The document describes an evolutionary algorithm for learning stochastic context-free grammars (SCFGs) to model RNA secondary structure. The algorithm starts with an initial population of grammars and uses mutations like adding/deleting rules and breeding grammars to generate new grammars. Grammars are selected for the next generation based on fitness metrics like sensitivity and specificity on RNA structure data. The results show grammars evolved by the algorithm achieve higher sensitivity and specificity than baseline grammars from Dowell & Eddy, although their data contains complex pseudoknot structures not modeled by SCFGs.
Evolutionary Algorithm for Optimal Connection Weights in Artificial Neural Ne...CSCJournals
A neural network may be considered as an adaptive system that progressively self-organizes in order to approximate the solution, making the problem solver free from the need to accurately and unambiguously specify the steps towards the solution. Moreover, Evolutionary Artificial Neural Networks (EANNs) have the ability to progressively improve their performance on a given task by executing learning. An evolutionary computation gives adaptability for connection weights using feed forward architecture. In this paper, the use of evolutionary computation for feed-forward neural network learning is discussed. To check the validation of proposed method, XOR benchmark problem has been used. The accuracy of the proposed model is more satisfactory as compared to gradient method.
This talk presents the results from one of our papers on the use of an evolutionary algorithm for an "inverse problem" on self-organised nano particles.
Evolutionary Algorithm for Optimal Connection Weights in Artificial Neural Ne...CSCJournals
A neural network may be considered as an adaptive system that progressively self-organizes in order to approximate the solution, making the problem solver free from the need to accurately and unambiguously specify the steps towards the solution. Moreover, Evolutionary Artificial Neural Networks (EANNs) have the ability to progressively improve their performance on a given task by executing learning. An evolutionary computation gives adaptability for connection weights using feed forward architecture. In this paper, the use of evolutionary computation for feed-forward neural network learning is discussed. To check the validation of proposed method, XOR benchmark problem has been used. The accuracy of the proposed model is more satisfactory as compared to gradient method.
This talk presents the results from one of our papers on the use of an evolutionary algorithm for an "inverse problem" on self-organised nano particles.
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 ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , 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 ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , 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 ji
ex , seq[i] if i= j
max
{
max
i≤k j
V x Vy V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z
max
V x d V y
d
score[y ,i1, j−1]⋅wx , y ,d , d⋅1seq[i]=d∧seq[ j]=d
9. CYK
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i= j
max
{
max
i≤k j
V x Vy V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , y , z
max
V x d V y
d
score[y ,i1, j−1]⋅wx , y ,d , d⋅1seq[i]=d∧seq[ j]=d
score[x ,i , j]=
{
0 if ji
ex , seq[i] if i=j
max
i≤kj
V x V y V z
score[y ,i ,k]⋅score[z ,k1, j]⋅tx , 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
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!