Added link and reworded small section

learning/bayesian/index.md

@@ -26,7 +26,7 @@ $$ p(S) = \prod_{i=1}^n p(w_n). $$
 For simplicity, assume that our language corpus consists of a single sentence, "Probabilistic graphical models are fun. They are also powerful." We can estimate the probability of each of the individual words based on the counts. Our corpus contains 10 words with each word appearing once, and hence, each word in the corpus is assigned a probability of 0.1. Now, while testing the generalization of our model to the English language, we observe another sentence, "Probabilistic graphical models are hard." The probability of the sentence under our model is
 $$0.1 \times 0.1 \times 0.1 \times 0.1 \times 0 = 0$$. We did not observe one of the words ("hard") during training which made our language model infer the sentence as impossible, even though it is a perfectly plausible sentence.
 
-Out-of-vocabulary words are a common phenomena even for language models trained on large corpus. One of the simplest ways to handle these words is to assign a prior probability of observing an out-of-vocabulary word such that the model will assign a low, but non-zero probability to test sentences containing such words. In practice in modern systems, a system of [tokenization](https://ai.googleblog.com/2021/12/a-fast-wordpiece-tokenization-system.html) is used where a set of fundamental tokens can be combined to form any word. Hence the word "Hello" as a single token and the word "Bayesian" is encoded as "Bay" + "esian" under the common Byte Pair Encoding. This can be viewed as putting a prior over all words, where longer words are less likely.
+Out-of-vocabulary words are a common phenomena even for language models trained on large corpus. One of the simplest ways to handle these words is to assign a prior probability of observing an out-of-vocabulary word such that the model will assign a low, but non-zero probability to test sentences containing such words. As an aside, in modern systems, [tokenization](https://ai.googleblog.com/2021/12/a-fast-wordpiece-tokenization-system.html) is commonly used, where a set of fundamental tokens can be combined to form any word. Hence the word "Hello" as a single token and the word "Bayesian" is encoded as "Bay" + "esian" under the common Byte Pair Encoding. This can be viewed as putting a prior over all words, where longer words are less likely.
 
 ## Setup
 
@@ -119,7 +119,7 @@ In other words, if the prior is a Dirichlet distribution with parameter $$(\alph
 
 Many distributions have conjugate priors. In fact, any exponential family distribution has a conjugate prior. Even though conjugacy seemingly solves the problem of computing Bayesian posteriors, there are two caveats: 1. Usually practitioners will want to choose the prior $$p(\theta)$$ to best capture his or her knowledge about the problem, and using conjugate priors is a strong restriction. 2. For more complex distributions, the posterior computation is not as easy as those in our examples. There are distributions for which the posterior computation is still NP hard. 
 
-Conjugate priors is a powerful tool used in many real world applications such as topic modeling (e.g. latent dirichlet allocation) and medical diagnosis. However, practitioners should be mindful of its short-comings and consider and compare with other tools such as MCMC or variational inference (also covered in these lecture notes). 
+Conjugate priors is a powerful tool used in many real world applications such as topic modeling (e.g. latent dirichlet allocation) and medical diagnosis. However, practitioners should be mindful of its short-comings and consider and compare with other tools such as MCMC or variational inference (also covered in [https://ermongroup.github.io/cs228-notes/inference/sampling/](these lecture notes)).