Artificial Intelligence

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@ Ashek Mahmud Khan; Dept. of CSE (JUST); 01725-402592

01725-402592

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1(a) Defne Artificial Intelligence.

According to the father of Artificial Intelligence, John McCarthy, it is ―The science and engineering of

making intelligent machines, especially intelligent computer programs‖.

Artificial Intelligence is a way of making a computer, a computer-controlled robot, or a software think

intelligently, in the similar manner the intelligent humans think. A robot with artificial intelligence they are

organized into four categories:

Systems that think like humans.

Systems that act like humans .

Systems that think rationally.

Systems that act rationally.

1(a) Shortly explain the Turing Test of intelligence.

Turing test, in artificial intelligence, a test proposed (1950) by the English mathematician Alan M. Turing to

determine whether a computer can ―think.‖

Turing defined intelligent behavioras the ability to achieve human level performance in all cognitive tasks,

sufficient to fool an interrogator. The computer would need to possess th e following capabilities:

Natural language processing to enable it to communicate successfully in English (or some Other

human language);

Knowledge representation to store information provided before or during the interrogation;

Automated reasoning to use the stored information to answer questions and to draw new

conclusions;

Machine learning to adapt to new circumstances and to detect and extrapolate patterns.

Turing‘s test deliberately avoided direct physical interaction between the interrogator and the computer,

because physical simulation of a person is unnecessary for intelligence.

Systems that act like humans

You enter a room which has a computer terminal. You have a fixed period of time to type what you

want into the terminal, and study the replies. At the other end of the line is either a human being or a

computer system.

If it is a computer system, and at the end of the period you cannot reliably determine whether it is a

system or a human, then the system is deemed to be intelligent.

The Turing Test approach

a human questioner cannot tell if, there is a computer or a human answering his question, via

teletype (remote communication)

The computer must behave intelligently

Intelligent behavior

to achieve human-level performance in all cognitive tasks

These cognitive tasks include:

Natural language processing, for communication with human.

http://global.britannica.com/technology/artificial-intelligence

http://global.britannica.com/biography/Alan-Turing

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Knowledge representation

to store information effectively & efficiently

Automated reasoning

to retrieve & answer questions using the stored information

Machine learning

to adapt to new circumstances

1(b) Define Agent. Describe how agents interact with environments.

Agent: An agent is anything that can perceive its environment through sensors and acts upon that

environment through effectors.

A human agent has sensory organs such as eyes, ears, nose, tongue and skin parallel to the sensors,

and other organs such as hands, legs, mouth, for effectors.

A robotic agent replaces cameras and infrared range finders for the sensors, and various motors and

actuators for effectors.

A software agent has encoded bit strings as its programs and actions.

1(c) Define rational agent. Explain the general agent program.

Rational agent: A rational agent always performs right action, where the right action means the action that

causes the agent to be most successful in the given percept sequence. The problem the agent solves is

characterized by Performance Measure, Environment, Actuators, and Sensors (PEAS).

There are four types of agent program-

(i) Simplex reflex agents

(ii) Model based reflex agents

(iii) Goal-based agents

(iv) Utility-based agents.

Simplex reflex agents: They choose actions only based on the current percept. Their environment is

completely observable.

Model based reflex agents: They use a model of the world to choose their actions. They maintain an

internal state.

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Goal-based agents: They choose their actions in order to achieve goals. Goal-based approach is more

flexible than reflex agent since the knowledge supporting a decision is explicitly modeled, thereby allowing

for modifications.

Utility Based Agents: They choose actions based on a preference (utility) for each state. Goals are

inadequate when −

There are conflicting goals, out of which only few can be achieved.

Goals have some uncertainty of being achieved and you need to weigh likelihood of success against

the importance of a goal.

2(b) Describe the Model based reflex agents.

Model based reflex agents: They use a model of the world to choose their actions. They maintain an

internal state.

Model − the knowledge about how the things happen in the world.

Internal State − It is a representation of unobserved aspects of current state depending on percept history.

Updating the state requires the information about −

How the world evolves.

How the agent‘s actions affect the world.

3(a) Define Knowledge.

