Perplexity Calculator

Background Knowledge

Language Modeling is a fundamental task in Natural Language Processing (NLP) that involves predicting the next word in a sequence of words. A bigram model is a type of language model that predicts the next word based on the previous word. The probability of a word $w_i$ given the previous word $w_{i-1}$ is denoted as $P(w_i | w_{i-1})$. Laplace smoothing is a technique used to avoid zero probabilities by adding a small value to the numerator and denominator of the probability calculation.

The concept of perplexity is used to evaluate the performance of a language model. It measures how well the model predicts a sample of text. A lower perplexity indicates better performance. The perplexity calculation involves summing the log probabilities of each word in the test sentence and then exponentiating the average of these log probabilities. This calculation provides a measure of how well the model predicts the test sentence.

In the context of this problem, we need to calculate the perplexity of a language model on a test sentence using a bigram model with Laplace smoothing. This requires understanding the concepts of language modeling, bigram models, Laplace smoothing, and perplexity calculation. We also need to be familiar with the input and output formats specified in the problem description.

Algorithm/Approach

The general approach to solving this problem involves the following steps:

• Train a bigram model using the provided training sentences
• Calculate the probability of each word in the test sentence using the trained model and Laplace smoothing
• Calculate the perplexity of the test sentence using the log probabilities of each word
• Output the perplexity rounded to 4 decimal places