操作数不能与形状 (100,) (8,8) 一起广播

Question

I was making Baysien model Type-II to finding the maximum likelihood to estimate “most probable” values for hyper-parameters. After I try to run the code below I got some of error that shown in compute_posterior function. It might be something wrong with the shape.

def compute_posterior(PHI, t, alph, s2):
    M = PHI.shape[1]
    beta = 1/s2
    H = beta*(PHI.T @ PHI) + alph*np.eye(M)
    SIGMA = np.linalg.inv(H)
    Mu = beta * (SIGMA @ (PHI.T @ t))
    #
    return Mu, SIGMA


# Marginal log likelihood
#
# Version 1 Log Marginal (ideal)
#
def compute_log_marginal(PHI, t, alph, s2):
    #
    # Exploit the shape of C and the fact that M < N (usually)
    #
    N, M = PHI.shape
    beta = 1 / s2
    Mu, SIGMA = compute_posterior(PHI, t, alph, s2)
    #
    # Constant factor
    #
    logML = -N * np.log(2 * np.pi)
    #
    # log determinant factor (log|C|)
    #
    # If SIGMA becomes singular, sgn<0
    #
    sgn, logdet = np.linalg.slogdet(SIGMA)
    #
    if sgn < 0:
        print("Error with alpha={0}, s2={1}".format(alph, s2))
        raise np.linalg.LinAlgError("logdet sign is negative - something is wrong!")
    #
    logML += logdet + N*np.log(beta) + M*np.log(alph)
    #
    # data term (t'Ct)
    #
    logML -= beta * (t.T @ (t - PHI @ Mu))
    #
    logML = logML / 2.0
    #
    return logML

log_alph = np.linspace(-3, 6, n)
log_s2 = np.linspace(-4, 4, n)

x = df.values[:, 0:8]
t = df.values[:, 8]

n  = 100

Z = np.empty((n, n))
Z_max = []
al = []
rr = []
for i, a in enumerate(log_alph):
    for j, r in enumerate(log_s2):
        Z[i, j] = compute_log_marginal(x,t,log_alph,log_s2)
        Z_max.append(Z[i, j])
        maximum = max(Z_max)
        print(maximum)

#         if Z[i, j] == -11.627510277032485:
#             al.append(a)
#             rr.append(r)

# maximum = max(Z_max)
# print(al)
# print(rr)
# print(maximum)
# maximum = -11.627510277032485



plt.contourf(log_a, log_r, Z.T)
print('The maximum point is:',maximum )
print('The max log_alpha is:',al[0] )
print('The max log_r  is:',rr[0] )
plt.xlabel('log alpha')
plt.ylabel('log r')
plt.title('Contour of log alpha and log r')

After I compile I got this error, I still don't know how to figure it out

'
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-260-c7f0396b4046> in <module>
     14 for i, a in enumerate(log_alph):
     15     for j, r in enumerate(log_s2):
---> 16         Z[i, j] = compute_log_marginal(x,t,log_alph,log_s2)
     17         Z_max.append(Z[i, j])
     18         maximum = max(Z_max)

<ipython-input-233-45cfae272a38> in compute_log_marginal(PHI, t, alph, s2)
     19     N, M = PHI.shape
     20     beta = 1 / s2
---> 21     Mu, SIGMA = compute_posterior(PHI, t, alph, s2)
     22     #
     23     # Constant factor

<ipython-input-233-45cfae272a38> in compute_posterior(PHI, t, alph, s2)
      2     M = PHI.shape[1]
      3     beta = 1/s2
----> 4     H = beta*(PHI.T @ PHI) + alph*np.eye(M)
      5     SIGMA = np.linalg.inv(H)
      6     Mu = beta * (SIGMA @ (PHI.T @ t))

ValueError: operands could not be broadcast together with shapes (100,) (8,8) 

'

Answer 1

H = beta*(PHI.T @ PHI) + alph*np.eye(M)

split operations in this line and figure out which one is throwing errors If your logic is ok, check if all matrices have the shape that you expect. If shapes are ok note that @ is matrix multiplication and * is elementwise multiplication. Nex time you post code try to include smaller part that is more readable or include code that everyone will be able to execute, to debug it.