Knowledge representation and reasoning (KR) is the field of artificial intelligence (AI) dedicated to

representing information about the world in a form that a computer system can utilize to solve complex

tasks such as diagnosing a medical condition or having a dialog in a natural language.

The total Turing Test

Turing‘s test deliberately avoided direct physical interaction between the interrogator and the computer,

because physical simulation of aperson is unnecessary for intelligence. However, theso-called total Turing

Test includes a video signal so that the interrogator can test the subject‘s perceptual abilities, as well as the

opportunity for the interrogator to pass physical objects" through the hatch." To pass the total Turing Test,

the computer will need

computer vision to perceive objects, and

robotics to move them about.

Systems that think like humans: cognitive modeling

If we are going to say that a given program thinks like a human, we must have some way of determining

how humans think. We need to get inside the actual workings of human minds. There are two ways to do

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this: through introspection—trying to catch our own thoughts as they go by—or through psychological

experiments.

Cognitive Science

―The exciting new effort to make computers think … machines with minds in the full and literal

sense‖ (Haugeland)

―[The automation of] activities that we associate with human thinking, activities such as decision-

making, problem solving, learning …‖ (Bellman)

Thinking rationally: The laws of thought approach

The Greek philosopher Aristotle was one of the first to attempt to codify "right thinking," that is, irrefutable

reasoning processes. His famous syllogisms provided patterns for argument structures that always gave

correct conclusions given correct premises. For example,"Socrates is aman; all men are mortal; there fore

Socrates is mortal." These laws of thought were supposed to govern the operation of the mind, and initiated

the field of logic.

―The study of mental facilities through the use of computational models‖ (Charniak and McDermott)

―The study of the computations that make it possible to perceive, reason, and act‖ (Winston)

Systems that act rationally: “Rational agent”

Acting rationally means acting so as to achieve one‘s goals, given one's beliefs. An agent is just something

that perceives and acts.

Rational behavior: doing the right thing

The right thing: that which is expected to maximize goal achievement, given the available

information

Giving answers to questions is ‗acting‘.

I don't care whether a system:

replicates human thought processes

makes the same decisions as humans

uses purely logical reasoning

Study AI as rational agent –

2 advantages:

It is more general than using logic only

Because: LOGIC + Domain knowledge

It allows extension of the approach with more scientific methodologies

Rational agents

An agent is an entity that perceives and acts

This course is about designing rational agents

Abstractly, an agent is a function from percept histories to actions:

[f: P* A]

For any given class of environments and tasks, we seek the agent (or class of agents) with the best

performance

Caveat: computational limitations make perfect rationality unachievable

Design best program for given machine resources

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From the above two definitions, we can see that AI has two major roles:

Study the intelligent part concerned with humans.

Represent those actions using computers.

Goals of AI

To Create Expert Systems − the systems which exhibit intelligent behavior, learn, demonstrate,

explain, and advice its users.

To Implement Human Intelligence in Machines − Creating systems that understand, think, learn,

and behave like humans. Or,

build and understand intelligent systems/agents

synergy between

philosophy,

psychology and cognitive science

computer science and engineering

mathematics and physics

The Foundation of AI

Philosophy

At that time, the study of human intelligence began with no formal expression

Initiate the idea of mind as a machine and its internal operations

Mathematics formalizes the three main area of AI: computation, logic, and probability

Computation leads to analysis of the problems that can be computed

complexity theory

Probability contributes the “degree of belief” to handle uncertainty in AI

Decision theory combines probability theory and utility theory (bias)

Psychology

How do humans think and act?

The study of human reasoning and acting

Provides reasoning models for AI

Strengthen the ideas

humans and other animals can be considered as information processing machines

Computer Engineering

How to build an efficient computer?

Provides the artifact that makes AI application possible

The power of computer makes computation of large and difficult problems more easily

AI has also contributed its own work to computer science, including: time-sharing, the linked

list data type, OOP, etc.

Some Advantages of Artificial Intelligence

more powerful and more useful computers

new and improved interfaces

solving new problems

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better handling of information

relieves information overload

conversion of information into knowledge

The Disadvantages

increased costs

difficulty with software development - slow and expensive

few experienced programmers

Few practical products have reached the market as yet.

What Contributes to AI?

