Artificial intelligence course work

Artificial Intelligence
Course Work
By: Mr. Ganesh Ingle

Course
(Fundamentals of Artificial Intelligence)

Course Main Topic/Chapters
Fundamentals of Artificial Intelligence
Searching Planning
Knowledge Representation
Uncertainty

Section 1: Topics/Contents
Fundamentals of Artificial Intelligence
Introduction, A.I. Representation, Non-AI & AI Techniques, Representation of
Knowledge, Knowledge Base Systems, State Space Search, Production Systems,
Problem Characteristics, types of production systems, Intelligent Agents and
Environments, concept of rationality, the nature of environments, structure of
agents, problem solving agents, problem formulation
Searching Planning
Blocks world, STRIPS, Implementation using goal stack, Partial Order Planning,
Hierarchical planning, and least commitment strategy. Conditional Planning,
Continuous Planning Machine Learning Algorithms

Knowledge based agents, Wumpus world, Propositional Logic: Representation,
Inference, Reasoning Patterns, Resolution, First order Logic: Representation,
Inference, Reasoning Patterns, Resolution, Forward and Backward Chaining. Basics
of PROLOG: Representation, Structure, Backtracking, Expert System.
Uncertainty
Non Monotonic Reasoning, Logics for Non Monotonic Reasoning, Forward rules and
Backward rules, Justification based Truth Maintenance Systems, Semantic Nets
Statistical Reasoning, Probability and Bayes’ theorem, Bayesian Network, Markov
Networks, Hidden Markov Model, Basis of Utility Theory, Utility Functions.

Representation of Knowledge
1.AI agents deal with knowledge (data)
• Facts (believe & observe knowledge)
• Procedures (how to knowledge)
• Meaning (relate & define knowledge)
2.Right representation is crucial
• Early realisation in AI
• Wrong choice can lead to project failure
• Active research area

Choosing a Representation
1. For certain problem solving techniques
• ‘Best’ representation already known
• Often a requirement of the technique
• Or a requirement of the programming language (e.g. Prolog)
2. Examples
• First order theorem proving… first order logic
• Inductive logic programming… logic programs
• Neural networks learning… neural networks
3. Some general representation schemes
• Suitable for many different (and new) AI applications

Some General Representations
1. Logical Representations
2. Production Rules
3. Semantic Networks
• Conceptual graphs, frame
What is a Logic?
• A language with concrete rules
• No ambiguity in representation (may be other errors!)
• Allows unambiguous communication and processing
• Very unlike natural languages e.g. English
• Many ways to translate between languages
• A statement can be represented in different logics
• And perhaps differently in same logic
• Expressiveness of a logic
• How much can we say in this language?
• Not to be confused with logical reasoning
• Logics are languages, reasoning is a process (may use logic)

Syntax and Semantics
1.Syntax
• Rules for constructing legal sentences in the logic
• Which symbols we can use (English: letters, punctuation)
• How we are allowed to combine symbols
2.Semantics
• How we interpret (read) sentences in the logic
• Assigns a meaning to each sentence
3.Example: “All lecturers are seven foot tall”
• A valid sentence (syntax)
• And we can understand the meaning (semantics)
• This sentence happens to be false (there is a counterexample)

Propositional Logic
1.Syntax
• Propositions, e.g. “it is wet”
• Connectives: and, or, not, implies, if (equivalent)
• Brackets, T (true) and F (false)
2.Semantics (Classical AKA Boolean)
• Define how connectives affect truth
• “P and Q” is true if and only if P is true and Q is true
• Use truth tables to work out the truth of statements

Predicate Logic
1.Predicate Logic
2. Propositional logic combines atoms
• An atom contains no propositional connectives
• Have no structure (today_is_wet, john_likes_apples)
3. Predicates allow us to talk about objects
• Properties: is_wet(today)
• Relations: likes(john, apples)
• True or false
4. In predicate logic each atom is a predicate
• e.g. first order logic, higher-order logic

1.First Order Logic
2.More expressive logic than propositional
• Used in this course
3.Constants are objects: john, apples
4.Predicates are properties and relations:
• likes(john, apples)
5.Functions transform objects:
• likes(john, fruit_of(apple_tree))
6.Variables represent any object: likes(X, apples)
7.Quantifiers qualify values of variables

Example: FOL Sentence
Example: FOL Sentence
1. “Every rose has a thorn”
2. For all X
• if (X is a rose)
• then there exists Y
• (X has Y) and (Y is a thorn)

