ICS321 – MANAGEMENT INFORMATION SYSTEMS

Week 9

REVIEW Key Information Systems

ERP SCM CRM

What are the 2 objectives? What are the gaps in expectations? Online vs Offline Customer Service

5P’s of Online Customer Service?

THIS WEEK Decision Support & Artificial

Intelligence Brainpower for your Business

We’ve discussed Databases Good Data -> Good Information ->

Better Decisions -> Competitive Advantage

TYPES OF DECISION Structured Decisions

No ‘feel’ or intuition; Given a set of inputs the ‘right’ decision can be calculated.

Unstructured Decisions There could be many ‘right’ answers, and

no precise way to select the best

TYPES OF DECISION Recurring

Decisions that need to be made each week or month.

Non-Recurring Or Ad hoc. Infrequent or perhaps a one off decision.

SATISFICING “Satisfied” & “Sufficient” A choice which meets your needs & is

satisfactory without necessarily being the best possible choice.

Example Goals: Fair Price Reasonable Profit High Growth (rather than ‘maximum

growth’)

EXAMPLES Insurance company investigates risk

exposure when insuring drivers with history of DUI. DSS revealed that married male homeowners in their 40s were rarely repeat offenders – an opportunity to increase market share without increasing risk exposure.

A railroad company tests rails to prevent derailments, and uses a DSS to schedule rail testing – reducing its rail caused accidents without increasing costs.

‘INTELLIGENT’ AGENTS Agents act within an environment Some agents perform better than

others, which suggests rationality; A rational agent is one that can behave as

well as possible. Some environments are more

complicated than others, so some agents can naturally be more successful that others.

AGENT An agent is anything which perceives its

environment and acts upon it. Perception is through sensors Action is through actuators

Special agent 007 perceives using eyes, ears etc. and acts using arms, guns etc.

An automated agent perceives using a camera or temperature monitor and acts using motors or sending network packets.

PERCEPTS A percept is any inputs received by the

agent at any given instant. Hence a percept sequence is a sequence

of percepts over time. Generally agents should use their entire

percept sequence (complete history of anything the agent has perceived) to make a choice between actions. How do you feel about this?

VACUUM CLEANER MAN IN VACUUM CLEANER WORLD

A ‘simple’ intelligent agent! There is a problem in Vacuum Cleaner

World…. This calls for Vacuum Cleaner Man. Vacuum cleaner world has 2 locations; ‘A’ and

‘B’ - the locations can sometimes be dirty. Vacuum cleaner man can perceive whether

he is in location A or location B, and whether the location is dirty or not.

Vacuum cleaner man can choose whether to suck dirt, move left, move right or do nothing.

VACUUM CLEANER WORLD

A B

SIMPLE AGENT FUNCTION A simple agent function could be;

“If the current square is dirty, suck! Otherwise move to the other square.”

Is this a good function? Or bad? Is it an intelligent function? Or stupid?

A SUCCESSFUL AGENT A rational agent should do the right

thing every time - when the right thing will cause the agent to be successful.

Ergo, we need a way of measuring success, i.e. we need some criteria for what is considered successful.

So what is success for Vacuum Cleaner Man?

PERFORMANCE MEASURES A performance measure is a test for an agents

success. We could use a subjective measure - asking the

agent how well they ‘think’ they’ve done, but they might be delusional.

Instead we use a objective measure imposed by the agent designer.

A performance measure for Vacuum Cleaner Man could be “The amount of dirt cleaned in an 8 hour shift” Is this good?

PERFORMANCE MEASURES Vacuum Cleaner Man could simply clean up

dirt and then dump it on the floor again, in order to maximise its performance.

As a rule it is better to design a performance measure based on what one wants in an environment, rather than according to how you expect the agent to act.

I.e. a more suitable performance measure could be the number of clean squares at each time interval.

PERFORMANCE MEASURES It is often hard to set performance measures, as

even this measure is based on average cleanliness over time. Which is better between: A mediocre agent who works all the time. An energetic agent who takes long breaks.

This question really has big implications, compare it to a reckless life of highs and lows vs a safe but boring existence? An economy where everyone lives in moderate poverty, or where some are really rich and others really poor.

RATIONALITY To decide what is rational at any given

point an agent needs to know; The performance measure which defines

its success. An agents prior knowledge of the

environment (if it is unknown a certain amount of exploration is needed)

The actions an agent can perform. The percept sequence to date.

OMNISCIENCE VS RATIONALITY Its worth clarifying that agents aren’t expected

to be Omniscient - that would be impossible. As intelligent humans we make mistakes even if we

act in an entirely rational manner. Indeed we normally decide on our own actions based on our own percept sequences.

Even as intelligent humans there are things beyond our control or knowledge - unexpected interrupts.

Rationality maximises expected performance, perfection maximises actual performance.

EXPLORATION It is rare for an environment to be entirely

known when the agent is being designed - such as in the limited vacuum cleaner example.

When an agent is initially dumped in an environment, it often (intentionally or not) performs some actions in order to modify future percepts.

By this definition an agent would then learn from the things it perceives.

LEARNING A successful rational agent should learn

about its environment to improve its behaviour.

An agents computation thus occurs at 3 levels; First, when the agent is designed, the

designer performs some. Second, when deciding on its next action

the agent performs some. Third, when the agent learns from

experience to modify its behaviour.

LEARNING The ability to learn sets us, and intelligent

agents apart from many low intelligent species. Many species with limited intelligence are unable to

learn. A dung beetle picks up a dung ball, carries it to the

entrance of its nest and then plugs the hole. If the dung ball is taken from it while on route to the entrance, it continues attempting to plug the hole.

An agent which relies on prior knowledge and doesn’t learn from its percepts lacks autonomy.

