In this assignment we will be training a language model to build a spell checker. Specifically, we will be implementing part of a noisy-channel model for spelling correction. We will give the likelihood term, or edit model, and Our job is to make a language model, the prior distribution in the noisy channel model. At test time we will be given a sentence with exactly one typing error. We then select the correction which gets highest likelihood under the noisy-channel model, using Our language model as the prior. Our language models will be evaluated for accuracy, the number of valid corrections, divided by the number of test sentences.

• Laplace Unigram Model - A unigram model with add-one smoothing. Treat out-of- vocabulary items as a word which was seen zero times in training.
• Laplace Bigram Model - A bigram model with add-one smoothing.
• Stupid Back-Off Model - Uses an unsmoothed bigram model combined with backoff to an add-one smoothed unigram model
• Custom Language Model - Uses a smoothened Bigram and Unigram model estimating probabilities in a fashion similar to stupid back off but slightly different.

The code SpellChecker.py returns the metrics used for evaluation.

The results are:

Uniform Language Model : 
correct: 31 total: 471 accuracy: 0.065817
Laplace Unigram Language Model: 
correct: 52 total: 471 accuracy: 0.110403
Laplace Bigram Language Model: 
correct: 65 total: 471 accuracy: 0.138004
Stupid Backoff Language Model: 
correct: 86 total: 471 accuracy: 0.182590
Custom Language Model: 
correct: 90 total: 471 accuracy: 0.191083

The required parameters for accuracy were:

Model Name                         Accuracy
*******************************************
Laplace Unigram Language Model       0.11 
Laplace Bigram Language Model        0.13
Stupid Backoff Language Model        0.18
Custom Language Model                0.18

As we can clearly see, the given resuts are well above the required metrics.