Language modelling

Description of this Post

1 Example of Categorical Distribution

• Vocabulary:
  V=3, {dog, cat,bird}

• Num Observations:
  N=9

• Categories:
  C=3, {negative, neutral, positive}

• Dataset:
  D={(class1, word1)…}

1.1 Formula for parameter estimation

Here the denominator means to count all pairs that have the same class

• Tabular Representation:

\[ W|C=c \, \textasciitilde \, \text{ Categorical}(\theta_{1:V}^{(c)}) \]

• The dataset:

• Maximum Likelihood Estimates:

2 Smoothing

For instance if I have to compute the prob for \(\theta_{bird}^{neg}=\frac{0}{3}\) then because I will have a zero probability then I can use only the count plus some constant (smoothing)so that the probability estimate does not become \(0\)

For instance:

Here 0.1 is the smoothing constant

So if not smoothing then use probs, if use smoothing the we use the counts

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