Artificial Intelligence 18. Revision Lecture

Course V231

Department of Computing

Imperial College

© Simon Colton

Overview

Exams: style and example questions– Covered in next Thursday’s lecture (12pm)

Today we review the course material– Could you get a job in the AI industry?– Knowledge, understanding, abilities

What can I get you to write about? What can I get you to explain? What can I get you to do?

Try not to infer anything explicit about the exam!– Disclaimer: I may miss something today which appears on the

exam. I will certainly cover more stuff than is on the exam.

Four General Areas Covered

General notions of AI– Characterisations, autonomous agents, search, – Representations, game playing to demonstrate these notions

Automated reasoning– Predicate logic, automating deduction,– Resolution theorem proving, constraint solving

Machine learning– Overview (FIND-S), decision trees,– Artificial Neural Networks, Inductive Logic Programming

Evolutionary approaches– Genetic algorithms, genetic programming

Characterisations of AI

All about understanding– Know that there are different ways to split up AI

Long term goals – weak & strong AI Inspirations, e.g., brain, society, logic, evolution,… Methodologies: scruffies (me) and neat (good AI people) Techniques, representations, applications, products

– An important characterisation: Into general problems to be solved,

– E.g., learning, proving, competing, communicating, creating,– Exhibiting life, etc.

Artificial Intelligence Agents

Knowledge:– Definitions of rational, autonomous, agents– What we have to worry about internally (agent)

Environmental knowledge, utility functions, goals, etc. Software engineering considerations

– What we have to worry about externally (environment) Accessibility, determinism, episodes, etc.

Understanding– Why we use agents as a concept in AI– Why we worry about rationality and autonomy

Search in Problem Solving

Knowledge– How to specify a problem as a search problem

Initial state, operators, goal test– What the general problems are in search applications

What are you looking for (path or artefact)? Completeness/soundness, time/space tradeoffs, background

– Types of uninformed search Depth first, breadth first, iterative deepening, bidirectional

– Difference between path cost and heuristic functions– Types of heuristic search

Uniform path cost, greedy, A*, IDA* Admissible heuristics, comparing heuristics with effective branching

– Hill climbing searches Local max/min problems, random restart, simulated annealing

Search in Problem Solving

Understanding– Agenda analogy and graph analogy– Why we have to search for an answer to problems (+coursework)– Why we need different types of search

Uninformed searches, heuristic searches– Why completeness & soundness are important notions– Why heuristics are needed, what they are in general

Abilities– Specify a problem as a search problem– Simulate a specific kind of search

E.g., which nodes are expanded next (draw graph, etc.)– Calculate effective branching rates, compare heuristics

Calculate search space sizes, calculate heuristic measures

Knowledge Representation

Knowledge– General types of representation available

Logical, graphical, production rules, frames– Logical representations available

Propositional, predicate, higher order, fuzzy, etc.

Understanding– Why different representations are required– Limitations of each representation– Expressiveness in logical representations

Abilities– Represent information

Logically, as semantic networks, in a frame based way, etc.

Game Playing

Knowledge– What a zero-sum two player game is– What the minimax principle is in general, what cutoff search is– Evaluations functions, weighted linear functions– Alpha-beta pruning– Expectimax, chance nodes

Understanding– Why using minimax strategies is rational

Abilities– Write down entire search trees for simple games– Propagate scores from the bottom to top of the trees– Work out the next move for a player, including expectimax

Representing Knowledgein Predicate Logic

Knowledge– Syntax and semantics of first order predicate logic

Sentences, connectives, constants, predicates, variables, functions, quantifiers, etc.

– What quantifiers mean, their scope, etc.– Instantiation, ground variables, etc.– Horn clauses, logic programs, body, head– How search is undertaken in Prolog, LIPS, WAM– OR-parallelism, AND-parallelism

Representing Knowledgein Predicate Logic

Understanding– Differences between propositional and predicate logic

Benefits to predicate logic (expressivity) – What the terms syntax and semantics mean– Prolog is a declarative, not procedural language – How logic-based expert systems work in general

Abilities– Translate English to first order predicate logic– Translate first order predicate logic to English

(Without making mistakes either way!)– Simulate a Prolog-style search– Identify parts of logic sentences and logic databases

e.g., quantifiers, constants, head, body, literal, Horn clauses

Making Deductive Inferences

Knowledge– That and, or are commutative, distributive– Some commonly used propositional equivalence rules

Double negation, rules [E1], [E4], [E5], de Morgans law

– Some commonly used implication rules Unit resolution, and elimination, or introduction, Existential elimination, etc.

