fonnesbeck / bios8366 Goto Github PK

Moving to URLs will allow notebooks to be standalone.

In the Expectation and Maximization notebook,

I am not sure, but can you check the following E-step

     a = psi * (x == 0)
     b = (1-psi)*poisson.pmf(x, mu)

is correct? The following can be correct.

    a = (1-psi) * (x == 0)
    b = psi*poisson.pmf(x, mu)

Excellent work.
And I found a typo in Section3_1-Expectation-Maximization.ipynb-General formulation

from scipy.stats.distributions import norm

def e_step(x, mu, sigma, psi):
    a = psi * norm.pdf(x, mu[0], sigma[0])
    b = (1. - psi) * norm.pdf(x, mu[1], sigma[1])
    return b / (a + b)

should be

def e_step(x, mu, sigma, psi):
    a = (1. - psi) * norm.pdf(x, mu[0], sigma[0])
    b =  psi * norm.pdf(x, mu[1], sigma[1])
    return b / (a + b)

Becasue m_step output psi of second distribution and to be consistent with formula.

The conditional function takes as input (x_new, x, y, params), there is no need to pass y in the function. By definition of conditional probability above conditional distribution, "x_new" represent "x" and "x" represent "y".

Correct implementation would be:

def conditional(x_new, x, params):
B = exponential_cov(x_new, x, params)
C = exponential_cov(x, x, params)
A = exponential_cov(x_new, x_new, params)
mu = np.linalg.inv(C).dot(B.T).T.dot(x) // y is replace by x.
sigma = A - B.dot(np.linalg.inv(C).dot(B.T))
return(mu.squeeze(), sigma.squeeze())