stochastic context free grammar
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STOCHASTIC CONTEXT FREE GRAMMAR. PARSING & USE. OUTLINE. Introduction to Stochastic Context Free Grammar(SCFG) Parsing of SCFG Use to RNA secondary structure prediction. SCFG. Chomsky hierarchy:. CONTEXT FREE GRAMMAR It’s a triple where: ∑ = set of terminal symbols(alphabet)

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Presentation Transcript
  • Introduction to Stochastic Context Free Grammar(SCFG)
  • Parsing of SCFG
  • Use to RNA secondary structure prediction

Chomsky hierarchy:

  • It’s a triple where:
  • ∑ = set of terminal symbols(alphabet)
  • V = set of non terminal symbols
  • R = set of production rules in the form:
  • S=special start symbol and ∑ П V=Φ

A string can be derived from another string ( ) if:

and the production is a production of the grammar.


A Stochastic Context Free Grammar is a quadruple G=(∑,V,R,P):

Probability function


Def.: Let G=(∑,V,R,P) a SCFG and a derivation sequence d,

where is a string of non terminal symbols, the probability of the derivation d is:



  • Grammar can be ambiguous
  • Def. : The probability of SCFG G that produce the string s, is: , where are the derivation sequences that produces s.
  • Chomsky Normal Form(CNF)
  • Def.: A CFG(or SCFG) is in CNF if all the rules are in this form:

B and C non terminal symbol

αis a single terminal symbol

scfg parsing
SCFG - Parsing
  • Parsing process




Parse tree

Give a sequence and a grammar, which is the best parse tree that generate the sequence, wath is which is the parse tree with the highest probability?

CYK algorithm

scfg parsing1
SCFG - Parsing
  • CYK algorithm (Cocke-Younger-Kasami)
  • High usedfor NLP(NaturalLanguage Processing)
  • Dynamicprogramming
  • Work with SCFG in CNF
scfg parsing2
SCFG – Parsing
  • Input: SCFG G in CNF and word s.
  • Data Structure: dynamic programming 3-D arrray holds the maximum probability for a constituent with non terminal a spanning words i…j. Back-pointers to construct the parse tree.
  • Output: maximum probability parse.
scfg parsing3
SCFG - Parsing
  • Initialization: n = length of ,R = number of nonterminals in G.

Table P[n,n,R] = 0 // set all values in table to 0.

Triples G[n,n,R] = triples of (position,nonterminal1,nonterminal2). //traceback pointers

For j = 1 to n do

for all unit productions of type do

if s[j] == then

set P[j,1,V] = Pv() // the probability of the production

set G[j,1,V] = new Triple(0,0,0) // indicates no further traceback - i.e. a child node

end if

end for

end for

scfg parsing4
SCFG - Parsing
  • Mainloop:

//i is the length of the span, j the start and k where to split into two subspans

for i = 2 to n do

for j = 1 to n-i+1 do

for k = 1 to i-1 do

for all productions of type do

set newprob = P[j, k, X] *P[j + k, i – k, Y ]*pv(XY )

if newprob > P[j, i, V ] then

set P[j, i, V ] = newprob

set G[j, i, V] = new Triple(k,X,Y) // new traceback // point

end if

end for

end for

end for

end for

P[1][n][Start symbol in G] holds the probability of the most likely parse.

scfg parsing5
SCFG - Parsing
  • Memory cost: O(n^2*M)
  • Time cost: O(n^3*T)

n=length of the input string

M=number of non terminal symbols

T=number of production rules in the type V-->XY

scfg use
SCFG - Use
  • RNA primary structure: a nucleotide sequence constituent the mulecule, represented with a single string of the {a,c,g,u} alphabet
  • RNA secondary structure: refer to the retreat of the sequence(that is the primary structure) to her-self, due to the action of hydrogen link.
scfg use1
SCFG - Use

Stem & loop

scfg use2
SCFG - Use
  • The secondarystructureof RNA isimportantbecause:
  • RNA “preserve” thisstructureduring the time
  • It’s common findsimilar RNA thathave the similarsecondarystructure, butdifferntsequenceofnucleotides
  • Evolutionof the RNA “follow” hisstructure

Sequenceanalysisof RNA is more difficultthan DNA and otherproteins

scfg use3
SCFG - Use
  • Problem:

- Prediction of RNA secondary structure for a single sequence?

Analogy with SCFG

Calculate the most likely “parse tree” that derive a string

scfg use4
SCFG - Use
  • Simple grammar for RNA:
  • S -> gSc | cSg | aSu | uSa | ε (complementary couples)
  • S -> aS | cS | gS | uS (left single basis)
  • S -> Sa | Sc | Sg | Su (right single basis)
  • S -> a | c | g | u (single basis)
  • S -> SS (fork)
scfg use5
SCFG - Use

Nucleotides sequence


RNA secondary structure

Parse tree