Artificial intelligence is a science and technology based on disciplines such as Computer Science, Biology,

Psychology, Linguistics, Mathematics, and Engineering. A major thrust of AI is in the development of

computer functions associated with human intelligence, such as reasoning, learning, and problem solving.

Search

Search is the fundamental technique of AI.

Possible answers, decisions or courses of action are structured into an abstract space, which

we then search. Search is the systematic examination of states to find path from the start/root

state to the goal state.

Search is either "blind" or ―uninformed":

blind

we move through the space without worrying about what is coming next, but

recognising the answer if we see it

informed

We guess what is ahead, and use that information to decide where to look

next.

We may want to search for the first answer that satisfies our goal, or we may want to keep searching

until we find the best answer.

Knowledge Representation & Reasoning

The second most important concept in AI

If we are going to act rationally in our environment, then we must have some way of describing that

environment and drawing inferences from that representation.

Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of

reasoning, such as the application of rules or the relations of sets and subsets.

https://en.wikipedia.org/wiki/Logic

https://en.wikipedia.org/wiki/Set_theory

https://en.wikipedia.org/wiki/Subset

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Reasoning

It is the set of processes that enables us to provide basis for judgment, making decisions, and prediction.

There are broadly two types −

Planning

Given a set of goals, construct a sequence of actions that achieves those goals:

often very large search space

but most parts of the world are independent of most other parts

often start with goals and connect them to actions

no necessary connection between order of planning and order of execution

What happens if the world changes as we execute the plan and/or our actions don‘t produce

the expected results?

Decide what actions to use to achieve some set of objectives

Learning

It is the activity of gaining knowledge or skill by studying, practicing, being taught, or experiencing

something. Learning enhances the awareness of the subjects of the study. The ability of learning is

possessed by humans, some animals, and AI-enabled systems. Learning is categorized as −

Auditory Learning − It is learning by listening and hearing. For example, students listening to

recorded audio lectures.

Episodic Learning – To learn by remembering sequences of events that one has witnessed or

experienced. This is linear and orderly.

Motor Learning − It is learning by precise movement of muscles. For example, picking objects,

Writing, etc.

Observational Learning – To learn by watching and imitating others. For example, child tries to

learn by mimicking her parent.

Perceptual Learning − It is learning to recognize stimuli that one has seen before. For example,

identifying and classifying objects and situations.

Relational Learning − It involves learning to differentiate among various stimuli on the basis of

relational properties, rather than absolute properties. For Example, Adding ‗little less‘ salt at the time

of cooking potatoes that came up salty last time, when cooked with adding say a tablespoon of salt.

Spatial Learning − It is learning through visual stimuli such as images, colors, maps, etc. For

Example, A person can create roadmap in mind before actually following the road.

Stimulus-Response Learning − It is learning to perform a particular behavior when a certain

stimulus is present. For example, a dog raises its ear on hearing doorbell.

Interacting with the Environment

In order to enable intelligent behaviour, we will have to interact with our environment.

Properly intelligent systems may be expected to:

accept sensory input

vision, sound, …

(i) Inductive Reasoning

(ii) Deductive Reasoning

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interact with humans

Understand language, recognise speech, and generate text, speech and graphics.

modify the environment

robotics

History of AI

Year Milestone / Innovation

1923 Karel Čapek play named ―Rossum's Universal Robots‖ (RUR) opens in London, first use of the

word "robot" in English.

1943 Foundations for neural networks laid.

1945 Isaac Asimov, Columbia University alumni, coined the term Robotics.

1950 Alan Turing introduced Turing Test for evaluation of intelligence and published Computing

Machinery and Intelligence.

1956 Demonstration of the first running AI program at Carnegie Mellon University.

1958 John McCarthy invents LISP programming language for AI.

1964 Danny Bobrow's dissertation at MIT showed that computers can understand natural language well

enough to solve algebra word problems correctly.

1965 Joseph Weizenbaum at MIT built ELIZA, an interactive problem that carries on a dialogue in

English.

1969 Scientists at Stanford Research Institute Developed Shakey, a robot, equipped with locomotion,

perception, and problem solving.

1973 The Assembly Robotics group at Edinburgh University built Freddy, the Famous Scottish Robot,

capable of using vision to locate and assemble models.