Higher Order Logic
Higher Order Logic
1. More expressive than first order
2. Functions and predicates are also objects
• Described by predicates: binary(addition)
• Transformed by functions: differentiate(square)
• Can quantify over both
3. E.g. define red functions as having zero at 17
4. Much harder to reason with

Beyond True and False
Beyond True and False
1. Multi-valued logics
• More than two truth values
• e.g., true, false & unknown
• Fuzzy logic uses probabilities, truth value in [0,1]
2. Modal logics
• Modal operators define mode for propositions
• Epistemic logics (belief)
• e.g. p (necessarily p), p (possibly p), …
3. Temporal logics (time)
1. e.g. p (always p), p (eventually p), …

Non-Logical Representations?
1. Production rules
2. Semantic networks
• Conceptual graphs
• Frames
3. Logic representations have restricitions and can be hard to work with
• Many AI researchers searched for better representations

1.Production Rules
2. Rule set of <condition,action> pairs
• “if condition then action”
3. Match-resolve-act cycle
• Match: Agent checks if each rule’s condition holds
• Resolve:
• Multiple production rules may fire at once (conflict set)
• Agent must choose rule from set (conflict resolution)
• Act: If so, rule “fires” and the action is carried out
4. Working memory:
• rule can write knowledge to working memory
• knowledge may match and fire other rules

Production Rules Example
1. IF (at bus stop AND bus arrives) THEN action(get on the bus)
2. IF (on bus AND not paid AND have oyster card) THEN action(pay with oyster)
AND add(paid)
3. IF (on bus AND paid AND empty seat) THEN sit down
4. conditions and actions must be clearly defined can easily be expressed in
first order logic!

Graphical Representation
1. Humans draw diagrams all the time, e.g.
2. Causal relationships
1. And relationships between ideas

Graphical Representation
1. Graphs easy to store in a computer
2. To be of any use must impose a formalism
3. Jason is 15, Bryan is 40, Arthur is 70, Jim is 74
4. How old is Julia?

1.Semantic Networks
• Because the syntax is the same
• We can guess that Julia’s age is similar to
Bryan’s
• Formalism imposes restricted syntax

Semantic Networks
1. Graphical representation (a graph)
• Links indicate subset, member, relation, ...
2. Equivalent to logical statements (usually FOL)
• Easier to understand than FOL?
• Specialised SN reasoning algorithms can be
faster
3. Example: natural language understanding
• Sentences with same meaning have same
graphs
• e.g. Conceptual Dependency Theory (Schank)

1.Conceptual Graphs
1. Semantic network where each graph represents a single
proposition
2. Concept nodes can be
• Concrete (visualisable) such as restaurant, my dog Spot
• Abstract (not easily visualisable) such as anger
3. Edges do not have labels
• Instead, conceptual relation nodes
• Easy to represent relations between multiple objects

Frame Representations
1. Semantic networks where nodes have structure
• Frame with a number of slots (age, height, ...)
• Each slot stores specific item of information
2. When agent faces a new situation
• Slots can be filled in (value may be another frame)
• Filling in may trigger actions
• May trigger retrieval of other frames
3. Inheritance of properties between frames
• Very similar to objects in OOP

Example: Frame Representation

1.Flexibility in Frames
2. Slots in a frame can contain
• Information for choosing a frame in a situation
• Relationships between this and other frames
• Procedures to carry out after various slots filled
• Default information to use where input is missing
• Blank slots: left blank unless required for a task
• Other frames, which gives a hierarchy
3. Can also be expressed in first order logic

1.Representation & Logic
• AI wanted “non-logical representations”
• Production rules
• Semantic networks
• Conceptual graphs, frames
• But all can be expressed in first order logic!
• Best of both worlds
• Logical reading ensures representation well-defined
• Representations specialised for applications
• Can make reasoning easier, more intuitive

AI
Hard AI Soft AI

AI
Act
Like Human
Turing Test
Playing chess by machine and human in
different rooms with observer not
knowing which room has machine
Complete Turring Test
NLP: Natural language representation
KR: Knowledge representation
Movement: Robotics
Rationally
Rational Agent
approach
Think
Like Human
Cognitive Approach
ANN design
ANN training
Activation functions
Weights to the ANN
Rationally
Law of Thought
Approach
i/p 1=Ram is human
i/p =All human are kind
o/p=Ram is Kind

How do our brains work?
Dendrites: Input
Cell body: Processor
Synaptic: Link
Axon: Output

How do ANNs work?
Output
x1x2xm
∑
y
Processing
Input
∑= X1+X2 + ….+Xm =y
. . . . . . . . . . . .

