introduction to artificial intelligence: applications in computational biology

Intelligent Systems Laboratory

Introduction to Artificial Intelligence: Applications in

Computational Biology

Susan M. Bridges [email protected]

mailto:[email protected]


Outline• What is AI?

• Search

• Expert systems

• Uncertainty

• Machine learning

• Data mining


Intelligent Systems and Computational Biology

• First applications (DNA) in which great progress was made were digital• Signal processing algorithms• Text processing techniques

• Many of the most interesting and difficult problems to be tackled are analog• Protein structure• Gene expression• Metabolic networks


Definitions of AI(What is AI?)

• Rich, E. and K. Knight . 1991. Artificial Intelligence. New York: McGraw-Hill.

“Artificial intelligence (AI) is the study of how to make computers do things which at the moment, people do better.”


Another definition of AI• Winston, Patrick Henry. 1984. Artificial Intelligence.

1984. Addison-Wesley, Reading, MA.

“Artificial Intelligence is the study of ideas that enable computers to be intelligent. Intelligence includes: ability to reason, ability to acquire and apply knowledge, ability to perceive and manipulate things in the physical world, and others.”


Why Study AI?

• Understand human human intelligence

• Develop “intelligent” machines• Robotics

• Programs with intelligent properties


Acting Rationally:Turing Test Approach

Interrogator


AI Tasks

• Mundane tasks• Perception

» Vision

» Speech

• Natural Language» Understanding

» Generation

» Translation

• Common sense reasoning

• Robot control

• Formal tasks• Games

• Mathematics» Geometry

» Logic

» Integral calculus

• Expert tasks• Engineering

• Scientific analysis

• Medical diagnosis

• Financial analysis


Intelligent Agents• Agent

• Perceives its environment using sensors• Acts on environment using effectors

• Rational agent • An agent that does the right thing • Basis for action

» A measure of degree of success.» Knowledge of what has been perceived so far.» The actions that the agent can perform

• Autonomous Agent• Learns from experience• Makes independent decisions


Major Topics

• Search

• Knowledge Representation

• Machine Learning


Problem-solving agent• A type of goal-based agent

• Find sequence of actions that lead to a desirable state

• Intelligent agents should make a set of changes in the state of the environment that maximizes the performance measure

• Life is simpler if we can set a goal and aim to satisfy it.


Components of a problem• Initial state• Set of possible actions

• actions can be described as operators» an operator describes an action by specifying the state that can be

reached by carrying out an action in a particular state

• actions can be described in terms of a successor function S. Given a particular state x, S(x) returns the set of states reachable from x by any single action.

Operator aState x State y


State Space• The set of all states reachable from the initial

state by any sequence of actions

• A path in the state space is a sequence of actions leading from one state to another

• The agent can apply a goal test to any single state to determine if it is a goal state.

• If one path is preferable to another, then we may need to compute path cost (g).


5 4

7

6 1 8

3 2

1 2

7

8

3

4

6 5

Initial State Goal State

States Goal Test

Operators Path Cost


Mathiston

PhebaWest Point

Maben

Starkville

Columbus

Ackerman

Sturgis Artesia

Crawford

BrooksvilleLouisville

Mayhew

Problem: Find route from Louisville to West Point


LouisvilleA. The initial state

Louisville

Ackerman Starkville Brooksville

B. After expanding Louisville

C. After expanding Ackerman

Louisville

Ackerman Starkville Brooksville

Maben Sturgis Louisville


Some terms• New states are generated from old states by

operators.

• This is called expanding the state.

• The choice of which state to expand first is called the search strategy

• Result is called a search tree

• The set of nodes waiting to be expanded is called the fringe or frontier


Search Strategies• Requirements for a good search strategy

• causes motion

• is systematic

• State space can usually be represented as a tree or a graph

• Two important parameters of a tree• branching factor (b)

• depth (d)


Two Types of Searches• Uninformed or blind search

• systematically generate states

• test states to see if they are goal states

• Informed or heuristic search• use knowledge about the problem domain

• explore search space more efficiently

• may sacrifice accuracy for speed


Breadth-first search• All nodes at each depth d are expanded

before any nodes at depth d+1


Depth-first search Always expands one of the nodes at the

deepest level of the tree Parameter m is the maximum depth


What is a heuristic?(rule of thumb)

• A heuristic is a formalized rule for choosing those branches in a state space that are most likely to lead to an acceptable solution (Luger and Stubblefield, 1998).

