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Artificial Intelligence and Learning Algorithms
Presented By Brian M. Frezza 12/1/05
Game Plan
• What’s a Learning Algorithm?• Why should I care?
– Biological parallels
• Real World Examples• Getting our hands dirty with the algorithms
– Bayesian Networks– Hidden Markov Models– Genetic Algorithms– Neural Networks
• Artificial Neural Networks Vs Neuron Biology– “Fraser’s Rules”
• Frontiers in AI
HardMath
What’s a Learning Algorithm?
• “An algorithm which predicts data’s future behavior based on its past performance.”– Programmer can be ignorant of the data’s
trends.• Not rationally designed!
– Training Data– Test Data
Why do I care?
• Use In Informatics– Predict trends in “fuzzy” data
• Subtle patterns in data• Complex patterns in data• Noisy data
– Network inference– Classification inference
• Analogies To Chemical Biology – Evolution– Immunological Response– Neurology
• Fundamental Theories of Intelligence– That’s heavy dude
Street Smarts
• CMU’s Navlab-5 (No Hands Across America)– 1995 Neural Network Driven Car– Pittsburgh to San Diego: 2,797 miles (98.2%)– Single hidden layer backpropagation network!
• Subcellular location through fluorescence– “A Neural network classifier capable of recognizing the patterns of all major subcellular
structures in fluorescence microscope images of HeLa cells” M. V. Boland, and R. F. Murphy, Bioinformatics (2001) 17(12), 1213-1223
• Protein secondary structure prediction• Intron/Exon predictions• Protein/Gene network inference• Speech recognition• Face recognition
The Algorithms
• Bayesian Networks• Hidden Markov Models• Genetic Algorithms
• Neural Networks
Bayesian Networks: Basics
• Requires models of how data behaves– Set of Hypothesis: {H}
• Keeps track of likelihood of each model being accurate as data becomes available– P(H)
• Predicts as a weighted average – P(E) = Sum( P(H)*H(E) )
Bayesian Network Example
• What color hair will Paul Schaffer’s
kids have if he marries Redhead? – Hypothesis
• Ha(rr) rr x rr: 100% Redhead
• Hb(Rr) rr x Rr: 50% Redhead 50% Not
• Hc(RR) rr x RR: 100% Not
• Initially clueless:– So P(Ha) = P(Hb) = P(Hc) = 1/3
Bayesian Network: Trace
Ha: 100% RedheadHb: 50% Redhead 50% Not
Hc: 100% Not
Redhead 0Not 0
HypothesisHistory
Likelihood's
1/31/31/3
P(Hc)P(Hb)P(Ha)
= P(red|Ha)*P(Ha) + P(red|Hb)*P(Hb) + P(red|Hc)*P(Hc)= (1)*(1/3) + (1/2)*(1/3) + (0)(1/3)
=(1/2)
Prediction: Will their next kid be a Redhead?
Bayesian Network:Trace
Ha: 100% RedheadHb: 50% Redhead 50% Not
Hc: 100% Not
Redhead 1Not 0
HypothesisHistory
Likelihood's
01/21/2
P(Hc)P(Hb)P(Ha)
= P(red|Ha)*P(Ha) + P(red|Hb)*P(Hb) + P(red|Hc)*P(Hc)= (1)*(1/2) + (1/2)*(1/2) + (0)(1/3)
=(3/4)
Prediction: Will their next kid be a Redhead?
Bayesian Network: Trace
Ha: 100% RedheadHb: 50% Redhead 50% Not
Hc: 100% Not
Redhead 2Not 0
HypothesisHistory
Likelihood's
01/43/4
P(Hc)P(Hb)P(Ha)
= P(red|Ha)*P(Ha) + P(red|Hb)*P(Hb) + P(red|Hc)*P(Hc)= (1)*(3/4) + (1/2)*(1/4) + (0)(1/3)
=(7/8)
Prediction: Will their next kid be a Redhead?
Bayesian Network: Trace
Ha: 100% RedheadHb: 50% Redhead 50% Not
Hc: 100% Not
Redhead 3Not 0
HypothesisHistory
Likelihood's
01/87/8
P(Hc)P(Hb)P(Ha)
= P(red|Ha)*P(Ha) + P(red|Hb)*P(Hb) + P(red|Hc)*P(Hc)= (1)*(7/8) + (1/2)*(1/8) + (0)(1/3)
=(15/16)
Prediction: Will their next kid be a Redhead?
Bayesian Networks Notes
• Never reject hypothesis unless directly disproved
• Learns based on rational models of behavior– Models can be extracted!
• Programmer needs to form hypothesis beforehand.