AUTONOMY A rational agent should be

autonomous. If Vacuum Cleaner Man can learn to

foresee where dirt might appear is more successful.

However, autonomy needn’t exist from the start. The designer needs to install some existing

knowledge of the environment, otherwise the agent would just act randomly.

TASK ENVIRONMENT Before moving on to examine how to

design agents, lets investigate further the types of environment in which the agent might work.

FULLY OBSERVABLE VS PARTIALLY OBSERVABLE

Can the agents sensors gain access to the state of the entire environment at any given point in time? An environment where the agent can

observe all relevant aspects in the environment is effectively fully observable too.

Vacuum Cleaner Man can only detect dirt in the square he is occupying, I.e. partially observable.

DETERMINISTIC VS STOCHASTIC An environment is deterministic if its

subsequent state is entirely dependent on the current state and the actions of the agent. Stochastic environments are where

aspects of the environment can be changed by external influences.

An environment which is deterministic except for the actions of other agents is strategic.

EPISODIC VS SEQUENTIAL Episodic environments are where each

decision is unaffected by previous decisions, choices must depend solely on the current episode. Examining defects on a production line is

episodic, while playing chess is sequential Episodic environments are simpler than

sequential, as agents don’t need to plan or think ahead.

STATIC VS DYNAMIC A dynamic environment is an

environment that can change while the agent is making a decision. A static environment waits for the agent to

act. In a semidynamic environment the

environment doesn’t change while the agent makes a decision, but the agents performance might - for instance where the agent is under time pressure

DISCRETE VS CONTINUOUS Percepts can be discrete or continuous,

actions can be discrete or continuous and the state of the environment could be discrete or continuous. In discrete state environments there are a

limited number of actions (for example), in opposed to a continuous range of possibilities.

SINGLE AGENT VS MULTIAGENT Obviously a single agent environment is one in

which only one agent exists. But for multi agent environments what is considered an agent, and what is a stochastically behaving object? Is the dirt appearing in Vacuum World an agent or not? A competitive multiagent environment is where

maximising one agents performance minimises anothers.

A cooperative multiagent environment is where maximising one agents performance enhances the performance of another - like avoiding collisions when driving.

DIFFERENT ENVIRONMENTS Examine these environments;

Chess with a clock Medical Diagnosis

The hardest case would be a partially observable, stochastic, sequential, dynamic, continuous and multiagent.

Most real situations need to be treated as stochastic rather than deterministic - why?

AGENT STRUCTURE Agents need to map certain actions onto

appropriate percepts. That is initiate appropriate actuators in response to sensor input.

Ergo, a simple agent program could involve table look up. Take readings from the sensors and look up the appropriate response.

This simple agent structure would do exactly what we require, but, Chess exists in a tiny, well behaved world with known

limits, yet the lookup table for chess would need to have 10150 entries!

AGENT STRUCTURE So, there is a need to translate massive look up

tables into short lines of code; there is an analogy of moving from large square root

look up tables to 5 lines of code running on a calculator.

So, next lets examine 4 basic kinds of agent program; Simple reflex agents Model based reflex agents Goal based agents Utility based agents

SIMPLE REFLEX AGENTS A simple reflex agent bases actions on the current

input only - ignoring the percept sequence. This leads to reflex reactions - if car in front is braking,

then brake! The agent code here is simple, but of very limited

intelligence. If the environment in not entirely observable in a single

instance, decisions can be weak - what if the car in front puts its lights on - is that distinguishable from braking?

Infinite loops are also often unavoidable.

MODEL BASED REFLEX AGENTS A model based reflex agent extends the simple reflex

agent, by encoding a model of the environment it exists in.

For parts of the environment which are unobservable, a model is built based on what is known both about how the environment should be and information gathered from the percept sequence.

In this case the new percept is used in a function to update the state of the environment. The agent then reviews this state and its rules to make a decision, rather than just reviewing the new percept.

GOAL BASED AGENTS Goal based agents add a further parameter to their

decision algorithm - the goal. Whereas reflex agents just react to existing states, goal

based agents consider their objectives and how best to move to wards achieving them.

Hence a goal based agent uses searching and planning to construct a future, desired state. When the brake lights of the car in front go on, the agent

would surmise that in normal environments the car in front will slow down, it would then decide that the best way of achieving its goal (getting to point B) would be to not hit the car in front, and hence decide braking was a good idea.

UTILITY BASED AGENTS Goals are crude objectives - often a binary

distinction between happy and unhappy. Life is more complex than that, so utility attempts to create a better model of success. The car can get to its destination in many ways,

through many routes, but some are quicker, safer, more reliable or cheaper than others. Utility creates a model whereby these performance measures are quantified.

The car could brake behind the car in front, or it could overtake - one option is quicker, and one option is safer!

LEARNING AGENTS The agents discussed so far are

preprogrammed - given the constraints of the environment, their objectives and the mapping of how to achieve them.

A further subset of agents, learning agents, can be set loose in an initially unknown environment and work out their own way of achieving success.

GAME THEORY Two suspects, A and B, are arrested by the police.

The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, the police can sentence both prisoners to only six months in jail for a minor charge. If each betrays the other, each will receive a two-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So the question this dilemma poses is: What will happen? How will the prisoners act?

ACTING UNDER UNCERTAINTY

ACTING UNDER UNCERTAINTY Suppose we need to check in at the airport and

need to choose a time to set off. Plan A60 involves leaving 60 minutes before check-in - we could assume this was a good plan.

We can’t say “Plan A60 will get us to the airport in time”, only “Plan A60 will get us to the airport in time so long as we have enough gas, and there are no accidents, and the car doesn’t break down, and check-in doesn’t close early, and…”

Perhaps Plan B90 would be better?

