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Diffstat (limited to 'posts')
| -rw-r--r-- | posts/2019-02-14-raise-your-elbo.md | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/posts/2019-02-14-raise-your-elbo.md b/posts/2019-02-14-raise-your-elbo.md index 43a841a..d4e2227 100644 --- a/posts/2019-02-14-raise-your-elbo.md +++ b/posts/2019-02-14-raise-your-elbo.md @@ -230,7 +230,7 @@ $$\begin{aligned} **Remark**. The k-means algorithm is the $\epsilon \to 0$ limit of the GMM with constraints $\Sigma_k = \epsilon I$. See Section -9.3.2 of Bishop 1995 for derivation. It is also briefly mentioned there +9.3.2 of Bishop 2006 for derivation. It is also briefly mentioned there that a variant in this setting where the covariance matrix is not restricted to $\epsilon I$ is called elliptical k-means algorithm. @@ -323,7 +323,7 @@ $X = V_s \Sigma_s^{{1 \over 2}}$, where $U_s$ (resp. $V_s$) is the matrix of the first $s$ columns of $U$ (resp. $V$) and $\Sigma_s$ is the $s \times s$ submatrix of $\Sigma$. -One can compare pLSA1 with LSA. Both proceudres produce embeddings of +One can compare pLSA1 with LSA. Both procedures produce embeddings of $d$ and $x$: in pLSA we obtain $n_z$ dimensional embeddings $\xi_{\cdot, u}$ and $\eta_{\cdot, w}$, whereas in LSA we obtain $s$ dimensional embeddings $D_{u, \cdot}$ and $X_{w, \cdot}$. @@ -547,7 +547,7 @@ $q_2^*$ (M-step). It is also called mean field approximation (MFA), and can be easily generalised to models with more than two groups of latent variables, see -e.g. Section 10.1 of Bishop 1995. +e.g. Section 10.1 of Bishop 2006. ### Application to mixture models @@ -660,7 +660,7 @@ More specifically: The E-step and M-step can be computed using (9.1) and (9.3)(9.7)(9.9) in the previous section. The details of the computation can be found in -Chapter 10.2 of Bishop or the Attias. +Chapter 10.2 of Bishop 2006 or Attias 2000. ### LDA @@ -1089,7 +1089,7 @@ References models.\" In Advances in neural information processing systems, pp. 209-215. 2000. - Bishop, Christopher M. Neural networks for pattern recognition. - Oxford university press, 1995. + Springer. 2006. - Blei, David M., and Michael I. Jordan. "Variational Inference for Dirichlet Process Mixtures." Bayesian Analysis 1, no. 1 (March 2006): 121--43. <https://doi.org/10.1214/06-BA104>. |