Unigram probability from a corpus

Background

The unigram probability of a word is the simplest language model: its relative frequency in a corpus, $P(w) = \text{count}(w)/N$. This is the maximum-likelihood estimate under a bag-of-words (unigram) model — the starting point before adding context (bigrams, n-grams) or smoothing.

Problem statement

Implement unigram_probability(corpus, word) returning the relative frequency of word:

$$P(w) = \frac{\text{count}(w)}{N}$$

where $N$ is the total number of whitespace-separated tokens. Round to 4 decimals.

Input

• corpus — str: text, tokenised by whitespace.
• word — str: the target token.

Output

Returns a float in $[0, 1]$ (rounded to 4 decimals).

Examples

Example 1

Input:  corpus = "<s> Jack I like </s> <s> Jack I do like </s>", word = "Jack"
Output: 0.1818

Explanation: the corpus has 11 tokens and "Jack" appears twice, so $P(\text{Jack}) = 2/11 \approx 0.1818$.

Constraints

• Tokenise by whitespace (split()) and count exact-match tokens.
• $P(w) = \text{count}(w)/N$, rounded to 4 decimals.
• A word absent from the corpus has probability 0.

Notes

• This MLE estimate gives probability 0 to unseen words — the motivation for smoothing (add-one/Laplace) in real language models.
• Summed over the whole vocabulary, the unigram probabilities form a valid distribution (they total 1).