The Algorithms
• Bayesian Networks• Hidden Markov Models• Genetic Algorithms
• Neural Networks
Hidden Markov Models(HMM)
• Discrete learning algorithm– Programmer must be able to categorize predictions
• HMMs also assume a model of the world working behind the data
• Models are also extractable• Common Uses
– Speech Recognition– Secondary structure prediction– Intron/Exon predictions– Categorization of data
Hidden Markov Models: Take a Step Back
• 1st order Markov Models:– Q{States}– Pr{Transition}– Sum of all P(T) out of state = 1
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
1st order Markov Model Setup
• Pick Initial state: Q1
• Pick Transition Probabilities:
• For each time step– Pick a random number 0.0-1.0
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
P1 P2 P3 P4
0.6 0.2 0.9 0.4
1st order Markov Model Trace
• Current State: Q1 Time Step = 1• Transition probabilities:
• Random Number:– 0.22341
• So Next State:– 0.22341 < P1
• Take P1
– Q2
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
P1 P2 P3 P4
0.6 0.2 0.9 0.4
1st order Markov Model Trace
• Current State: Q2 Time Step = 2
• Transition probabilities:
• Random Number:– 0.64357
• So Next State:– No Choice, P = 1– Q3
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
P1 P2 P3 P4
0.6 0.2 0.9 0.4
1st order Markov Model Trace
• Current State: Q3 Time Step = 3• Transition probabilities:
• Random Number:– 0.97412
• So Next State:– 0.97412 > 0.9
• Take 1-P3
– Q4
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
P1 P2 P3 P4
0.6 0.2 0.9 0.4
1st order Markov Model Trace
• Current State: Q4 Time Step = 4
• Transition probabilities:
• I’m going to stop here.
• Markov Chain:– Q1, Q2, Q3, Q4
Q1
Q4
Q2
Q3
P1
P2
1-P1-P2
P3
1-P3
1
1-P4
P4
P1 P2 P3 P4
0.6 0.2 0.9 0.4
What else can Markov do?
• Higher Order Models– Kth order
• Metropolis-Hastings– Determining thermodynamic equilibrium
• Continuous Markov Models– Time step varies according to continuous
distribution
• Hidden Markov Models– Discrete model learning
Hidden Markov Models (HMMs)
• A Markov Model drives the world but it is hidden from direct observation and its status must be inferred from a set of observables. – Voice recognition
• Observable: Sound waves• Hidden states: Words
– Intron/Exon prediction• Observable: nucleotide sequence• Hidden State: Exon, Intron, Non-coding
– Secondary structure prediction for protein• Observable: Amino acid sequence• Hidden State: Alpha helix, Beta Sheet, Unstructured
Hidden Markov Models: Example• Secondary Structure Prediction
ObservableStates
HiddenStates
UnstructuredAlphaHelix
BetaSheet
His Asp Arg Phe Ala Cis Ser Gln Glu Lys
Leu Met Asn Ser Tyr Thr Ile Trp Pro ValGly
Hidden Markov Models: Smaller Example
GT CA
ExonIntergenic
Intron
ObservableStates
HiddenStates
• Exon/Intron Mapping
P(Ex|Ex)
P(In|Ex)
P(In|Ex) P(It|It)P(Ig|It)
P(Ex|It)
P(Ig|Ig)
P(Itr|Ig)P(Ex|Ig)
P(A|Ex)P(A|It)
P(A|Ig)
P(C|It)P(G|It)P(T|It)P(T|Ex) P(G|Ex) P(C|Ex)
P(C|Ig)
P(T|Ig) P(G|Ig)
Hidden Markov Models: Smaller Example
• Exon/Intron Mapping
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
m
Hid
den
Sta
te
Observable
0.010.890.1
ItIgEx
Starting Distribution
Hidden Markov Model
• How to predict outcomes from a HMM
• Brute force:
– Try every possible Markov chain• Which chain has greatest probability of
generating observed data?
