NLP2020
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What is the criterion that defines that two random variables X and Y are independent using conditional probability:
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Consider a distribution object as a software engineering pure interface. List 5 methods that can be computed over a distribution with their signature:
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Given a distribution p with parameters w, and an observed dataset D, the Bayes formula states that: p(w | D) = p(D | w) p(w) / p(D) Indicate the definition of the following terms: Posterior: Prior: Likelihood:
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Indicate which formula is optimized for each of the following two estimation methods: Maximum Likelihood Estimator (MLE): w* = Maximum a posteriori estimator (MAP): w* =
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Bayesian estimation differs from MLE and MAP because it does not provide a pointwise estimator of the parameters of a distribution given a dataset. What does it do instead? How can Bayesian estimation be used to perform prediction?
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When performing feature extraction over words, list 3 types of features that are typically useful. For each one, provide an estimate of the expected number of values for the feature given a training dataset containing N tokens and V distinct words.
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List 3 methods that are useful to reduce the dimension of a Bag of Word feature representation for documents. For each method, explain why the simplification induced by the method is intuitively justified.
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Describe the TF-IDF method - why is it useful and how is it computed (intuitively - without detailed formula)
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Learning a Bayes classifier without independence assumptions requires an unrealistic number of training examples. Compute the number of parameters to be learned for a model Y = f(X) where Y is a boolean variable, and X is vector of N boolean features. What is the number of parameters under Naive Bayes assumptions? p(Y | X) = p(X | Y) p(Y) / p(X) Number of parameters for p(Y) Number of parameters for p(X | Y) Number of parameters under Naive Bayes independence assumption:
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Consider the task of classifying first-names as masculine vs. feminine. Explain why a Naive Bayes model that considers features (suffix[-1], suffix[-2]) (that is, 2 features for the last 2 letters in the word) behaves differently from one that considers a single feature (suffix[-12]) - that is, a single feature containing the last 2 letters.
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