1979 The first computer-controlled autonomous vehicle, Stanford Cart, was built.

1985 Harold Cohen created and demonstrated the drawing program, Aaron.

1990 Major advances in all areas of AI −

Significant demonstrations in machine learning

Case-based reasoning

Multi-agent planning

Scheduling

Data mining, Web Crawler

natural language understanding and translation

Vision, Virtual Reality

Games

1997 The Deep Blue Chess Program beats the then world chess champion, Garry Kasparov.

2000 Interactive robot pets become commercially available. MIT displays Kismet, a robot with a face

that expresses emotions. The robot Nomad explores remote regions of Antarctica and locates

meteorites.

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The „von Neuman‟ Architecture

Problem Solving

Problem solving also includes decision making, which is the process of selecting the best suitable alternative

out of multiple alternatives to reach the desired goal are available.

Perception

It is the process of acquiring, interpreting, selecting, and organizing sensory information.

Linguistic Intelligence

It is one‘s ability to use, comprehend, speak, and write the verbal and written language. It is important in

interpersonal communication.

Symbolic and Sub-symbolic AI

Symbolic AI is concerned with describing and manipulating our knowledge of the world as explicit

symbols, where these symbols have clear relationships to entities in the real world.

Sub-symbolic AI (e.g. neural-nets) is more concerned with obtaining the correct response to an input

stimulus without ‗looking inside the box‘ to see if parts of the mechanism can be associated with

discrete real world objects.

This course is concerned with symbolic AI.

AI Applications

AI has been dominant in various fields such as −

Gaming − AI plays crucial role in strategic games such as chess, poker, tic-tac-toe, etc., where

machine can think of large number of possible positions based on heuristic knowledge.

Natural Language Processing − It is possible to interact with the computer that understands natural

language spoken by humans.

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Expert Systems − There are some applications which integrate machine, software, and special

information to impart reasoning and advising. They provide explanation and advice to the users.

Vision Systems − these systems understand, interpret, and comprehend visual input on the

computer. For example,

o A spying aero plane takes photographs, which are used to figure out spatial information or

map of the areas.

o Doctors use clinical expert system to diagnose the patient.

o Police use computer software that can recognize the face of criminal with the stored portrait

made by forensic artist.

Speech Recognition − Some intelligent systems are capable of hearing and comprehending the

language in terms of sentences and their meanings while a human talks to it. It can handle different

accents, slang words, noise in the background, change in human‘s noise due to cold, etc.

Handwriting Recognition − the handwriting recognition software reads the text written on paper by

a pen or on screen by a stylus. It can recognize the shapes of the letters and convert it into editable

text.

Intelligent Robots − Robots are able to perform the tasks given by a human. They have sensors to

detect physical data from the real world such as light, heat, temperature, movement, sound, bump,

and pressure. They have efficient processors, multiple sensors and huge memory, to exhibit

intelligence. In addition, they are capable of learning from their mistakes and they can adapt to the

new environment

Other application areas:

Bioinformatics:

Gene expression data analysis

Prediction of protein structure

Text classification, document sorting:

Web pages, e-mails

Articles in the news

Video, image classification

Music composition, picture drawing

Natural Language Processing.

Perception.

What is Intelligence composed of?

The intelligence is intangible. It is composed of −

Reasoning

Learning

Problem Solving

Perception

Linguistic Intelligence

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Logic

First-order logic

First-order logic is symbolized reasoning in which each sentence, or statement, is broken down into a

subject and a predicate. The predicate modifies or defines the properties of the subject. In first-order logic, a

predicate can only refer to a single subject. First-order logic is also known as first-order predicate calculus

or first-order functional calculus.

A sentence in first-order logic is written in the form Px or P(x), where P is the predicate and x is the subject,

represented as a variable. Complete sentences are logically combined and manipulated according to the

same rules as those used in Boolean algebra.