– Viterbi algorithm• Dynamic programming approach
Viterbi Algorithm: Trace
0.80.020.18It
0.010.90.09Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = P(A|Ex) * Start Exon = 3.3*10-2
Introgenic = P(A|Ig) * Start Ig = 2.2*10-1
Intron = P(A|It) * Start It = 0.14 * 0.01 = 1.4*10-3
G
T
A
G
A
G
C
G
G
T
A
A
T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex) = 4.6*10-2
Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig) = 2.8*10-2
Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It) = 1.1*10-3
G
T
A
G
A
G
C
G
G
T
A
A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex) = 1.1*10-2
Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig) = 3.5*10-3
Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It) = 1.3*10-3
G
T
A
G
A
G
C
G
G
T
A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex)Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig)Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It)
G
T
A
G
A
G
C
G
G
T
2.9*10-44.3*10-42.4*10-3A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex)Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig)Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It)
G
T
A
G
A
G
C
G
G
7.8*10-56.1*10-57.2*10-4T
2.9*10-44.3*10-42.4*10-3A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex)Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig)Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It)
G
T
A
G
A
G
C
G
7.2*10-51.8*10-55.5*10-5G
7.8*10-56.1*10-57.2*10-4T
2.9*10-44.3*10-42.4*10-3A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex)Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig)Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It)
G
T
A
G
A
G
C
2.9*10-52.2*10-64.3*10-6G
7.2*10-51.8*10-55.5*10-5G
7.8*10-56.1*10-57.2*10-4T
2.9*10-44.3*10-42.4*10-3A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Viterbi Algorithm: Trace
0.80.020.18It
0.010.50.49Ig
0.20.10.7Ex
ItIgEx
Hidden State Transition Probabilities
0.20.50.160.14It
0.250.250.250.25Ig
0.140.110.420.33Ex
CGTA
Observable State Probabilities
To
Fro
mH
idd
en S
tate
Observable
0.010.890.1
ItIgEx
Starting Distribution
Example Sequence: ATAATGGCGAGTG
Exon = Max( P(Ex|Ex)*Pn-1(Ex), P(Ex|Ig)*Pn-1(Ig), P(Ex|It)*Pn-1(It) ) *P(T|Ex)Introgenic =Max( P(Ig|Ex)*Pn-1(Ex), P(Ig|Ig)*Pn-1(Ig), P(Ig|It)*Pn-1(It) ) * P(T|Ig)Intron = Max( P(It|Ex)*Pn-1(Ex), P(It|Ig)*Pn-1(Ig), P(It,It)*Pn-1(It) ) * P(T|It)
4.7*10-103.6*10-111.1*10-10G
1.2*10-91.2*10-101.4*10-9T
9.2*10-94.1*10-104.9*-9A
8.2*10-82.7*10-98.4*-9G
2.0*10-79.1*10-91.1*10-7A
1.8*10-63.5*10-89.1*10-8G
4.6*10-62.8*10-77.2*10-7C
2.9*10-52.2*10-64.3*10-6G
7.2*10-51.8*10-55.5*10-5G
7.8*10-56.1*10-57.2*10-4T
2.9*10-44.3*10-42.4*10-3A
1.3*10-33.5*10-31.1*10-2A
1.1*10-32.8*10-24.6*10-2T
1.4*10-32.2*10-13.3*10-2A
IntronIntrogenicExon
Hidden Markov Models
• How to Train an HMM– The forward-backward algorithm
• Ugly probability theory math:
• Starts with an initial guess of parameters• Refines parameters by attempting to reduce the
errors it provokes with fitted to the data.– Normalized probability of the “Forward probability” of
arriving at the state given the observable cross multiplied by the backward probability of generating that observable given the parameter.
CENSORED
The Algorithms
• Bayesian Networks• Hidden Markov Models• Genetic Algorithms
• Neural Networks
Genetic Algorithms
• Individuals are series of bits which represent candidate solutions– Functions– Structures– Images– Code
• Based on Darwin evolution– individuals mate, mutate, and are selected
based on a Fitness Function
Genetic Algorithms
• Encoding Rules– “Gray” bit encoding
• Bit distance proportional to value distance
• Selection Rules– Digital / Analog Threshold
– Linear Amplification Vs Weighted Amplification
• Mating Rules– Mutation parameters– Recombination parameters
Genetic Algorithms
• When are they useful?– Movements in sequence space are funnel shaped
with fitness function• Systems where evolution actually applies!
• Examples– Medicinal chemistry– Protein folding– Amino acid substitutions– Membrane trafficking modeling– Ecological simulations – Linear Programming– Traveling salesman
The Algorithms
• Bayesian Networks• Hidden Markov Models• Genetic Algorithms
• Neural Networks
Neural Networks
• 1943 McCulloch and Pitts Model of how Neurons process information– Field immediately splits
• Studying brain’s– Neurology
• Studying artificial intelligence– Neural Networks
Neural Networks: A Neuron, Node, or Unit
Σ(W)- W0,c
Activation Function Output
Wa,c
Wb,c
W0,c
(Bias)
Wc,n
a z (Bias)
Neural Networks: Activation Functions
Sigmoid Function(logistic function)
Threshold Function
Zero point set by bias
In In
out out+1 +1
Threshold Functions can makeLogic Gates with Neurons!