– I tend to supply inference rules in exams Not simple/common ones

– Different ways of chaining together inference steps Forward/backward chaining, proof by contradiction

Making Deductive Inferences

Understanding– What it means for two sentences to be logically equivalent– What it means for a sentence to be false– What it means for one sentence to entail another– How rewrite rules can be used for proving equivalences

Abilities– Use truth tables to

Show equivalences, tautologies, that a statement is false That one statement implies another

– Apply inference rules Show what’s above and below the line

– Translate sentences: Be fluent in rewriting sentences

The Resolution Method

Knowledge– What conjunctive normal form is– What a substitution is, what unification does– Overview of the unification algorithm– The resolution rule

Unit resolution, full resolution, generalised resolution

Understanding– That resolution is refutation-complete– Why we need conjunctive normal form/unification– Why the occurs-check is important in unification

The Resolution Method

Abilities– Translate something into conjunctive normal form

By using equivalence rules Organising quantifiers, standardising variables, etc. Existential elimination

– Put a constant in place of an existential variable– Not using full skolemisation (we skipped over that)

– Prepare a set of sentences for use in a resolution proof Needs all sentences as single clauses (just split them)

– Find a unifying set of substitutions Apply them to unify two sentences

Resolution Theorem Proving

Knowledge– Specifying a problem as axioms and theorem– As a search problem: operators, initial states (CNF), the goal test– Dealing with equality (demodulation)– Heuristic strategies:

Unit preference, set of support, input resolution, subsumption– Overview of some other topics

Higher order proving, interactive, etc.

Understanding– Why deriving the empty clause means a contradiction– Why we negate the theorem statement– Why proof by contradiction is valid– Know that resolution has been applied to mathematics

Resolution Theorem Proving

Abilities:– Prove a theorem using the resolution method

Remember to negate theorem statement Follow proof all the way Draw the proof tree Or organise the resolution steps in a way

– Which makes me think you know what you’re doing

– Deduce something from a set of axioms Not necessarily related to proving something

Overview of Machine Learning Knowledge

– What ML problem constituents are: Examples (pos & neg), background information What kind of errors can occur in the data

– What ML method constituents are: Representation of solutions (v. important) How to search for solutions, how to choose between solutions

– Occam’s (Ockham’s) razor: choose simplest if all else equal

– The FIND-S method Simple, guaranteed to find the most specific solutions

– How we assess hypotheses False negatives, false positives Predictive accuracy on training set, test set, comprehensibility

– How we assess learning methods: cross-validation, hold-back Definition of overfitting

Overview of Machine Learning

Understanding– Learning from examples– How induction differs from deduction– That positives and negatives are:

Correct and incorrect classifications– What robustness means– That hypothesis accuracy doesn’t necessarily mean that the

method is a good one That methods can overfit data (memorise)

Abilities– Specify machine learning problems– Identify problem constituents/method constituents– Simulate search in the FIND-S method

Decision Tree Learning

Knowledge– What entropy and information gain are– How the ID3 algorithm works– How we can try to avoid overfitting trees– What are good problems for decision tree approaches

Attribute-value pairs, discrete values, etc.

Understanding– What the tree representation is

Why it is both a graphical and a logical representation How it can be thought of as a categorisation problem

– What entropy is estimating

Decision Tree Learning

Abilities– To read decision trees– To construct decision trees from English

specifications– Specify a learning problem for decision tree learning– Calculate entropy and information gain for attributes– Simulate the ID3-algorithm in action

Calculate information gain, choose attributes, restrict data (Sv), how/when to end branches

Two Layer ANNs

Knowledge– How information is stored in an ANN (in the weights)

How weighted sums are calculated– How ANNs are used to classify examples– What are input/hidden/output units/layers– What a perceptron is

Threshold functions: step, sigma, linear– Perceptron training rule

Using a learning rate How to calculate weight changes

– Target and observed output values for output units Epochs over all the examples

– What linearly seperable means, what boolean function means

Two Layer ANNs

Understanding– Difference between symbolic and non-symbolic representations– Motivation from biology (and the limitations of this)– Why perceptrons are limited– Why linear separability is required for perceptrons to learn

something– Why learning rate is usually set to a small value (undo previous)

Abilities– Write down a perceptron to calculate a given function (e.g., boolean)– Describe what a ANN would calculate– Propagate values from left to right to make classifications– Calculate weight changes in the perceptron learning rule– Simulate the perceptron learning rule

Multi-layer ANNs

Knowledge– Perceptron units in multi-layer ANNs– How sigmoid units calculate outputs from weighted sums

Formula for the sigma function– How feed forward networks calculate values

How these values are turned into classifications– Backpropagation Learning Routine

Overview of how this works (prop-back), epochs, weight changes, initial random assignment of weights, etc.

