Is squaring s correct here?

[dims12]

In ppca.__fit_ml you are writing

ppca/src/pca/ppca.py

Line 94 in 8b9a0f2

ss = np.sqrt(np.maximum(0, ss**2 - self.prior_sigma))

which probably corresponds with

in Bishop, Tipping.

In other words, you are calculating eigenvalue by squaring singular value.

Is this correct? Shouldn't it be divided by number of samples also?

[cangermueller]

I think this is correct since ss are singular values (sqrt(K)).

[dims12]

ss are singular values of y, according to here

ppca/src/pca/ppca.py

Line 88 in 8b9a0f2

[u, s, v] = np.linalg.svd(self.y - mu)

and to obtain K, we should turn it to eigenvalues, which are ss**2/self.n, and finally I would write

ss = np.sqrt(np.maximum(0, ss**2/self.n - 1))

Isn't this correct?

[cangermueller]

Now I see your point. Do the singular values scale with self.n? If yes, you are correct.

[WilliamXWL]

Hey,
shouldn't it be ss = np.sqrt(np.maximum(0, ss**2 - sigma)) ?

self.prior_sigma is set to be 1 permanently, while in the paper, sigma is estimated by sigma = 1.0 / (self.p - self.q) * np.sum(s[self.q:]**2)