# What is probability?

Linguistics 570 Homework 6 For Homework 6, answer the following questions to the best of your ability. Answers to all are derived from material in J&M, M&S, papers assigned in class, and/or class lectures.Document Preview:

Linguistics 570 Homework 6 For Homework 6, answer the following questions to the best of your ability. Answers to all are derived from material in J&M, M&S, papers assigned in class, and/or class lectures. Turn-in a softcopy in CollectIt by the deadline. Questions: 1. A and B are two random variables. Given P(A), P(B), and P(A,B), how do you calculate P(A|B) and P(B|A)? 2. Tag the sentence John said that he would call Mary tomorrow. Use PTB tags. 3. List all the word bigrams in the sentence John called Mary yesterday. 4. Draw an FSA that will accept the regular expression (a | b | c)+cdb* 5. Given a POS tagging problem using an HMM, describe why a dynamic programming algorithm like Viterbi is essential. 6. Given the following HMM: Start (p): BOS 1.0 A (transition): BOS N 0.2 BOS V 0.1 N V 0.5 N N 0.3 V V 0.1 V N 0.1 B (emission): N time 0.2 V time 0.1 N flies 0.1 V flies 0.4 What is the best state sequence for the sentence time flies? What is its probability?7. Given the following HMM, what’s the most probable output for the sequence quite quite fast? What is its probability? quite fast quite fast 0.2 0.8 0.7 0.3 0.8 end start JJ RB 1 1 0.1 0.2 0.9 8. Describe the B-I-O annotation scheme, and provide two examples in NLP where it is applied. Describe the implementation in the two examples you provide. 9. In a POS tagging task, let V be the size of the vocabulary (i.e., the number of words), and T be the size of the tagset. Suppose we use the following features for the task: a. Previous word w-1 b. Current word w0 c. Next word w+1 d. Surrounding words w-1 w+1 e. Previous tag t-1 f. Previous two tags t-2 t-1 How many features are there in total? 10. For a classifier, what is an Attribute-Value Table? What is a Confusion Matrix, and how can you use a Confusion Matrix to drive feature engineering.11.