000
011
01∩
Logical AndW0,c = 1.5
Wb,c = 1
Wa,c = 1
A
B
Σ(W)- W0,ca z (Bias)
Output
If ( Σ(w) – Wo,c > 0 )
Then FIRE
Else
Don’t
(Bias)
And Gate: Trace
W0,c = 1.5
Wb,c = 1
Wa,c = 1
-1.5
Off
Off
Off-1.5 < 0(Bias)
And Gate: Trace
W0,c = 1.5
Wb,c = 1
Wa,c = 1
-0.5
On
Off
Off-0.5 < 0(Bias)
And Gate: Trace
W0,c = 1.5
Wb,c = 1
Wa,c = 1
-0.5
Off
On
Off-0.5 < 0(Bias)
And Gate: Trace
W0,c = 1.5
Wb,c = 1
Wa,c = 1
0.5
On
On
On0.5 > 0(Bias)
Threshold Functions can makeLogic Gates with Neurons!
W0,c = 0.5
Wb,c = 1
Wa,c = 1
A
Σ(W)- W0,ca z (Bias)
If ( Σ(w) – Wo,c > 0 )
Then FIRE
Else
Don’t
(Bias)
010
111
01U
Logical OrB
Or Gate: Trace
W0,c = 0.5
Wb,c = 1
Wa,c = 1
-0.5
Off
Off
Off-0.5 < 0(Bias)
Or Gate: Trace
W0,c = 0.5
Wb,c = 1
Wa,c = 1
0.5
On
Off
On0.5 > 0(Bias)
Or Gate: Trace
W0,c = 0.5
Wb,c = 1
Wa,c = 1
0.5
Off
On
On0.5 > 0(Bias)
Or Gate: Trace
W0,c = 0.5
Wb,c = 1
Wa,c = 1
1.5
On
On
On1.5 > 0(Bias)
Threshold Functions can makeLogic Gates with Neurons!
W0,c = -0.5
Wa,c = -1
Σ(W)- W0,ca z (Bias)
If ( Σ(w) – Wo,c > 0 )
Then FIRE
Else
Don’t
(Bias)Logical Not
10
01!
Not Gate: Trace
W0,c = -0.5
Wa,c = -1
-0.5
Off
On0.5 > 0(Bias)
0 – (-0.5) = 0.5
Not Gate: Trace
W0,c = -0.5
Wa,c = -1
-0.5
On
Off-0.5 < 0(Bias)
-1 – (-0.5) = -0.5
Feed-Forward Vs. Recurrent Networks
• Feed-Forward– No Cyclic connections– Function of its current
inputs– No internal state other
then weights of connections
• “Out of time”
• Recurrent– Cyclic connections– Dynamic behavior
• Stable• Oscillatory• Chaotic
– Response depends on current state
• “In time”
– Short term memory!
Feed-Forward Networks
• “Knowledge” is represented by weight on edges– Modeless!
• “Learning” consists of adjusting weights• Customary Arrangements
– One Boolean output for each value– Arranged in Layers
• Layer 1 = inputs
• Layer 2 to (n-1) = Hidden
• Layer N = outputs– “Perceptron” 2 layer Feed-Forward network
Layers
Input Output
Hidden layer
Perceptron Learning
• Gradient Decent used to reduce error
• Essentially: – New Weight = Old Weight + adjustment– Adjustment = α X error X input X d(activation function)
• α = Learning Rate
CENSORED
Hidden Network Learning
• Back-Propagation
• Essentially: – Start with Gradient Decent from output– Assign “blame” to inputting neurons proportional to
their weights– Adjust weights at previous level using Gradient
decent based on “blame”
CENSORED
They don’t get it either:Issues that aren’t well understood
• α (Learning Rate)
• Depth of network (number of layers)
• Size of hidden layers– Overfitting
– Cross-validation
• Minimum connectivity– Optimal Brain Damage Algorithm
• No extractable model!
How Are Neural Nets Different From My Brain?
1. Neural nets are feed forward– Brains can be recurrent with feedback loops
2. Neural nets do not distinguish between + or – connections
– In brains excitatory and inhibitory neurons have different properties• Inhibitory neurons short-distance
3. Neural nets exist “Out of time”– Our brains clearly do exist “in time”
4. Neural nets learn VERY differently– We have very little idea how our brains are learning
“Fraser’s” Rules
“In theory one can, of course, implement biologically realistic neural networks, but this is a mammoth task. All kinds of details have to be gotten right, or you end up with a
network that completely decays to unconnectedness, or one that ramps up its connections until it basically has a seizure.”
Frontiers in AI
• Applications of current algorithms• New algorithms for determining
parameters from training data– Backward-Forward– Backpropagation
• Better classification of the mysteries of neural networks
• Pathology modeling in neural networks• Evolutionary modeling