1. SCFG evolutionary algorithm

2. SCFG design
● Dowell & Eddy (2004)
G1: S  dS d ∣ d S ∣ S d ∣ SS ∣ 
G2: S  d S d ∣ d L ∣ Rd ∣ LS
L  d S d ∣ aL
R  Rd ∣ 
G3: S  d S ∣ d S d S ∣ 
G4: S  d S ∣ T ∣ 
T  T d ∣ d S d ∣ T d S d
G5: S  LS ∣ L
L  d F d ∣ d
F  d F d ∣ LS

3. SCFG design
● Dowell & Eddy (2004)
G1: S  dS d ∣ d S ∣ S d ∣ SS ∣ 
G2: S  d S d ∣ d L ∣ Rd ∣ LS
L  d S d ∣ aL
R  Rd ∣ 
G3: S  d S ∣ d S d S ∣ 
G4: S  d S ∣ T ∣ 
T  T d ∣ d S d ∣ T d S d
G5: S  LS ∣ L
L  d F d ∣ d
F  d F d ∣ LS

4. Search for better SCFGs
● Evolutionary algorithm
● Initial population
● Mutation model
● Breeding model
● Selection

5. Normal form
● Chomsky Normal Form
● CNF makes it hard to determine the associated structure
● Use a different normal form A  BC
A  d
A  d B d
A  BC
A  d
A  

6. CYK
V x
Vy Vz
i k k+1 j
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z

7. CYK
V x
Vy Vz
i k k+1 j
V x
Vy
i+1 j -1
i j
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z

8. CYK
V x
Vy Vz
i k k+1 j
V x
Vy
i+1 j -1
i j
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i= j
max
{
max
i≤k j
V x Vy V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z
max
V x d V y
d
score[y ,i1, j−1]⋅wx , y ,d , d⋅1seq[i]=d∧seq[ j]=d

9. CYK
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i= j
max
{
max
i≤k j
V x Vy V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z
max
V x d V y
d
score[y ,i1, j−1]⋅wx , y ,d , d⋅1seq[i]=d∧seq[ j]=d
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z

10. Initial population
● Use grammars from Dowell&Eddy
● biased search
● Use random grammars
● hard to generate random grammars
● Use small grammars with only 2 nonterminals

11. Mutations
● Insert rule
● Delete rule
● Modify rule
● Modify start variable
● Add nonterminal + 2 new rules
● Simulate rule A → B

12. Mutations
● Insert rule
● Delete rule
● Modify rule
● Modify start variable
● Add nonterminal + 2 new rules
● Simulate rule A → B
● Problem with what probabilities should these mutations occur?

13. Mutations
● Insert rule 4 / 13
● Delete rule 1 / 13
● Modify rule 2 / 13
● Modify start variable 1 / 13
● Add nonterminal + 2 new rules 4 / 13
● Simulate rule A → B 1 / 13
Everything else: uniform
● Problem with what probabilities should these mutations occur?

14. Breeding
● Captivate characteristics of two grammars in one
Initial grammars:
● G1
with nonterminals V1
, V2
, ..., Vn
● G2
with nonterminals W1
, W2
, ..., Wm
Bred grammar:
● G with nonterminals S, V2
, ..., Vn
, W2
, ..., Wm
● The set of rules for G is simply the union from G1
and G2
with
V1
and W1
replaced by S
● Properties

15. Decisions, decisions...
● How to select the grammars to mutate?
● How to select the grammars to breed?
● depending on the fitness of the grammar
– just one mutation or breeding is unlikely to improve fitness
– could bias the search
● independent of the fitness
– escape local optimum

16. Selection
● Fitness:
● RNA 2nd
structure metrics
● sensitivity and specificity
● Using fitness
● select deterministically
● select probabilistically
● Next generation
● mutated/bred grammars – better for escaping local optimum
● both “old” grammars and mutated/bred grammars

17. RNA metrics
S1
( . . . . . . )
S2
. . ( . . ) . .
S . . . . . . . .
distance(S1, S) = distance (S2, S) ?
distance(S1, S) ≠ distance (S2, S) ?

18. RNA metrics
S1
( . . . . . . )
S2
. . ( . . ) . .
S . . . . . . . .
distance(S1, S) = distance (S2, S) ?
distance(S1, S) ≠ distance (S2, S) ?
● Different metrics – different characteristics

19. Results
G0: A  BA ∣ d ∣ d C d
B  d ∣ d C d
C  BA ∣ d C d
G5: A  CC ∣ CB ∣ BC ∣ EC ∣ d A d ∣ d E d
B  d
C  CD ∣ Bb ∣ d A d
D  GC ∣ d C d
E  AB ∣ CD ∣ d
F  AB
G  FB
G7: A  DE ∣ AB ∣ BA ∣ AH ∣ d ∣ d F d ∣ d H d
B  d
C  d H d
D  BB ∣ AC
E  d ∣ d H d
F  FB ∣ CF ∣ d
G  GH ∣ d H d ∣ dC d
H  FA ∣ AF ∣ HH ∣ d B ∣ d H d
Gram
Dowell&Eddy RNA strand
sens spec sens spec
G0 0.465 0.406 0.496 0.479
G5 0.487 0.432 0.469 0.467
G7 0.465 0.376 0.526 0.479

20. Results
G0: A  BA ∣ d ∣ d C d
B  d ∣ d C d
C  BA ∣ d C d
G5: A  CC ∣ CB ∣ BC ∣ EC ∣ d A d ∣ d E d
B  d
C  CD ∣ Bb ∣ d A d
D  GC ∣ d C d
E  AB ∣ CD ∣ d
F  AB
G  FB
G7: A  DE ∣ AB ∣ BA ∣ AH ∣ d ∣ d F d ∣ d H d
B  d
C  d H d
D  BB ∣ AC
E  d ∣ d H d
F  FB ∣ CF ∣ d
G  GH ∣ d H d ∣ dC d
H  FA ∣ AF ∣ HH ∣ d B ∣ d H d
Gram
Dowell&Eddy RNA strand
sens spec sens spec
G0 0.465 0.406 0.496 0.479
G5 0.487 0.432 0.469 0.467
G7 0.465 0.376 0.526 0.479
D&E data contains pseudoknots!