Download presentation

Presentation is loading. Please wait.

Published byShakira Gillham Modified over 3 years ago

1
Albert Gatt Corpora and Statistical Methods – Lecture 7

2
Smoothing (aka discounting) techniques Part 2

3
Overview… Smoothing methods: Simple smoothing Witten-Bell & Good-Turing estimation Held-out estimation and cross-validation Combining several n-gram models: back-off models

4
Rationale behind smoothing Sample frequencies seen events with probability P unseen events (including “grammatical” zeroes”) with probability 0 Real population frequencies seen events (including the unseen events in our sample) + smoothing to approximate Lower probabilities for seen events (discounting). Left over probability mass distributed over unseens (smoothing). results in

5
Laplace’s law, Lidstone’s law and the Jeffreys-Perks law

6
Instances in the Training Corpus: “inferior to ________” F(w)

7
Maximum Likelihood Estimate F(w) Unknowns are assigned 0% probability mass

8
Actual Probability Distribution F(w) These are non- zero probabilities in the real distribution

9
LaPlace’s Law (Add-one smoothing) F(w)

10
LaPlace’s Law (Add-one smoothing) F(w)

11
LaPlace’s Law F(w) NB. This method ends up assigning most prob. mass to unseens

12
Generalisation: Lidstone’s Law P = probability of specific n-gram C(x) = count of n-gram x in training data N = total n-grams in training data V = number of “bins” (possible n-grams) = small positive number M.L.E: = 0 LaPlace’s Law: = 1 (add-one smoothing) Jeffreys-Perks Law: = ½

13
Jeffreys-Perks Law F(w)

14
Objections to Lidstone’s Law Need an a priori way to determine. Predicts all unseen events to be equally likely Gives probability estimates linear in the M.L.E. frequency

15
Witten-Bell discounting

16
Main intuition A zero-frequency event can be thought of as an event which hasn’t happened (yet). The probability of it happening can be estimated from the probability of sth happening for the first time. The count of things which are seen only once can be used to estimate the count of things that are never seen.

17
Witten-Bell method 1. T = no. of times we saw an event for the first time. = no of different n-gram types (bins) NB: T is no. of types actually attested (unlike V, the no of possible types in add- one smoothing) 2. Estimate total probability mass of unseen n-grams: each token is an event & each new type is an event so above equation gives MLE of the probability of a new type event occurring (“being seen for the first time”) This is the total probability mass to be distributed among all zero events (unseens) no of actual n-grams (N) + no of actual types (T)

18
Witten-Bell method 3. Divide the total probability mass among all the zero n-grams. Can distribute it equally. 4. Remove this probability mass from the non-zero n-grams (discounting):

19
Witten-Bell vs. Add-one If we work with unigrams, Witten-Bell and Add-one smoothing give very similar results. The difference is with n-grams for n>1. Main idea: estimate probability of an unseen bigram from the probability of seeing a bigram starting with w1 for the first time.

20
Witten-Bell with bigrams Generalised total probability mass estimate: No. bigram types beginning with w x No. bigram tokens beginning with w x Estimated total probability of bigrams starting with some word w x

21
Witten-Bell with bigrams Non-zero bigrams get discounted as before, but again conditioning on history: Note: Witten-Bell won’t assign the same probability mass to all unseen n- grams. The amount assigned will depend on the first word in the bigram (first n- 1 words in the n-gram).

Similar presentations

OK

Chapter 6: Statistical Inference: n-gram Models over Sparse Data

Chapter 6: Statistical Inference: n-gram Models over Sparse Data

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on cross sectional study Ppt on world television day Ppt on tcp ip protocol architecture definition Ppt on regular expression Ppt on electric current and circuits Ppt on trade promotion Ppt on reproductive system of human body Fab ms ppt online Ppt on social etiquettes tips Professional ppt on home automation