How ANNs work? Inputs
Weights
Bias value
Hidden layer
Sigmoid function
Activation function
Back propagation
Output
Fitness function

Learning by trial‐and‐error
Continuous process of:
Trial:
Processing an input to produce an output (In terms of
ANN: Compute the output function of a given input)
Evaluate:
Evaluating this output by comparing the actual output
with the expected output.
Adjust:
Adjust the weights.

1. Supervised Training.
 Inputs and the outputs are provided by user
 Compares resulting outputs w.r.t. desired outputs
 Errors are back propagated, causing the system to adjust the weights
which control the network.
2. Unsupervised, or Adaptive Training.
 Inputs dataset but no desired outputs for comparison
 System itself must decide what features will use to group the input data
 Present time, unsupervised learning is not well understood
CHARACTERISTICS TRADITIONAL COMPUTING
(including Expert Systems)
ARTIFICIAL NEURAL
NETWORKS
Processing style
Functions
Sequential Logically (left brained) via
Rules Concepts
Calculations
Parallel Gestault (right brained)
via Images Pictures Controls
Learning Method
Applications
by rules (didactically) Accounting
word processing math inventory
digital communications
by example (Socratically) Sensor
processing speech recognition
pattern recognition text recognition
ANN Training

 AI takes decision to generate true or false output
(Mathematical logic/ Propositional Logic-PL)
 AI takes decisions with prediction
1. Predicated logic / First order predicate logic (FOL)
2. SET theory
 AI takes decision to be or not to be
1. Resolution
2. FOL to CNF
 AI searches data for self evolving/training(Complete Data Structure)
AI systems dependencies
Blind Search (UN Informed)
1. BFS
2. DFS
3. DLS
4. Depth limited search
5. Interactive Deeping Search
6. Bi Directional search
Heuristic Search (Informed)
1. Best First search
2. A*
3. Greedy Search

 1. Heuristics
Generic heuristics are Ant Colony Optimization2 and genetic algorithms3. The
first is based on how simple ants are able to work together to solve complex
problems; the latter is based on the principle of survival of the fittest.
 2. Support Vector Machines
SVM classification models can also be found in image recognition, e.g. face
recognition, or when handwriting is converted to text.
 3. Artificial Neural Networks
For image recognition purposes, typically Convolutional networks are used, in
which only groups of neurons from one layer are connected to groups of
neurons in the next layer. For speech recognition purposes, typically Recurrent
networks are used, that allow for loops from neurons in a later layer back to
an earlier layer.
Non-AI & AI Techniques,

 4. Markov Decision Process
Based on the probabilities and rewards a policy (function) can be made using
the initial and final state. inventory planning problem - a stock keeper or
manager has to decide how many units have to be ordered each week. The
inventory planning can be modeled as an MDP, where the states can be
considered as positive inventory and shortages.
 5. Natural Language Processing
Analysing the grammar of the text and the way the words are arranged, so that
the relationship between the words is clear. The Part-of-Speech tag from the
lexical analysis is used and then grouped into small phrases, which in turn can
also be combined with other phrases or words to make a slightly longer phrase.
This is repeated until the goal is reached: every word in the sentence has been
used. The rules of how the words can be grouped are called the grammar and
can take a form like this: D+N = NP, which reads: a Determiner + Noun = Noun
Phrase. The final result is depicted in the figure.

 The techniques used within the domain of Artificial
Intelligence are actually just advanced forms of statistical
and mathematical models. All these models cleverly put
together provide us with tools to compute tasks that were
previously thought to be reserved for humans. In
subsequent blogs we will dive deeper into business
applications, some associated technology trends, and the
top 5 risks and concerns.