ACTING UNDER UNCERTAINTY While Plan B90 increases the ‘degree of belief’ that

we will get to the airport on time, it also introduces a likely long unproductive wait at the airport.

To maximise an agents performance, the relative importance of both goals needs to be considered; ‘getting to the airport’ ‘avoiding a long wait’

The rational decision is A60, but how do we draw that conclusion?

DIAGNOSIS Diagnosis is a task aimed at dealing with

uncertainty normally using probability theory to construct a degree of belief in various statements. Your car won’t start, so there’s a 80% chance the battery

is dead. You’ve got pain in your left calf so there’s a 70% chance

you’ve pulled a muscle, and a 2% chance your leg has fallen off.

Probability provides a way of summarising the uncertainty that comes from our laziness and ignorance.

PROBABILITY Probability is based on our percepts of the

environment - what we know about the environment. My doctor said golf caused my shoulder injury as soon

as he knew I played golf - even though the shoulder injury dates from before I started playing golf.

When we pick a card there is a 1/52 chance it is the Ace of Spades, after we look at it, the chance is either 0 or 1.

Probabilities can change when more evidence is acquired.

PROBABILITY Note that while probabilities may

change as more evidence is acquired, it is the degree of belief which changes, NOT changes to the actual state of the environment. In a changing environment, similar

approaches can be taken with consideration for situations, intervals and events.

UTILITY THEORY Utility Theory represents preferences for

certain states - the quality of a state being useful; Is it preferable to choose plan C1440 (leaving for the

airport 24 hours early) which has a 99.999% probability of success over plan A60, which has a 95% probability of success? Given the poor utility of the long wait, perhaps not.

Should I stop playing golf to improve my ‘lack of shoulder pain’ utility, and risk lowering my ‘playing golf pleasure’ utility?

DECISION THEORY Decision Theory = Probability Theory +

Utility Theory. An agent is rational if they choose the

action which yields the highest utility averaged across all possible outcomes of the action.

The principle of Maximum Expected Utility (MEU).

DOMAIN RANDOM VARIABLES Boolean Random Variables

Late<True, False> Discrete RandomVariables

Weather<Sunny, Rainy, Snowy, Cloudy> Continuous Random Variables

Temperature = 30.2

ATOMIC EVENTS Atomic Events are a particular

combination of states; Late = True, Weather = Cloudy Late = False, Weather = Sunny

The existence of certain atomic events can lead to certain understandings; Late = False, Weather = Rainy, means

<Rainy => Late> = False

PRIOR PROBABILITY Unconditional Probabilities can be

assigned to each state - degree of belief with no other information; P(Weather = Sunny) = 0.8 P(Weather = Rainy) = 0.1 P(Weather = Cloudy) = 0.0999 P(Weather = Snowy) = 0.0001

JOINT PROBABILITY

The probabilities for a combination of random variables can be stored in a grid - 2 or more dimensional. Take a simple example with 3 boolean variables,

Late, Male, AM.

LateNot LateMale Not MaleMale Not Male

AM 0.220.250.080.02not AM 0.1 0.180.1 0.05

JOINT PROBABILITY The sum of all probabilities adds up to

1. Suppose we want to know the

probability of being male OR late; P(Male OR Late) =

0.22+0.25+0.1+0.18+0.08+0.1 = 0.93 Or the probability of being male AND

late; P(Male AND Late) = 0.22+0.1 = 0.32

Thus we can deduce probabilities given certain inputs.

JOINT PROBABILITY Suppose we add a further random

variable - the weather. We have to expand our table, in reality

adding 4 times the size of the weather, one for each weather condition.

In doing this it is reasonable to ask how the former and latter table are related; how does P(Late, AM, Male, Weather = sunny) relate to P(Late, AM, Male)?

PRODUCT RULE We can use the ‘Product Rule’

The probability of a and b is the same as the probability of b multiplied by the probability of a given that b is the case;

P(a^b) = P(a|b)P(b) Or in our case;

P(Late, AM, Male, Weather = sunny) = P(Weather = sunny | Late, AM, Male)P(Late, AM, Male)

The probability of a man being late on a sunny morning is the same as the probability of it being sunny given that a man is late in the morning, multiplied by the probability of a man being late in the morning.

HANG ON A MINUTE! Let’s review that;

“The probability of a man being late on a sunny morning is the same as the probability of it being sunny given that a man is late in the morning, multiplied by the probability of a man being late in the morning.”

Unless we are a weathermonger, the probability of it being sunny isn’t influenced by a man’s morning tardiness!

PRODUCT RULE The Product Rule can be stated in 2 ways;

P(a^b) = P(a|b)P(b) P(a^b) = P(b|a)P(a)

Or in our case; P(Late, AM, Male, Weather = sunny) = P(Late, AM,

Male | Weather = sunny)P(Weather = sunny) The probability of a man being late on a sunny

morning is the same as the probability of a man is late in the morning given that it is sunny, multiplied by the probability of it being sunny.

JOINT PROBABILITIES There is intuitively something more satisfactory about this

statement - perhaps the weather could be a factor in determining lateness.

We could expand our knowledge about the domain by adding further random variables - perhaps adding Transport<Car, Bike, Walk> or FavouriteFood<Icecream, Steak, Fish>.

Transport ‘might’ have a direct influence over tardiness - it could be argued that ‘walkers’ should set off earlier, but surely FavouriteFood can be considered ‘Independent’.

When Independence can be found, the subset of data to be analysed can be greatly reduced.

BAYES’ LAW Given

P(a^b) = P(a|b)P(b) P(a^b) = P(b|a)P(a)

Then, P(b|a)P(a) = P(a|b)P(b)

And so, P(b|a) = P(a|b)P(b) / P(a)

Great! - so what?