• Used two ways• some problems do not have exact solutions, so we

just do the best we can (medical diagnosis)

• there may be an exact solution, but it may be very expensive to find


Hill Climbing• Use an heuristic function (or objective or

evaluation function) to decide which direction to move in the search space.

• Always move toward the state that appears to be best (basing all decisions on local information).

• Assume that we want to maximize the value of the function.

• Can also be used for minimization (called gradient descent)


1 2 3

7 8 4

6 5

1 2 3

7 4

6 8 5

1 2 3

7 8 4

6 6 5

1 2 3

7 8 4

6 5h=

Goal

1 2 3

8 4

7 6 5

Steepest Ascent Hill Climbing

Using Manhattan Distance

Heuristic

h= h=

1 2 3

7 8 4

7 6 5

h=

1 2 3

7 8 4

6 6 5

h=


A* Search• Minimizing the total path cost

• Combines uniform-cost search and greedy search.

• Evaluation function:f(n) = g(n) + h(n)

g(n): cost of path from start to node n

h(n): estimate of cost of path from n to goal

f(n): estimated cost of the cheapest solution through n


Goal: Minimum length path.

Is h(n) an admissible heuristic?

f(n) = g(n) + h(n)

K (18) L ( 3) M(2) N(9) O(5) P(2) Q(10) R(12)

S (18) T(0) U (0)

A(22)

B (18) C (21) D (8)

E(12) F(7) G (9) H(6) I (13) J(14)

d = 0

d = 1

d = 2

d = 3

d = 4

5 103

6 12 4 7 8 11

3 11 4 2 7 1 5 12 3 4

3 4 14 6 5

Numbers in parentheses are h(n)

Numbers on edges are operator costs


Multiple Sequence Alignment • DNA and protein sequences

• Alignment of multiple sequences created by inserting gaps to shift characters to matching positions

ATCG -ATCG- TGA --T-GA

GAT GAT---

• Optimal alignment maximizes the number of matching positions

Multiple Sequence Alignment As State-Space Search

(Eric Hansen, Rong Zhou)

ATCG -ATCG- TGA --T-GA

GAT GAT---

start

goal

Space Complexity: O (LN) Time Complexity: O (2NLN)Where L is the average length of sequences and N is the number of sequences

Nodes pruned by Anytime A*

An Illustration of Anytime A*

0 918

5 617

4 718

7 415

8 314

9 213

3 716

2 818

11 011

1 919

6 516

4 718

3 819

2 920

g hf

f = g + 2h

Goal

g hf

= expanded node

g hf= stored but not

expanded node

Total number of nodes stored = 8


Genetic Algorithms• Search procedure based on a simple model

of evolution

• Uses a “random” process to explore search space

• Has been applied in many domains


Terminology• Begin with a population of individuals. Each individual

represents a solution to the problem we are trying to solve.

• A data structure describes the genetic structure of the individual. (Assume for initial discussion that this is a string of 0’s and 1’s).

• In genetics, the strings are called chromosomes and the bits are called genes.

• The string associated with each individual is its genotype

• Selection is based on fitness of individuals


The Genetic Algorithm• Each evolving population of individuals is

called a generation.

• Given a population of individuals corresponding to one generation, the algorithm simulates natural selection and reproduction in order to obtain the next generation.


Three basic operations• Reproduction:

• Individuals from one generation are selected for the next generation

• Crossover: • Genetic material from one individual is exchanged

with genetic material from another individual

• Mutation: • Genetic material is altered


General GA ProcedureSelection, crossover, and mutation operations

Initial population

Parent candidate pool Father and

Mother

Offspring

Crossover and mutate

Next generation populationConverge?