 What is a knowledge-based system?
A system which is built around a knowledge base. i.e. a
collection of knowledge, taken from a human, and stored in
such a way that the system can reason with it.
 What is knowledge?
Knowledge is the sort of information that people use to solve
problems.
Knowledge includes: facts, concepts, procedures, models,
heuristics, examples.
Knowledge may be: specific or general, exact or fuzzy,
procedural or declarative
Knowledge Base Systems

 The task that an expert system performs will generally be
regarded as difficult.
 An expert system almost always operates in a rather
narrow field of knowledge. The field of knowledge is
called the knowledge domain of the system.
 There are many fields where expert systems can usefully
be built.
 There are many fields where they can’t.
 Note also that an expert can usually explain and justify
his/her decisions.
Expert Systems

 Developing an expert system usually costs a great deal of
time & money
 Historically, there has been a high failure rate in E.S.
projects
 The project may well fail during development - most
likely during the “knowledge acquisition” phase.
 The development may succeed, but the organisation may
fail to accept and use the finished system.
Disadvantages of Expert Systems

 Introduction
Different searches that can be used to explore the search space in order to find a
solution. Before an AI problem can be solved it must be represented as a state space.
The state space is then searched to find a solution to the problem. A state space
essentially consists of a set of nodes representing each state of the problem, arcs
between nodes representing the legal moves from one state to another, an initial
state and a goal state. Each state space takes the form of a tree or a graph. Factors
that determine which search algorithm or technique will be used include the type of
the problem and the how the problem can be represented. Search
 Techniques that will be examined in the course include:
• Depth First Search
• Depth First Search with Iterative Deepening
• Breadth First Search
• Best First Search
• Hill Climbing
• Branch and Bound Techniques
• A* Algorithm
State Space Search

Classic AI Problems
Traveling Salesman
Towers of Hanoi
8-Puzzle
State Space Search

The production system is a model of computation that can
be applied to implement search algorithms and model
human problem solving. Such problem solving knowledge
can be packed up in the form of little quanta called
productions. A production is a rule consisting of a situation
recognition part and an action part. A production is a
situation-action pair in which the left side is a list of things
to watch for and the right side is a list of things to do so.
When productions are used in deductive systems, the
situation that trigger productions are specified combination
of facts. The actions are restricted to being assertion of
new facts deduced directly from the triggering combination.
Production systems may be called premise conclusion pairs
rather than situation action pair..
Production Systems

A production system consists of following components.
(a ) A set of production rules, which are of the form A®B. Each rule consists of left
hand side constituent that represent the current problem state and a right hand side
that represent an output state. A rule is applicable if its left hand side matches with
the current problem state.
(b) A database, which contains all the appropriate information for the particular
task. Some part of the database may be permanent while some part of this may
pertain only to the solution of the current problem.
(c) A control strategy that specifies order in which the rules will be compared to
the database of rules and a way of resolving the conflicts that arise when several
rules match simultaneously.
(d) A rule applier, which checks the capability of rule by matching the content state
with the left hand
side of the rule and finds the appropriate rule from database of rules.
Production Systems

The production system can be classified as monotonic, non-
monotonic, partially commutative and commutative.
Production Systems

Features of Production System
• Simplicity
• Modularity
• Modifiability
• Knowledge intensive
Disadvantages of production system
• Opacity
• Inefficiency
• Absence of learning
• Conflict resolution
Production Systems

Intelligent Agents and Environments

Simple reflex agents

Model-based reflex agents

Goal-based agents

Learning Agent
 Learning element :It is responsible for making improvements by learning
from the environment
 Critic: Learning element takes feedback from critic which describes how
well the agent is doing with respect to a fixed performance standard.
 Performance element: It is responsible for selecting external action
 Problem Generator: This component
is responsible for suggesting actions
that will lead to new and informative
experiences.

Rationality is nothing but status of being reasonable,
sensible, and having good sense of judgment. Rationality is
concerned with expected actions and results depending
upon what the agent has perceived. Performing actions with
the aim of obtaining useful information is an important part
of rationality.
The rationality of the agent is measured by its performance
measure, the prior knowledge it has, the environment it
can perceive and actions it can perform.
Concept of rationality

A rational agent needs to be designed, keeping in mind the
type of environment it will be used in. Below are the types:
• Fully observable and partially observable
• Deterministic and Stochastic
• Static and Dynamic
• Discrete and Continuous
• Single agent and Multi-agent
• Rational agents or Problem-solving agents in AI mostly
used these search strategies or algorithms to solve a
specific problem and provide the best result. Problem-
solving agents are the goal-based agents and use atomic
representation.