BAYES’ LAW Requires 2 unconditional probabilities

and 1 conditional probability, to calculate 1 further conditional probability! But, if we have those probabilities, then it

can be very useful.

BAYES’ LAW IN ACTION Meningitis causes patients to have stiff necks

50% of the time. The probability of having meningitis is 1 in 50,000 and the probability that any patient has a stiff neck is 1 in 20. P(s|m) = 0.5 P(m) = 1/50000 P(s) = 1/20 P(m|s) = P(s|m)P(m)/P(s) = (0.5*(1/50000))/(1/20)

= 0.0002 or 1 in 5,000

BAYESIAN NETWORKS With more variables, and more

conditional probabilities, the environments get increasingly more complicated. Exact inference is often replaced by

Approximate Inference based on sampling different possible states.

We will leave this kind of problem, and investigate utility further.

JUST IMAGINE You’ve just won a tv gameshow…

$1,000,000 But do you want to gamble? Toss a

coin, if you win you get $3,000,000 – you lose you get $0.

Why?

CHOICES A: 80% chance of $4,000 B: 100% chance of $3,000

Why?

MORE CHOICES C: 20% chance of $4,000 D: 25% chance of $3,000

Why?

QUOTE In 1662, French Philosopher Arnauld

said; “To judge what one must do to obtain a

good or avoid an evil, it is necessary to consider not only the good and the evil in itself, but also the probability that it happens or does not happen: and to view geometrically the proportion that all these things have together.”

More recently text move away from ‘good’ and ‘evil’, and talk about utility.

UTILITY Suppose we can calculate the utility of any

particular state given a utility function; U(S)

In reality this is often cumbersome, but for simplicity lets suppose…

Should an agent perform action A, there are a set of different possible outcomes Resulti(A). Given the evidence (E), that the agent has about the environment probabilities for each Result can be assigned; P(Resulti(A)|Do(A), E)

UTILITY (2) We can then calculate the expected

utility for performing that action given the evidence;EU(A|E) = ΣP(Resulti(A)|

Do(A),E)U(Resulti(A))

Maximum Expected Utility (MEU) states that a rational agent should choose the action which maximises the agents expected utility.

MAXIMUM EXPECTED UTILITY Great! We’ve solved A.I.! All we need to

do is calculate the action which is likely to return the maximum expected utility and set our agent loose!

Sadly computations are often prohibitive. Knowing the initial state of the world requires

perception Computing P(Resulti(A)|Do(A),E) requires a

complete causal model (NP-Hard reasoning in Bayesian Networks).

Computing the Utility of each state (U(Resulti(A)) requires searching or planning as an agent can’t assess the utility of a state until it knows where it can go from there.

MAXIMUM EXPECTED UTILITY Is it the only rational way? Why is maximising average utility so special? Why not minimise the worst possible loss? Couldn’t an agent act rationally by

expressing preferences between states without giving them numeric values?

Perhaps a rational agent has a preference structure too complex to be captured by a simple number?

Why should a suitable utility function exist at all?

MAXIMUM EXPECTED UTILITY To constrain the field of utility theory we will

consider six ‘axioms’, known as ‘the axioms of utility theory’. The most obvious semantic constraints on

preferences. Orderability Transitivity Continuity Substitutability Monotonicity Decomposability

BUT FIRST… Some notation;

A > B (A is preferable to B)A ~ B (The agent is indifferent

between A and B)A>~B (The agent prefers A to B, or

is indifferent between them)

AXIOM #1 Orderability

Given any two states, a rational agent must either prefer one to the other or else rate the two as equally preferable. That is the agent cannot avoid deciding – refusing to bet is like refusing to let time pass.

(A>B) (B>A) (A~B)

AXIOM #2 Transitivity

Given any three states, if an agent prefers A to B, and prefers B to C, the agent must prefer A to C.

(A>B) (B>C) → (A>C)

AXIOM #3 Continuity

If some state B is between A and C in preference, then there is some probability p for which the rational agent will be indifferent between getting B for sure, and the lottery that yields A with probability p and C with probability 1-p.

A>B>C → p [p,A; 1-p, C] ~ B

AXIOM #4 Substitutability

If an agent is indifferent between two lotteries, A and B, then the agent is indifferent between two more complex lotteries that are the same except that B is substituted for A in one of them. This holds regardless of the probabilities and the other outcome(s) in the lotteries.

A~B → [p, A; 1-p, C] ~ [p, B; 1-p, C]

AXIOM #5 Monotonicity

Suppose there are two lotteries that have the same two outcomes, A and B. If an agent prefers A to B, then the agent must prefer the lottery that has a higher probability for A (and vice versa).

A>B → (p ≥ q [p, A; 1-p, B] >~ [q, A; 1-q, B])

AXIOM #6 Decomposability

Compound lotteries can be reduced to simpler ones using the laws of probability. This has been called the “no fun in gambling” rule because it says that two consecutive lotteries can be compressed into a single equivalent lottery.

[p, A; 1-p, [q, B; 1-q, C]] ~ [p, A; (1-p)q, B; (1-p)(1-q), C]

AXIOM’S AND UTILITY Clearly the Axiom’s we’ve discussed don’t

actually mention utility – just preference. Fortunately preference is tightly linked to

utility, as a rational agent should prefer options with higher utility.

Preferences could be based on anything the agent likes – for instance an agent might prefer prime numbers, or old cars.

A utility function is more useful if preference is less arbitrary; with money it is normal to want more money than less money.