– Connectives: ∧, ∨, ¬, ⇒, ⇔

– Quantifiers:

• Universal: ∀ x: ( is_Man(x) ⇒ is_Mortal(x) )

• Existential: ∃ y: ( is_Father(y, fred) )

Example: Representing Facts in First-Order Logic

1. Lucy* is a professor

2. All professors are people.

3. Johan is the dean.

4. Deans are professors.

5. All professors consider the dean a friend or don‘t know him.

6. Everyone is a friend of someone.

7. People only criticize people that are not their friends.

8. Lucy criticized Johan.

Proof: Knowledge base

Knowledge Engineering

1. Identify the task.

2. Assemble the relevant knowledge.

3. Decide on a vocabulary of predicates, functions, and constants.

4. Encode general knowledge about the domain.

5. Encode a description of the specific problem instance.

http://searchcio-midmarket.techtarget.com/definition/Boolean

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6. Pose queries to the inference procedure and get answers.

7. Debug the knowledge base

Inference Procedures: Theoretical Results

• There exist complete and sound proof procedures for propositional and FOL.

Propositional logic

• Use the definition of entailment directly. Proof procedure is exponential in n, the number of symbols.

• In practice, can be much faster…

• Polynomial-time inference procedure exists when KB is expressed as Horn clauses: P1 ˄ P2 ˄ ........ ˄ Pn

Q where the Pi and Q are non-negated atoms.

First-Order logic

• Godel‘s completeness theorem showed that a proof procedure exists…

• But none was demonstrated until Robinson‘s 1965 resolution algorithm.

• Entailment in first-order logic is semidecidable.

Resolution Rule of Inference

Algorithm: Resolution Proof

Negate the original theorem to be proved, and add the result to the knowledge base.

Bring knowledge base into conjunctive normal form (CNF)

– CNF: conjunctions of disjunctions

– Each disjunction is called a clause.

Repeat until there is no resolvable pair of clauses:

– Find resolvable clauses and resolve them.

– Add the results of resolution to the knowledge base.

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– If NIL (empty clause) is produced, stop and report that the (original) theorem is true.

Report that the (original) theorem is false.

Resolution Example: Propositional Logic

Resolution Example: FOL

Axioms: Regular CNF

Resolution Theorem Proving

Properties of Resolution Theorem Proving:

– sound (for propositional and FOL)

– (refutation) complete (for propositional and FOL)

Procedure may seem cumbersome but note that can be easily automated. Just ―smash‖ clauses until empty

clause or no more new clauses

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Unification

Unify procedure: Unify (P, Q) takes two atomic (i.e. single predicates) sentences P and Q and returns a

substitution that makes P and Q identical.

Unifier: a substitution that makes two clauses resolvable

Rules for substitutions:

– Can replace a variable by a constant.

– Can replace a variable by a variable.

– Can replace a variable by a function expression, as long as the function expression does not contain the

variable.

Unification – Purpose

Unification (example)

Who does John hate? ∃ X: Hates (John, x)

Knowledge base (in clause form):

1. ¬ Knows (John, v) ∨ Hates (John, v)

2. Knows (John, Jim)

3. Knows (y, Leo)

4. Knows (z, Mother (z))

5. ¬ Hates (John, x) (since ¬ ∃ x: Hates (John, x) Ù∀ x: ¬Hates (John,x))

Resolution with 5 and 1:

unify(Hates(John, x), Hates(John, v)) = {x/v}

6. ¬ Knows (John, v)

Resolution with 6 and 2:

unify(Knows(John, v), Knows(John, Jim))= {v/Jim}

or resolution with 6 and 3:

unify(Knows (John, v), Knows (y, Leo)) = {y/John, v/Leo}

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or Resolution with 6 and 4:

unify(Knows (John, v), Knows (z, Mother(z))) = {z/John, v/Mother(z)}

Answers:

1. Hates(John,x) with {x/v, v/Jim} (i.e. John hates Jim)

2. Hates(John,x) with {x/v, y/John, v/Leo} (i.e. John hates Leo)

3. Hates(John,x) with {x/v, v/Mother(z), z/John} (i.e. John hates his mother

Converting More Complicated Sentences to CNF

1. Eliminate Implications

2. Move negations down to the atomic formulas

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3. Eliminâtes Existential Quantifier: Skolemization

4. Rename variables as necessary

We want no two variables of the same name.

5. Move the universal quantifiers to the left

This works because each quantifier uses a unique variable name.

What is state-space representation?

In control engineering, a state-space representation is a mathematical model of a physical system as a set of

input, output and state variables related by first-order differential equations. "State space" refers to the space

whose axes are the state variables.

