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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.
Late Not LateMale Not MaleMale Not Male
AM 0.220.25 0.080.02not 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 TREE
No. Patrons
YESNO
None SomeWaitEstimate?
Full
NO Alternate? Hungry? YES>60 30-60 10-30
<10
Fri/Sat?Reservation? Alternate?YES
No NoYes Yes
Bar? Raining?YES YES YESNO
No No NoYes Yes Yes
YESNO
No Yes
YESNO
No 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?
1
5
French
6
10
Italian
4
2
8
11
Thai
3
7
12
9
Burger
PATRONS?
Ah, that’s better!
Patrons?
1
5
None
6
10
Some
4
2
8
11
3
7
12
9
Full
WHAT A GREAT TREE!
But how do we make it?
Patrons?
NoneSome
Full
YESNO Hungry?
YES
NO
No Yes
Type
FrenchItalian Thai Burger
NO YESFri/Sat
YESNO
No 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 A
A
ContainmentA B
IntersectionA 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.