TOSSING THE COIN You’ve just won a tv gameshow…

$1,000,000 But do you want to gamble? Toss a coin, if

you win you get $3,000,000 – you lose you get $0. (0.5*3,000,000)+(0.5*0) = 1,500,000 (1*1,000,000) = 1,000,000

Hence the Expected Monetary Value (EMV) of gambling is higher – so why not gamble?

UTILITY AND MONEY The expected utility of accepting and

declining the gamble is not quite that straight forward… The utility of winning your first million is very high, in comparison with winning a million if you are already very rich. EU (Accept) = 0.5U(Sk) +0.5(Sk+3,000,000) EU (Decline) = U(Sk+1,000,000)

Research has shown that the utility of extra money is actually logarithmic rather than linear. If you already have 500,000,000, then gaining

another 1,000,000 is worth almost the same as gaining 3,000,000.

UTILITY AND MONEY Interestingly the logarithm curve is

repeated below the 0 line. – Someone with 10,000,000 debt might accept a gamble on a coin with 10,000,000 gain or 20,000,000 loss.

CHOICES A: 80% chance of $4,000 C: 20% chance of

$4,000 B: 100% chance of $3,000 D: 25% chance of

$3,000

So what about these choices? A=(0.8*4000)+(0.2*0)= 3200 B=3000*1 = 3000 C=(0.2*4000)+(0.8*0)=800 D=(0.25*3000)+(0.75*0) = 750 (3200/3000)=(800/750)

Proportionally they are the same – so why is B more appealing than A, and C more appealing than D. The answer lies in irrational regret.

MULTIATTRIBUTE UTILITY Money is a useful introduction to utility,

but often preferences are made over several attributes; For example when siting a new airport, we

might consider cost, noise disruption, safety issues etc.

For each option we can value each attribute to help us decide which is best.

DOMINANCE An option is strictly dominated by

another if it wins in all categories; If airport location A is cheaper, quieter, and

safer than B, then it has strict dominance.

A

BC

D

In this deterministic example, B is strictly dominant over A, while C and D are not.

DECISION NETWORK

Air Traffic

Litigation

Construction

Deaths

Noise

Cost

Airport Site

U

Ovals are Random VariablesRectangles are Decision NodesDiamonds are results of Utility Function

INFORMATION Thus far we have assumed that all

relevant information would be available to the agent to make their decision, however this is often not the case; consider a doctor diagnosing a patient – he

can’t possibly run every possible test. Hence it is worth trying to value

information.

THE VALUE OF INFORMATION Suppose an oil company hopes to buy

one of ‘n’ indistinguishable blocks of ocean drilling rights. Exactly 1 of the blocks contains oil worth $C and the cost of buying each block is $C/n.

If a seismologist was selling information about certain blocks, say block 3, how much would that information be worth?

OIL Now there is a 1/n chance of oil in block

3! Then the company would buy block 3 and

make the following profit;C - C/n

= (n-1)C/n

NO OIL There is a (n-1)/n chance of finding no

oil. So the company would buy another block; There is a 1/(n-1) chance of finding the oil

in another block, and the expected profit is;

C/(n-1)-C/n=C/n(n-1)

OVERALL Therefore the expected profit given the

information is;1/n * (n-1)C/n + (n-1)/n * C/n(n-1)= C/n

Ergo, the information is worth about as much as the block itself!

LEARNING Agents have a performance element,

which is what we have focused on so far; But they often also have a learning

element, which can modify the performance element to make better decisions.

LEARNING Learning can be;

Supervised Unsupervised or Reinforcement Learning

SUPERVISED LEARNING Learning a function from examples of

its inputs and corresponding outputs. Either input by a teacher or experimenting between actions and

resulting percepts E.g. if you are learning to drive, and I

shout ‘stop!’ or you experiment with different stopping distances under different conditions.

UNSUPERVISED LEARNING Learning patterns of inputs without

specific outputs. An agent could ‘get a feel’ for good and

bad situations without labeling them as such

E.g. getting a feel for good or bad traffic days without anyone telling you what they are.

REINFORCEMENT LEARNING A lack of arrival at a desired state

under certain actions suggests to the agent they are doing something wrong. Every time you drive over 160kmph you

get an expensive bill to repair your car… hmmm.. what are you doing wrong?

INDUCTIVE LEARNING Used for supervised learning

Given a set of inputs and corresponding outputs, derive a function that can be used for future approximation.

If we have lots of x and f(x), return h(x) to approximate f(x).

Here h stands for hypothesis.

INDUCTIVE LEARNING

Both are consistent hypotheses, but which one should we choose?

Ockham’s razor says to prefer the simplest consistent hypothesis.

INDUCTIVE LEARNING

A straight line approximation hypothesis may be more useful than a complex polynomial.

DECISION TREES One way of deriving an appropriate hypothesis is

to use a decision tree. For example the decision as to whether to wait for

a table at a restaurant may depend on several inputs; Alternative Choice? Bar? Fri/Sat? Hungry? No. of Patrons Price Raining? Reservation? Type of Food Wait Estimate.

To keep things simple we discretise the continuous variables (No. patrons, price, wait estimate)

POSSIBLE DECISION TREENo. Patrons

YESNONone Some

WaitEstimate?

Full

NO Alternate? Hungry? YES>60 30-60 10-30 <10

Fri/Sat?Reservation? Alternate?YESNo NoYes Yes

Bar? Raining?YES YES YESNO

No No NoYes Yes Yes

YESNONo Yes

YESNONo Yes

INDUCING A DECISION TREE Obviously if we had to ask all those

questions the problem space grows very fast.

The key is to build the smallest satisfactory decision tree possible.

Sadly this is intractable, so we will make do with building a smallish decision tree.

A tree is induced by beginning with a set of example cases.

EXAMPLE CASES

Sample cases for the restaurant domain.

STARTING VARIABLE First we have to choose a starting

variable, how about food type?Type?