Problem-solving agents
Goal Formulation-Set of one or more (desirable) world
states.(eg.Checkmate in Chess)
Problem Formulation-What actions and states to consider
given a goal and an initial state
Search for solution-Given the problem, search for a solution--
a sequence of actions to achieve the goal starting from initial
state
Execution of the solution

Goal Formulation-
Specify the objectives to be achieved
• goal - a set of desirable world states in which the
objectives have been achieved
• current / initial situation - starting point for the goal
formulation
• actions - cause transitions between world states

Problem Formulation
Actions and states to consider
states - possible world states
accessibility - the agent can determine via its sensors
in which state it is
consequences of actions - the agent knows the results
of its actions
levels - problems and actions can be specified at
various levels
constraints - conditions that influence the problem-
solving process
performance - measures to be applied
costs - utilization of resources

Problem Formulation
Problem Types
Not all problems are created equal
• Single-state problem
• Multiple-state problem
• Contingency problem
• Exploration problem

Course Work
(Searching Planning )

Partial Order Planning
Self Repairing Explorers
Monitors
Command dispatch
Fault protection
Attitude control
Mission Goal Scenario
Self-commanding
Self-diagnosing
Self-repairing
RECOVERY
Commanded at:
• Mission level
• Engineering level

Planning with Atomic Time
• Operator-based planning as search
• Declarative encoding of states and operators
• Partial order planning
• Planning problem
• Partial order planning algorithm

Operator-based Planning Problem
 Input
 Set of world states
 Action operators
 Fn: world-stateworld-state
 Initial state of world
 Goal
 partial state
(set of world states)
 Output
 Sequence of actions
 What assumptions are
implied?
 Atomic time.
 Agent is omniscient
(no sensing necessary).
 Agent is sole cause of
change.
 Actions have deterministic
effects.
 No indirect effects.
 STRIPS Assumptions
a
a
a
north11 north12
W0 W2W1

Planning with Atomic Time
• Operator-based planning as search
• Declarative encoding of state and operators
• Partial order planning
• Planning problem
• Partial order planning algorithm
Plan from goals, back to initial state
Search through partial plans
Representation:
• Operators given in declarative representation, rather than black box
functions.
• Plans represent only relevant commitments
(e.g., relevant ordering of operators, not total ordering)

POP(<A,O,L>, agenda, actions)
• <A,O,L>, A partial plan to expand
• Agenda: A queue of open conditions still to be satisfied: <p,
aneed >
• Actions: A set of actions that may be introduced to meet
needs.
• aadd: an action that produces the needed condition p for
aneed
• Athreat : an action that might threaten a causal link from
aproducer to aconsumer

POP(<A,O,L>, agenda, actions)
1. Termination: If agenda is empty, return plan <A,O,L>.
2. Goal Selection: select and remove open condition <p, aneed >
from agenda.
3. Action Selection: Choose new or existing action aadd that can
precede aneed and whose effects include p.
Link and order actions.
4. Update Agenda: If aadd is new, add its preconditions to agenda.
5. Threat Detection: For every action athreat that might threaten
some causal link from aproduce to aconsume, choose a consistent
ordering:
a) Demotion: Add athreat < aproduce
b) Promotion: Add aconsume < athreat
6. Recurse: on modified plan and agenda

Course Work
(Knowledge Representation)

Knowledge based agents, Wumpus world, Propositional Logic: Representation,
Inference, Reasoning Patterns, Resolution, First order Logic: Representation,
Inference, Reasoning Patterns, Resolution, Forward and Backward Chaining. Basics
of PROLOG: Representation, Structure, Backtracking, Expert System.

Logical Representations
● They are mathematically precise, thus we can analyze their limitations, their
properties, the complexity of inference etc.
● They are formal languages, thus computer programs can manipulate sentences
in the language.
● They come with both a formal syntax and a formal semantics.
● Typically, have well developed proof theories: formal procedures for reasoning
(achieved by manipulating sentences).