Evaluate fitness

Evaluate fitness and replace

Select parents

no

yes


Example of General GA Procedure

Selection, crossover, and mutation operations

Generation n 1 1 0

11 0 1

10 1 0

01 0 0

1

11 13 2 9

Reproduction 1 1 0

11 0 1

11 0 0

11 0 1

1Crossover

1 1 1 0 1

0 1 1

Mutation

1 0 0 1

1 0

0 1

1 1

1

0 1 1

1 0 1

0

1 0 1 1

0 0

1 0 0 1

1 1

Generation n+ 1

15 8 1 13


Two keys to the success of a GA

• Data structures for»Genes»Chromosomes»Population

• Fitness evaluation function


Knowledge Representation

• Semantic networks

• Frame based systems

• Rule based expert systems

• Ontologies

• Neural networks


Anything

AbstractObjects Events

Sets NumbersRepresentational

Objects

Intervals

Places

PhysicalObjects

Processes

Categories

Sentences Measurements

Moments

Times Weights

Things Stuff

Animals Agents

Humans


Expert Systems

• Rule based systems• Garnered a great deal of attention in the 1980’s

• Most famous examples are in medical domains

• Stimulated interest in “logic programming”

• Encode knowledge of people as sets of rules

• Still widely used

• Knowledge acquisition bottleneck


Representing Uncertainty

• Fuzzy logic

• Bayesian reasoning


Uncertainty versus Vagueness• Certainty–degree of belief

• there is a 50% probability of rain today

• I am 30 % sure the patient is suffering from pneumonia

• Vagueness–the degree to which an item belongs to a category• the man is tall

• move the wheel slightly to the left

• the patient’s lungs are highly congested


Fuzzy Sets Represent Vagueness

• Lotfi Zadeh popularized the idea in the 60’s

• Popular concept in Eastern philosophy

• Reasoning with fuzzy sets is called fuzzy logic

• Fuzzy logic is also called • approximate reasoning

• continuous logic


Fuzzy Set Definitions• Set membership can be expressed using a

characteristic (or descrimination) function

• Classic (or crisp) setsIf objects x are chosen from some universe X

• Fuzzy sets - an element can be a partial member of a set (grade of membership)

Aset ofelement an not is x if 0

Aset ofelement an is x if 1)(xA

0 A(x) 1


Examples of Fuzzy Concepts from Natural Language

• John is tall

• The weather is rainy

• Turn the volume up a little

• Dr. Bridges’ tests are long

• Add water until the dough is the right consistency

• There was very little change in the cost

• The water bill was somewhat high


Representing Fuzzy Sets• Enumeration of membership values of all

elements with non-zero membership

TALL = {.125/5.5, .5/6, .875/6.5, 1/7, 1/7.5, 1/8}

• Represent membership with a function


Functional Representations Fuzzy Set Tall

0

1

4 5 6 7

Tall

Height in feet

Membership


Linguistic (or Fuzzy)Variable• Usually corresponds to a noun

• The values of a linguistic variable are fuzzy sets (which correspond to adjectives)

• Examples:Linguistic variable Fuzzy sets

Height short medium tall

Weight light average heavy

Temperature cold cool typical warm hot

Speed slow medium fast


Linguistic Variable Temperature

30 40 50 60 70 80 90 100

0

1

Cold Normal Hot


Some Fuzzy Set Operations• Set union A B

A B(x)max(A(x),B(x)) for all x X

alternate syntax (join operator)

A B(x)A(x)B(x)) for all x X

• Set intersection A BAB(x)min(A(x),B(x)) for all x X

alternate syntax (meet operator)

A B(x)A(x) B(x)) for all x X


Fuzzy Reasoning• A fuzzy proposition is a statement that asserts a

value for a linguistic (or fuzzy) variable• Example: Joe’s height is medium

» Linguistic variable (noun) Joe’s height

» Fuzzy set (adjective) medium

» The fuzzy set “medium” is a value of the linguistic variable “Joe’s height”

• A fuzzy rule relates two or more fuzzy propositions

• Fuzzy inference techniques are used to draw conclusions using fuzzy rules


Example Fuzzy Rule

If speed is normal

then braking.force is medium

Speed

Normal = (0/0, .1/20, .8/40, 1/60, .1/80, 0/100)

braking.force

Medium = (0/0, .5/1, 1/2, 1/3, .2/4, 0/5)


J. Dickerson, D. Bedeant, Z.Cox, W. Qi, D. Ashlock, and E. Wurtele, Atlantic Symposium on Computational Biology and Genome Information Systems & Technology (CBGIST 2000,

26-30.


Bayesian Reasoning• Bayesian networks: Represent knowledge as

a network of random variables

• Many names and many variations• Belief networks

• Probabilistic networks

• Causal networks

• Knowledge Maps

• Influence Diagram (extension)

• Decision Network (extension)


Belief Network

Burglary Earthquake

Alarm

JohnCallsMaryCalls

P(B)

0.001P(E)

0.002

B E P(A|B,E) T T 0.95 T F 0.94 F T 0.29 F F 0.01

A P(J|A)

T 0.90

F 0.05

A P(M|A)

T 0.70

F 0.01


Classification of Learning Systems

• Supervised learning• Give the system a set of examples and an

“answer” for each example.• Train the system until it can give the correct

response to these examples (or most of them).