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CT-01 Using state space problem solve 8-puzzle problem.

8-Puzzle:

The 8-Puzzle involves moving the tiles on the board above into a particular configuration. The black square

on the board represents a space. The player can move a tile into the space, freeing that position for another

tile to be moved into and so on.

For example, given the initial state above we may want the tiles to be moved so that the following goal state

may be attained.

Figure 3.2: Eight-Puzzle Problem state space representation

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Blind Search: A blind search (also called an uninformed search) is a search that has no information about

its domain. The only thing that a blind search can do is distinguish a non-goal state from a goal state.

BLIND Search Methods: (i) Depth-first (ii) Breadth-first (iii) Non-deterministic search (iv)

Iterative deepening (v) Bi-directional search

Breadth-first search: Breadth-first search goes through the tree level by level, visiting all of the nodes on

the top level first, then all the nodes on the second level, and so on.

It starts from the root node, explores the neighboring nodes first and moves towards the next level

neighbors. It generates one tree at a time until the solution is found. It can be implemented using FIFO

queue data structure. In breadth-first search the frontier is implemented as a FIFO (first-in, first-out)

queue.

Advantages:

(i) Optimal solutions are always found

(ii) Multiple solutions found early

Disadvantages

(i) If solution path is long, the whole tree must be searched up to that depth

(ii) All of the tree generated must be stored in memory

Breadth-first algorithm:

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Trace of breadth -first for running example:

Speed (breadth-first)

If a goal node is found on depth m of the tree, all nodes up till that depth are created.

Thus: O (bm

)

Note: depth-first would also visit deeper nodes.

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Depth-First Search: Depth-first search goes through the tree branch by branch, going all the way down to

the leaf nodes at the bottom of the tree before trying the next branch over.

It is implemented in recursion with LIFO stack data structure. It creates the same set of nodes as Breadth-

First method, only in the different order.

Advantages:

May arrive at solutions without examining much of search space

Needs little memory (only node in current path needs to be stored)

Disadvantages:

May settle for non-optimal solution

May explore single unfruitful path for a long time

Depth-first algorithm:

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Trace of depth-first for running example:

Speed (depth-first):

In the worst case: the (only) goal node may be on the right-most branch,

Time complexities == bd +

b

d-1 + … + 1 = b

d+1 -1 /b-1

Thus: O (bd)

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Non-deterministic search:

Depth-limited search:

Iterative deepening: the best „blind‟ search.

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Bi-directional algorithm:

Properties (Bi-directional):

Complete: Yes.

Speed: If the test on common state can be done in constant time (hashing):

2 * O(bm/2

) = O(bm/2

)

Memory: similarly: O(bm/2

)

4 (a) Define Heuristic search.

Heuristic search: In computer science, artificial intelligence, and mathematical optimization, a heuristic is

a technique designed for solving a problem more quickly when classic methods are too slow or for finding

an approximate solution when classic methods fail to find any exact solution.

Heuristic or informed search exploits additional knowledge about the problem that helps direct search to

more promising paths.

A heuristic function, h (n), provides an estimate of the cost of the path from a given node to the closest goal

state. Must be zero if node represents a goal state. Example: Straight-line distance from current location to

the goal location in a road navigation problem.

Hill climbing

In computer science, hill climbing is a mathematical optimization technique which belongs to the family of

local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to

find a better solution by incrementally changing a single element of the solution. If the change produces a

better solution, an incremental change is made to the new solution, repeating until no further improvements

can be found. For example, hill climbing can be applied to the travelling salesman problem.

https://en.wikipedia.org/wiki/Computer_science

https://en.wikipedia.org/wiki/Artificial_intelligence

https://en.wikipedia.org/wiki/Mathematical_optimization

https://en.wikipedia.org/wiki/Problem_solving


https://en.wikipedia.org/wiki/Optimization_%28mathematics%29

https://en.wikipedia.org/wiki/Local_search_%28optimization%29

https://en.wikipedia.org/wiki/Incremental_heuristic_search

https://en.wikipedia.org/wiki/Travelling_salesman_problem

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Hill climbing_1 algorithm:

Beam Search

In computer science, beam search is a heuristic search algorithm that explores a graph by expanding the

most promising node in a limited set. Beam search is an optimization of best-first search that reduces its

memory requirements. Best-first search is a graph search which orders all partial solutions (states) according

to some heuristic which attempts to predict how close a partial solution is to a complete solution (goal state).

