diff options
Diffstat (limited to 'posts')
| -rw-r--r-- | posts/2019-02-14-raise-your-elbo.md | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/posts/2019-02-14-raise-your-elbo.md b/posts/2019-02-14-raise-your-elbo.md index 64dfd81..cf3911f 100644 --- a/posts/2019-02-14-raise-your-elbo.md +++ b/posts/2019-02-14-raise-your-elbo.md @@ -189,7 +189,7 @@ A different way of describing EM, which will be useful in hidden Markov model is: - At E-step, one writes down the formula - $$\sum_i \mathbb E_{p(z | x_{i}; \theta_t)} \log p(x_{i}, z; \theta). \qquad (2.5)$$ + $$\sum_i \mathbb E_{p(z_i | x_{i}; \theta_t)} \log p(x_{i}, z_i; \theta). \qquad (2.5)$$ - At M-setp, one finds $\theta_{t + 1}$ to be the $\theta$ that maximises the above formula. @@ -208,7 +208,7 @@ so we write $\eta_k = (\mu_k, \Sigma_k)$, During E-step, the $q(z_i)$ can be directly computed using Bayes' theorem: -$$r_{ik} = \mathbb P(z = k | x = x_{i}; \theta_t) +$$r_{ik} = \mathbb P(z_i = k | x = x_{i}; \theta_t) = {g_{\mu_{t, k}, \Sigma_{t, k}} (x_{i}) \pi_{t, k} \over \sum_{j = 1 : n_z} g_{\mu_{t, j}, \Sigma_{t, j}} (x_{i}) \pi_{t, j}},$$ where |