– How to avoid local minima Calculating network error (in overview) Adding momentum

– How to avoid overfitting Validation set, weight decay

Multi-Layer ANNs

Understanding– Why sigma being differentiable is important– Which kinds of problems are suitable for ANNs

Long training, short execution, comprehension not a problem, etc.– Why momentum works

Abilities– Feed values forward to calculate outputs, use to classify examples

E.g., numerical functions, pixel data, etc., – Calculate output values for the sigma function– Calculate error terms for the output units (given formula)– Calculate error terms for the hidden units (given formula)– Calculate weight changes using the error terms– Simulate the back-propagation algorithm

Using learning rate, momemtum, etc.

Inductive Logic Programming

Knowledge– Problem context and specification

Logic programs (background, E+, E-, hypothesis) Prior satisfiability and necessity Posterior satisfiability and sufficiency

– How we can invert resolution To use induction (rules given) to find new sentences Absorption, identification, etc. What V and W operators are

– How ILP systems search for hypotheses Specific to general (using induction) G to S (using deduction) How pruning and sorting increase efficiency How language restriction increase efficiency

Inductive Logic Programming

Understanding– Why logic programs are a good representation

Easy to read, logical– Why the problem specification is necessary– Why we invert resolution for our operators

Prove that the observations follows from axioms + H

Abilities– Apply rules of inference such as absorption

Rules would be given– Use resolution to demonstrate how the hypothesis proves the

observations (other sentences)– Determine which are more general/specific sentences using

entailment

Constraint Satisfaction Problems

Knowledge– What a formal representation of a CSP is

In terms of variables, domains, constraints (fully written out)– What a binary CSP is– What arc consistency is

How to make a problem specification arc-consistent– By removing values from domains of variables

– What happens in backtracking search– What forward checking is– What variable and value ordering heuristics do– What the fail first heuristic is

Understanding– Why we write out CSPs formally– Why we write out constraints as tuples which are allowed

Constraint Satisfaction Problems

More understanding– Why binary CSPs are important– Why forward checking works– Why fail first is so-called, and why it works– Why value-ordering methods may be bad ideas

Abilities– To specify a problem as a formal constraint satisfaction problem

(even if this is annoying for you!)– Translate constraint formalisms to general constraints (e.g.,

using less than/greater than in linear arithmetic)– Make problem specifications arc-consistent– Simulate back-tracking search (with forward checking)

Show understanding of fail-first etc. by doing hand calculations

Genetic Algorithms

Knowledge– Of the evolutionary approach in overview

Generate populations, fitness functions, recombination, etc.

– Canonical genetic algorithm Describe this schematically How individuals are selected to mate (fitness function, number

which are guaranteed entry into intermediate population) How pairs are chosen to mate, and chosen to produce

offspring How offspring are produced through recombination

Genetic Algorithms

Understanding– The inspiration from natural evolution (species/genes)

And its limitations

– That it’s difficult to specify solution representations– That it’s difficult to specify fitness functions– Why mutation is important (local maxima avoidance)

Abilities– Represent things (e.g., integers) as bit strings– Perform crossover and mutation operators

One point and two point crossover

– Calculate evaluation functions Use these in fitness functions for the intermediate population

Genetic Programming

Knowledge– Representation of programs as graphs

What result producing branches are– Specifying a problem for a GP approach

Solution space of programs, fitness function (evaluation function)– What the terminal set, function set, control parameters and

termination conditions are– How individuals are chosen for mating

Using fitness for probabilities for intermediate population– Or using tournament selection, or ranking

– What the reproduction, crossover and mutation operators do– What the crossover fragment is

Genetic Programming

Understanding– That it is automatic programming

That this is hard, other programs do this in a limited way– Why graphical representation of programs is good– That architecture altering operations are used

On more sophisticated program spaces– That GP can achieve human-level performance

Abilities– Translate from functions (with things like if-statements)

To graphs and back again– Determine function and terminal sets from programs– Perform crossover and mutation – Simulate (describe) how a GP approach would proceed