15

French

610

Italian

42

811

Thai

37

129

Burger

PATRONS?

Ah, that’s better!

Patrons?

15

None

610

Some

42

811

37

129

Full

WHAT A GREAT TREE!

But how do we make it?

Patrons?

None Some Full

YESNO Hungry?

YES

NONo Yes

Type

French Italian Thai Burger

NO YESFri/Sat

YESNONo Yes

HOW TO DO IT Choose the ‘best’ attribute each time,

then where nodes aren’t decided choose the next best attribute… Recurse!

CHOOSING THE BEST ChooseAttribute(attributes, examples)

How do you choose the best attribute? ‘Patrons’ isn’t perfect, but it’s ‘fairly good’. ‘Type’ is really useless

If perfect = 1, and completely useless = 0, how can we measure really useless and fairly good?

CHOOSING THE BEST The best attribute leads to a shallow decision

tree, by dividing the set as best it can, ideally a boolean test which splits positives and negatives perfectly.

A suitable measure therefore is the expected amount of information provided by the attribute.

Using a complex formula we can measure the amount of information required, and predict the amount of information still required after applying the attribute.

HOW GOOD IS THE DECISION TREE? A good tree can predict unforeseen

circumstances accurately, hence it makes sense to test unforeseen cases on a set of test data;1) Collect large set of Data2) Divide into 2 disjoint sets (training and test)3) Apply the algorithm to training set.4) Measure the percentage of accurate predictions in the test set.5) Repeat steps 1-4 for different sizes of sets.

ALAS Unless you are going to have massive

amounts of data the results might not be accurate as the algorithm shouldn’t see test data before acting as it might influence its results.

FURTHER PROBLEMS What if more than one case has the

same inputs but different outputs? Majority rule? Decision tree is then not 100% consistent. It may choose to use irrelevant information

just to divide the two sets, suppose if we added the variable colour of

shirt?

MORE PROBLEMS Missing Data

How should we deal with cases where not all data is known? Where should they be classified?

Multivalued Attributes What about infinitely valued attributes, such as

restaurant name? Continuous values for inputs

Should you use discretisation? A split point? Continuous output

Consider a formulaic response from regression.

FUZZY LOGIC Let’s consider getting a bit fuzzier! An expert might say;

“The Power transformer is slightly overloaded, but I can keep this load for a while.”

Experts have no trouble understanding this, but how can an expert system deal with such vagueness?

Such ‘Fuzziness’?

FUZZY LOGIC Fuzzy Logic is NOT Logic that is Fuzzy,

but logic used to describe the fuzziness.

Fuzzy Logic is the theory of sets to calibrate vagueness.

Fuzzy Logic is based on the idea that all things have degrees; Temperature, Height, Speed, Distance,

‘Chairness’ When does a hill become a mountain?

TRADITION Boolean (conventional) logic enforces

sharp distinctions, things are either a member of a set, or a non member. Either 0 or 1.

Tom is tall, at 181 cm, while Tim is small at 179cm.

But this is due to an arbitrary line drawn in the sand at 180cm.

POSSIBILITY THEORY A man who is 181cm is ‘possibly’ tall,

perhaps we could say with 0.86% possibility? i.e. it is likely that he is tall.

Lukasiewicz, a Polish philosopher, produced work in 1930 which led to this inexact reasoning, or possibility theory.

MAX BLACK (1937) A long line of chairs. At one end is a Chippendale. Next to it is a near Chippendale, so near to

being a Chippendale that it is indistinguishable from a Chippendale.

And so on with chairs becoming slightly less chairlike, until at the other end there is a log.

When does a chair become a log? Well, the % of people who would call each

element a chair!

COMPARISON

0 0 1 1 0 0.2 0.4 0.6 0.8 1

Boolean Logic Fuzzy Logic

ZADEH 1965 “Fuzzy Logic is determined as a set of

mathematical principles for knowledge representation based on degrees of membership rather than on crisp membership of classical binary logic”

Lofti Zadeh is Master of fuzzy logic.

PYTHAGORAS 400BC Q: Does the Cretan philosopher tell the

truth when he asserts that ‘All Cretan’s lie’?

Boolean Logic: Contradiction! Fuzzy Logic: The philosopher does and

does not tell the truth.

RUSSELL’S PARADOX The barber of a village gives a hair cut

only to those who do not cut their hair themselves. Who cuts the barber’s hair?

Boolean: Contradiction! Fuzzy Logic: The barber cuts and

doesn’t cut his own hair!

MEMBERSHIP OF THE TALL MEN SET

Name Height Degree of Membership

Crisp Fuzzy

Chris 208 1 1.00

Mark 205 1 1.00

John 198 1 0.98

Tom 181 1 0.82

David 179 0 0.78

Mike 172 0 0.24

Bob 167 0 0.15

Steven 158 0 0.06

Bill 155 0 0.01

Peter 152 0 0.00

TALL MEN1.00.80.60.40.20.0

Degree of Membership

150 160 170 180 190 200 210Height (cm)

1.00.80.60.40.20.0

Degree of Membership

150 160 170 180 190 200 210Height (cm)

SHORT, AVERAGE AND TALL

1.00.80.60.40.20.0

Degree of Membership

150 160 170 180 190 200 210Height (cm)

Short Average Tall

LINGUISTIC QUALIFIERS Language carries with it a set of modifiers

which can change the shape of a fuzzy set; for instance what is the relationship between ‘tall’

and ‘very tall’? Some perform ‘concentration’, such as ‘very’ some perform ‘dilation’, such as ‘more or

less’ The set of very tall men is different from the set of

more or less tall men. How about the difference between the set of

slightly hot and the set of moderately hot?

