lecture_06

lecture_06 - CSCI 5832 Natural Language Processing Jim...

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02/13/12 1 CSCI 5832 Natural Language Processing Jim Martin Lecture 6
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2 Today 1/31 Probability Basic probability Conditional probability Bayes Rule Language Modeling (N-grams) N-gram Intro The Chain Rule Smoothing: Add-1
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3 Probability Basics Experiment (trial) Repeatable procedure with well-defined possible outcomes Sample Space (S) the set of all possible outcomes finite or infinite Example coin toss experiment possible outcomes: S = {heads, tails} Example die toss experiment possible outcomes: S = {1,2,3,4,5,6} QuickTimeᆰ and a TIFF (Uncompressed) decomp are needed to see this pictur QuickTimeᆰ and a TIFF (Uncompressed) decom are needed to see this pictur Slides from Sandiway Fong
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4 Probability Basics Definition of sample space depends on what we are asking Sample Space (S): the set of all possible outcomes Example die toss experiment for whether the number is even or odd possible outcomes: {even,odd} not {1,2,3,4,5,6} QuickTimeᆰ and a TIFF (Uncompressed) decom are needed to see this pictur
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5 More Definitions Events an event is any subset of outcomes from the sample space Example Die toss experiment Let A represent the event such that the outcome of the die toss experiment is divisible by 3 A = {3,6} A is a subset of the sample space S= {1,2,3,4,5,6} Example Draw a card from a deck suppose sample space S = {heart,spade,club,diamond} ( four suits ) let A represent the event of drawing a heart let B represent the event of drawing a red card A = {heart} B = {heart,diamond} QuickTimeᆰ an TIFF (Uncompresse are needed to see t
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6 Probability Basics Some definitions Counting suppose operation o i can be performed in n i ways, then a sequence of k operations o 1 o 2 ...o k can be performed in n 1 × n 2 × ... × n k ways Example die toss experiment, 6 possible outcomes two dice are thrown at the same time number of sample points in sample space = 6 × 6 = 36 QuickTimeᆰ and a TIFF (Uncompressed) decom are needed to see this pictu
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7 Definition of Probability The probability law assigns to an event a number between 0 and 1 called P(A) Also called the probability of A This encodes our knowledge or belief about the collective likelihood of all the elements of A Probability law must satisfy certain properties
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8 Probability Axioms Nonnegativity P(A) >= 0, for every event A Additivity If A and B are two disjoint events, then the probability of their union satisfies: P(A U B) = P(A) + P(B) Normalization The probability of the entire sample space S is equal to 1, I.e. P(S) = 1.
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9 An example An experiment involving a single coin toss There are two possible outcomes, H and T Sample space S is {H,T} If coin is fair, should assign equal probabilities to 2 outcomes Since they have to sum to 1 P({H}) = 0.5 P({T}) = 0.5 P({H,T}) = P({H})+P({T}) = 1.0
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This note was uploaded on 02/11/2012 for the course ECE 5527 taught by Professor Staff during the Fall '11 term at FIT.

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lecture_06 - CSCI 5832 Natural Language Processing Jim...

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