But in beam search, only a predetermined number of best partial solutions are kept as candidates.

Beam search is the de facto method for translation decoding

very fast even in the worst-case

accurate in practice

implemented in many real-world systems

Goal: fast, optimal translation decoding

better understand what makes translation hard

quantify search error from beam search

(at some point) improve translation accuracy


https://en.wikipedia.org/wiki/Heuristic_%28computer_science%29

https://en.wikipedia.org/wiki/Search_algorithm

https://en.wikipedia.org/wiki/Best-first_search

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Greedy search algorithm

A greedy algorithm is an algorithm that follows the problem solving heuristic of making the locally optimal

choice at each stage with the hope of finding a global optimum. In many problems, a greedy strategy does

not in general produce an optimal solution, but nonetheless a greedy heuristic may yield locally optimal

solutions that approximate a global optimal solution in a reasonable time.

In general, greedy algorithms have five components:

1. A candidate set, from which a solution is created

2. A selection function, which chooses the best candidate to be added to the solution

3. A feasibility function, that is used to determine if a candidate can be used to contribute to a solution

4. An objective function, which assigns a value to a solution, or a partial solution, and

5. A solution function, which will indicate when we have discovered a complete solution

There are a few variations to the greedy algorithm:

Pure greedy algorithms

Orthogonal greedy algorithms

Relaxed greedy algorithms

Applications

Greedy algorithms mostly (but not always) fail to find the globally optimal solution, because they usually do

not operate exhaustively on all the data. They can make commitments to certain choices too early which

prevent them from finding the best overall solution later.

With a goal of reaching the largest-sum, at each step, the greedy algorithm will choose what appears to be

the optimal immediate choice, so it will choose 12 instead of 3 at the second step, and will not reach the best

solution, which contains 99.

Greedy search algorithm:

https://en.wikipedia.org/wiki/Algorithm

https://en.wikipedia.org/wiki/Problem_solving

https://en.wikipedia.org/wiki/Heuristic_%28computer_science%29

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Optimal Search

In computer science, an optimal binary search tree (BST), sometimes called a weight-balanced binary tree,

is a binary search tree which provides the smallest possible search time (or expected search time) for a given

sequence of accesses (or access probabilities).

Re-introduce the costs of arcs in the NET

At each step, select the node with the lowest accumulated cost.

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Uniform cost algorithm

Branch and bound

Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial

optimization problems, as well as general real valued problems. A branch-and-bound algorithm consists of a

systematic enumeration of candidate solutions by means of state space search.

The goal of a branch-and-bound algorithm is to find a value x that maximizes or minimizes the value of a

real-valued function f(x), called an objective function, among some set S of admissible, or candidate

solutions.

Optimal Uniform cost version

https://en.wikipedia.org/wiki/Algorithm

https://en.wikipedia.org/wiki/Discrete_optimization

https://en.wikipedia.org/wiki/Combinatorial_optimization



https://en.wikipedia.org/wiki/Mathematical_optimization

https://en.wikipedia.org/wiki/State_space_search

https://en.wikipedia.org/wiki/Candidate_solution

https://en.wikipedia.org/wiki/Candidate_solution

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Extension with heuristic estimates:

Replace the ‗accumulated cost‘ in the ‗extended uniform cost‘ algorithm by a function:

Where, cost (path) = the accumulated cost of the partial path h (T) = a heuristic estimate of the cost

remaining from T to a goal node. f (path) = an estimate of the cost of a path extending the current path to

reach a goal.

Example: Reconsider the straight-line distance:

h(T) = the straight-line distance from T to G

30


Estimate-extended Uniform cost algorithm:

A* search

IS: Branch and bound extended, Heuristic Underestimate extended, redundant path deletion

extended, Uniform Cost Search.

Note that redundant path deletion is based on the accumulated costs only, so that there is no problem

combining it with heuristic underestimates.

A* algorithm:

Date post:	16-Apr-2017
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