GRAPHICAL REPRESENTATION

1.00.80.60.40.20.0

Degree of Membership

150 160 170 180 190 200 210Height (cm)

Short Average Tall

VeryTall

VeryShort

‘VERY’ So how much is ‘very’? What is the power of

the concentration? How about a square; i.e. if Tom has a 0.86 membership of the set ‘tall

men’, then he has a 0.86*0.86 = 0.7396 membership of the set ‘very tall men’.

Similarly he has 0.864 = 0.547 membership of the set ‘very, very tall men’.

We can assign the power 3 to ‘extremely’ meaning that Tom has 0.863 = 0.6361 membership of the set ‘extremely tall men’.

DILATION Similarly the dilation modifiers can be

made into an equation; ‘More or Less’ is given the formula √,

i.e. Tom has √0.86 = 0.9274 membership of the set ‘more or less tall men’.

CANTOR’S SETS Cantor proposed several operations on

traditional sets, but how do they translate to fuzzy sets?

Complement

Not AA

ContainmentA B

Intersection A AB B Union

COMPLEMENT Who does not belong to the set?

The complement of a set is the opposite of a set. So if we have a set of tall men, the complement is not tall men.

With fuzzy logic, if Tom has 0.86 membership of ‘tall men’, then he has 0.14 membership of ‘not tall men’.

CONTAINMENT Which set belongs to other sets?

Well, ‘very tall men’ is a subset of ‘tall men’, which in turn is a subset of ‘men’.

With fuzzy logic, membership values can change for different sets and subsets.

INTERSECTION Which elements belong to both sets?

We’ve already seen how a man can be a member of ‘tall men’ and ‘average men’, simply by having a membership value for both sets.

UNION Which elements belong to either set?

Tom belongs to the tall set, so he belongs to the tall or fat set!

So, crisp and fuzzy sets hold the same properties, in fact crisp sets can be considered a special case of fuzzy sets.

MORE GENERAL SET RULES Commutativity

A B = B A A B = B A

Associativity A ( B C ) = ( A B ) C A ( B C ) = ( A B ) C

Distributivity A ( B C ) = ( A B ) ( A C ) A ( B C ) = ( A B ) ( A C )

Idempotency A A = A A A = A

MORE GENERAL SET RULES Identity

A undefined = A A unknown = A A undefined = undefined A unknown = unknown

Involution ¬(¬A) = A

Transitivity If (A ∈ B) (B ∈ C) then (A ∈ C)

De Morgan’s Laws ¬(A B) = ¬A ¬B ¬(A B) = ¬A ¬B

GENERAL SET RULES The general set rules apply equally

to fuzzy sets. The key difference is in degree of

membership, while entities are either members or not members for normal sets, they have degrees of membership for fuzzy sets. Set of Prime numbers : 5, 13 etc. Fuzzy set of tall men : degrees of

membership.

FUZZY RULES If x is A, then y is B.

Where x and y are variables, and A and B are values determined by fuzzy sets.

If Speed is >100, Then stopping_distance is long.

If Speed is <40, Then stopping_distance is short.

FUZZIER If Speed is Fast, then Stopping_Distance

is Long. If Speed is Slow, then Stopping_Distance

is Short.

Here perhaps speed has a numerical range 0-220 kmph, and Stopping_Distance has a numerical range 0-300m, but each has been broken into fuzzy sets (fast/slow) and (long/medium/short).

REASONING In classical reasoning, if an antecedent

is true, then the consequent is true, but with fuzzy sets;

The degree of membership in the antecedent set influences the degree of membership in the consequent set.

INFERENCE If Height is Tall, Then Weight is Heavy. From this we can estimate a mans weight

dependent on their height.

degree of membership

1 1

0 0160 180 200 220 240 70 80 90 100 110 120

height weight

HOW ABOUT THESE? If Service is Excellent, OR Food is Delicious,

then Tip is Generous. If Project_Duration is Long AND Project_Staff

is Large AND Project_Fund is Inadequate, then Risk is High.

If Temperature is Hot, then Hot_Water is Reduced (AND/OR) Cold_Water is Increased.

All of these rules are possible, with a bit more work!

MAMDANI INFERENCE A simple example;

2 Inputs Project_Funding (Fuzzified from crisp

percentage input to inadequate, marginal and adequate)

Project_Staffing (Fuzzified from crisp percentage input to small and large)

1 Output Risk (high, normal or low)

EXAMPLE’S RULES 3 Rules

If Project_Funding is Adequate, OR Project_Staffing is Small, Then Risk is Low.

If Project_Funding is Marginal AND Project Staffing is Large, Then Risk is Normal.

If Project_Funding is Inadequate, Then Risk is High.

MAMDANI INFERENCE 4 Steps

1) Fuzzification 2) Rule Evaluation 3) Aggregation of Rule Outputs 4) Defuzzification

FUZZIFICATION Take crisp inputs and determine their

fuzzy set memberships. Normally requires expert judgement.

For Example; Project_Funding at 35% has 0.5

membership of inadequate and 0.2 membership of marginal.

Project_Staffing at 60% has 0.1 membership of small and 0.7 membership of large.

RULE EVALUATION The next step is to apply fuzzy inputs to

the rule antecedents. Rule 1: If Project_Funding is Adequate, OR

Project_Staffing is Small, Then Risk is Low. P_F is 0 Adequate P_S is 0.1 Small Risk is 0.1 Low.

RULE EVALUATION Rule 2: If Project_Funding is Marginal AND

Project Staffing is Large, Then Risk is Normal.

P_F is 0.2 Marginal P_S is 0.7 LargeThere is a choice of ways to apply this, but we

choose ‘min’. Risk is 0.2 Normal.

