ESTIMATING PROBABILITIES*

Estimating Paired-Interaction Probabilities

Estimating Probabilities in PCFGs

CHAPTER 2 Estimating Probabilities

This is a rough draft chapter intended for inclusion in the upcoming second edition of the textbook Machine Learning, T.M. Mitchell, McGraw Hill. You are welcome to use this for educational purposes, but do not duplicate or repost it on the internet. For online copies of this and other materials related to this book, visit the web site www.cs.cmu.edu/∼tom/mlbook.html. Please send suggestions fo...

Estimating Probabilities of Default

We conduct a systematic comparison of confidence intervals around estimated probabilities of default (PD), using several analytical approaches from large-sample theory and bootstrapped small-sample confidence intervals. We do so for two different PD estimation methods—cohort and duration (intensity)—using twenty-two years of credit ratings data. We find that the bootstrapped intervals for the d...

Estimating Probabilities in PCFGs

◮ find P̂(N j → ζ) = C(N j→ζ) ∑ γ C(N j→γ) ◮ C(X) = count of how often rule X is used ◮ no annotation ⇒ no rule counts! =̂ hidden data problem – similar to Hidden Markov Models ◮ start with some initial rule probabilities, parse training sentences, use parse probabilities as indicator of confidence ◮ find expectation of how often a rule is used ◮ based on these expectations, maximize probabilities: