(-delta)
r_pos = phi_1(x_pos) / np.sqrt(a_pos)
r_neg = -phi_1(x_neg) / np.sqrt(a_neg)
v_pos = phi_2(x_pos) / a_pos
v_neg = phi_2(x_neg) / a_neg
rz = sigma_pos * r_pos + sigma_neg * r_neg
Dz = (r_pos - r_neg)**2
v = sigma_pos * sigma_neg * Dz + sigma_pos * v_pos + sigma_neg * v_neg
vz = np.mean(v)
return rz, vz