Rule 3: If Project_Funding is Inadequate, Then Risk is High.

P_F is 0.5 Inadequate Risk is 0.5 High.

AGGREGATION OF RULE OUTPUTS Summary

Risk is 0.1 Low. Risk is 0.2 Normal. Risk is 0.5 High.

Low Normal High

0 10 20 30 40 50 60 70 80 90 100

Risk

DEFUZZIFICATION Calculate the Centre of Gravity.

0 10 20 30 40 50 60 70 80 90 100

Risk

•((0+10+20)*0.1+(30+40+50+60)*0.2+(70+80+90+100)*0.5)/0.1+0.1+0.1+0.2+0.2+0.2+0.2+0.5+0.5+0.5+0.5 = 67.4•So the project risk is a member of high and normal, but a bigger member of high.

EXPERTS & EXPERT SYSTEMS Domain Experts

People who know about a domain – we are experts in the Payap domain.

Rule representation We represent what we know about a

domain in a set of rules that govern the domain;

If XXX then YYY Rules can be Relations, Recommendations,

Directives, Strategies or Heuristics.

CREATING AN EXPERT SYSTEM 5 key roles;

Project Manager Domain Expert Knowledge Engineer Programmer End User

DOMAIN EXPERT A knowledgeable and skilled person

capable of solving problems in the specified domain, having the greatest expertise in that domain. This expertise will be captured by the expert system, so they must be able to communicate their knowledge and participate in expert system development. This is the most important role.

KNOWLEDGE ENGINEER Someone capable of designing building

and testing an expert system. They begin by interviewing the expert to find out how to solve a particular problem. The knowledge engineer is responsible for capturing what reasoning methods are used to handle facts and rules, and then decide how to represent it in the system.

THE REST Programmer

Responsible for coding the domain knowledge in languages such as LISP or Prolog.

Project Manager Responsible for keeping the project on

track. End User

The people who are going to use the system once its complete.

PRODUCTION RULES Newell and Simon from CMU,

developed the production rule system in the early 70’s.

Basically humans solve problems by applying their knowledge (or production rules) to specific problem information.

Production rules are stored in long term memory, and problem specific information is stored in short term memory.

SYSTEM MODEL

RULE BASED EXPERT SYSTEM

EXPERT SYSTEM The knowledge base contains the

domain knowledge useful for problem solving – represented as rules; Relations, Recommendations, Directives,

Strategy, Heuristic. When the conditions of a rule are

satisfied then the action part is executed.

The database contains the facts which can be matched against the conditions.

EXPERT SYSTEM The inference engine performs this

reasoning, as we shall see, to reach as solution, linking rules to facts.

The explanation facilities crucially explain how the expert system reached its conclusions, to justify its advice.

The user interface is, well a user interface!

EXPERT SYSTEM EFFICIENCY Expert Systems are designed to

perform in the same way as an expert, therefore the primary concern is accuracy – it doesn’t matter how fast the system comes up with a wrong answer!

However, in many cases speed of reaching a solution is important – accurate decisions are not that useful if it is too late to apply the decisions.

CAN THEY BE WRONG? Of course

Human Experts are sometimes wrong, and yet we still trust them!

Likewise, the expert systems solutions may be wrong, but should we trust it?

EXPERT COMPARISON

EXPERT COMPARISON 2

CHAINING Often the action part of a rule, creates

a new fact to add to the database; If X is good, then Y is bad.

This would add ‘Y is bad’ to the facts in the database.

This matching can create inference chains, which illustrates how a conclusion is reached.

INFERENCE CYCLES

INFERENCE CHAIN

FORWARD CHAINING Or, “Data Driven Reasoning”. This is where we start from known data

and proceed forward. When a rule is fired new info is added to the database, until no further rules can be fired.

FORWARD CHAINING

FORWARD CHAINING Technique for gathering information

and inferring whatever can be inferred from it.

In forward chaining many rules are executed which may have nothing to do with the goal.

So if the goal is to infer a particular fact, forward chaining is inefficient.

BACKWARD CHAINING Or “Goal Driven Reasoning” The expert system begins with a goal,

and the expert system attempts to find the evidence to prove it.

First the knowledge base is searched to find rules that might have the desired solution (the then part), and then rules that can start those are searched for, with each rule being added to a stack.

BACKWARD CHAINING

FORWARDS OR BACKWARDS? Which is best?

Consider if trying to find the murderer on CSI?

or the disease on House? or deciding strategy on Survivor?

CONFLICT RESOLUTION What happens when rules contradict each

other? Highest Priority first?

Assuming rules can be placed in priority. Most Specific Rule?

The longest matching strategy, a specific rule processes more information than a general one, so one with more antecedents is likely to be more useful.

Most Recent Rule? The rule which has been fired most recently, i.e. whose

antecedent uses the most recently added data.

METAKNOWLEDGE Deciding which strategy to use is

stored in the metaknowledge – knowledge about knowledge.

And the rule is a metarule. Rules supplied by experts have higher

priority than those from novices. Rules governing the rescue of human life

have highest priority.

EXPERT SYSTEMS ADVANTAGES Natural Knowledge Representation

Everything is stored in easy to read and understand natural language.

Uniform Structure The syntax can be used in many different

situations. Knowledge / Processing Separation

Knowledge is separated from the inference engine, so different systems can be developed from the same knowledge.

Incomplete and uncertain knowledge Can easily be dealt with by an expert system.

EXPERT SYSTEMS DISADVANTAGES Opaque relations between rules.

It is difficult to see how individual rules affect the whole system.

Ineffective searching Searches are exhaustive – looking through all

rules everytime, which can make it slow. Learning

Expert systems can not learn, they can’t decide when to break the rules, or when to add a rule or modify one, as a human expert could.