• Unsupervised learning• Give the system a set of examples and let it

discover interesting patterns in the examples.

• Reinforcement learning• Learn from rewards and penalties


Feature Vectors• Simple representation

used by most learning systems.

• Represents each example as a vector or numbers • Quantities

• Nominal data

• Ordinal data#53 5.3 cold 3.2 blue 1


Neural Networks• Computational models “loosely” based on the

structure of the brain• Characteristics of the brain

• Large number of simple processing units (neurons)• Highly connected• No central control• Neurons are slow devices compared to digital computers• Can perform complex tasks in a short period of time• Neurons are failure-prone devices• Handles fuzzy situations very well.• Information accessed on the basis of content• Learns from experience


Neural Networks• Based on model of nervous system

• Large numbers of simple processing units

• Units are highly connected and connections are weighted.

• Highly parallel distributed control

• Emphasis on learning internal representations automatically


Neural Network Concepts• Cell or unit or neuron or node

• Autonomous processing unit that models a neuron• Purpose

» Receives information from other cells» Performs simple processing» Sends results on to one or more cells

• Layers • A collection of cells that perform a common function• Types:

» Input layer» Hidden layer» Output layer


Layers of Neurons

I1

I2

I3

H1

H2

O1

Input Layer Hidden Layer Output Layer


Properties• In general, there is no interconnection

between cells in the same layer

• Connections are one or two way communications links between two cells

• Weights are the strength of the connections. A weight wij is a real number than indicates the influence that cell ui has on cell uj


More about weights• Positive weights indicate reinforcement

• Negative weights indicate inhibition

• Weight of 0 indicates no influence or connection

• Weights may be initialized to one of these:• 0

• predefined values

• random values

• Weights are altered by experience


Multilayer Feed-Forward Networks

• Networks that are connected acyclic graphs

• Backpropagation• Most popular training method for feed forward layered

networks.

• Invented in 1969 by Bryson and Ho

• Ignored until 80’s

• Supervised learning technique


Back Propagation• Initialize the network with random weights

• Show it an input instance

• Compute the output

• Determine how much the output differs from the goal.

• Feed small adjustments to the weights back through the network based on the error.


General Algorithm for Training Network

Initialize NN

for epoch = 1 to MAXEPOCHS

for each input-output pair in the training set

present an example and compute error

adjust weights to reduce the error

compute mean-square-error for training set

for each input-output pair in the test set

compute error

compute mean-square-error for test set


Generalization

% correct

Training time (# of epochs)

Training set

Test set


Computational Biology Applications• Protein classification

• Sequence analysis

• DNA fragment assembly

• Prediction of transmembrane regions

• Phylogenetic classification of ribosome sequences

• And many more


Self-Organizing Maps• Also called Kohonen maps

• Used for unsupervised learning

• Widely applied for comparison of gene expression data


Principle of Self-Organizing Maps


Self-Organizing Map from Yeast Gene Expression Data

(German Florez)


Knowledge Discovery• Definition: Non-trivial extraction of implicit,

previously unknown, and potentially useful information from data.

• Applications in biology• Text mining

• Association rule mining


KDD Process

Data

Target Data

--- --- --- ------ --- --- ---

PreprocessedData

TransformedData

Patterns

Knowledge

Selection

Preprocessing

Transformation

Data Mining

Interpretation/Evaluation


Iterative Clustering Procedure( Wan, Bridges, J.Boyle, A.Boyle)

Download data from Genbank

Represent data using an appropriate method

Construct feature vector for each gene from POSITIONAL WEIGHT MATRICES

Cluster with K-clustering

Visualize results

Conclusions

Select clustering without clear patterns for further clustering

Positional Weight Matrix Representation


S. solfataricus with A, G box (2976)Clustering window (-48 to -1)

Nearby with A, G box (286)Cluster window (-24 to -1)

With A box (1656)

With A box (146)

With G box (1320)

With A and G box (142)

Distant with A box (1370)

Nearby with G box (571)

Distant with G box (749)

Clustering Results

introduction to artificial intelligence: applications in computational biology

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