Introduction to Prolog
What is Prolog? (continued)
• traditional programming languages are said to be procedural
• procedural programmer must specify in detail how to solve a
problem:
• mix ingredients;
• beat until smooth;
• bake for 20 minutes in a moderate oven;
• remove tin from oven;
• put on bench;
• close oven;
• turn off oven;
• in purely declarative languages, the programmer only states what
the problem is and leaves the rest to the language system
• We'll see specific, simple examples of cases where Prolog fits
really well shortly

Applications of Prolog
• intelligent data base retrieval
• natural language understanding
• expert systems
• specification language
• machine learning
• robot planning
• automated reasoning
• problem solving

• Backtracking in Prolog
• Who does Codd teach?
?- lectures(codd, Course), studies(Student, Course).
Course = 9311 Student = jack ; Course = 9314 Student = jill ; Course =
9314 Student = henry ;
• Prolog solves this problem by proceeding left to right and
then backtracking.
• When given the initial query, Prolog starts by trying to solve
lectures(codd, Course)
• There are six lectures clauses, but only two have codd as their first
argument.
• Prolog uses the first clause that refers to codd: lectures(codd, 9311).
• With Course = 9311, it tries to satisfy the next goal, studies(Student,
9311).
• It finds the fact studies(jack, 9311). and hence the first solution:
(Course = 9311, Student = jack)

Course Work
(Uncertainty)

Uncertainty
Non Monotonic Reasoning, Logics for Non Monotonic Reasoning, Forward rules and
Backward rules, Justification based Truth Maintenance Systems, Semantic Nets
Statistical Reasoning, Probability and Bayes’ theorem, Bayesian Network, Markov
Networks, Hidden Markov Model, Basis of Utility Theory, Utility Functions.

Probability and Bayes’ theorem,
Bayesian Network
Probability is numerical measure of the
likelihood of the occurrence of an
event.
Questions:
• what is a good general size for artifact samples?
• what proportion of populations of interest should we be
attempting to sample?
• how do we evaluate the absence of an artifact type in our
collections?

Bayesian Network
“frequentist” approach
probability should be assessed in purely objective
terms
no room for subjectivity on the part of individual
researchers
knowledge about probabilities comes from the
relative frequency of a large number of trials
this is a good model for coin tossing
not so useful for archaeology, where many of the
events that interest us are unique…

Bayesian approach
Bayes Theorem
Thomas Bayes
18th century English clergyman
concerned with integrating “prior knowledge” into
calculations of probability
problematic for frequentists
prior knowledge = bias, subjectivity…
Bayesian Network

Basic concepts
probability of event = p
0 <= p <= 1
0 = certain non-occurrence
1 = certain occurrence
.5 = even odds
.1 = 1 chance out of 10
Bayesian Network

Basic concepts
0 <= p <= 1
.5 = even odds
if A and B are mutually exclusive events:
P(A or B) = P(A) + P(B)
ex., die roll: P(1 or 6) = 1/6 + 1/6 = .33
possibility set:
sum of all possible outcomes
~A = anything other than A
P(A or ~A) = P(A) + P(~A) = 1
Bayesian Network

Basic concepts
0 <= p <= 1
.5 = even odds
if A and B are mutually exclusive
events:
P(A or B) = P(A) + P(B)
ex., die roll: P(1 or 6) = 1/6
+ 1/6 = .33
Bayesian Network
Basic concepts
possibility set:
sum of all possible
outcomes
~A = anything other than A
P(A or ~A) = P(A) + P(~A) = 1
discrete vs. continuous
probabilities
discrete
finite number of outcomes
continuous
outcomes vary along continuous
scale

Discrete probabilities
Bayesian Network
Continuous probabilities

Independent events
one event has no influence on the outcome of another event
if events A & B are independent
then P(A&B) = P(A)*P(B)
if P(A&B) = P(A)*P(B)
then events A & B are independent
coin flipping
if P(H) = P(T) = .5 then
P(HTHTH) = P(HHHHH) =
.5*.5*.5*.5*.5 = .55 = .03
if you are flipping a coin and it has already come up heads 6 times in a row,
what are the odds of an 7th head? =.5
note that P(10H) < > P(4H,6T)
lots of ways to achieve the 2nd result (therefore much more probable)
Bayesian Network

1. Mutually exclusive events are not independent
2. Rather, the most dependent kinds of events
• if not heads, then tails
• joint probability of 2 mutually exclusive events is 0
• P(A&B)=0
Conditional probability
concern the odds of one event occurring, given that another event has
occurred
P(A|B)=Prob of A, given B
P(B|A) = P(A&B)/P(A)
if A and B are independent, then
P(B|A) = P(A)*P(B)/P(A)
P(B|A) = P(B)
Bayesian Network

Bayes Theorem
Can be derived from the basic equation for conditional probabilities
Bayesian Network
     
       BAPBPBAPBP
BAPBP
ABP
|~~|
|
|



THANK YOU
Image Source
searchenterpriseai.techtarget.com
wikipedia

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