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Workshop on Artificial
Intelligence -
Introduction
Technozion 2018
Subhendu Dey
Technozion 2018 | Workshop on Artificial Intelligence 2
 What is meant by AI software
 The science behind the engineering
 How can we infuse AI in industry solution
 Some of the typical Industry use cases
 Some leading AI tools
Content
Technozion 2018 | Workshop on Artificial Intelligence 3
What is Artificially Intelligent Software
 A branch of computer science dealing with the simulation of intelligent behavior in
computers.
 The capability of a machine to imitate intelligent human behavior.
 Artificial intelligence (AI), the ability of a digital computer or computer-controlled robot to
perform tasks commonly associated with intelligent beings. The term is frequently applied
to the project of developing systems endowed with the intellectual processes characteristic
of humans, such as the ability to reason, discover meaning, generalize, or learn from
past experience.
 By AI we mean anything that makes machines act more intelligently. Our work includes
basic and applied research in machine learning, deep question answering, search and
planning, knowledge representation, and cognitive architectures.
Technozion 2018 | Workshop on Artificial Intelligence 4
 Artificial Intelligence (AI) is the specialized branch of computer science that
helps develop software systems endowed with the intellectual characteristic of
humans, such as the ability to understand and extract meaning from
unstructured data, reason, generalize, and/or learn from past experience.
Often AI enabled software uses foundational technologies like natural
language processing, computer vision, machine/deep learning, robotics
and others to provide manifestation of intellectual characteristics in the form of
deep question answering, search and planning, knowledge
representation, process automation and decisioning.
 AI Characteristics
 The Science behind
 Manifestation
What is Artificially Intelligent Software  contd.
Technozion 2018 | Workshop on Artificial Intelligence 5
 Ability to extract meaning out of source data
 Connect to disparate sources and ability to read data
in varied mode, volume and frequency
 Text analytics to understand unstructured data
 Identify named entities and relationship, through
deterministic rules, machine learned models
 Related the same to the enterprise ontology
 Image classification and annotation
 Classify image
 Identify parts of image
 Draw correlation between parts of image
 Add correlation within enterprise knowledge
Ability to extract, understand and relate
NITW is organizing Technozion this year in a grand
way
NITW = NNP
NITW is of type Engineering Institute
Technozion = NNP
Technozion is of type Technical Fest
ORG
INSTITUTE
ENGINEERING_INSTITUTE
Name = NITW
Syn = NIT Warangal
EVENT
PRIVATE_EVENT
COLLEGE_EVENT
TECHNICAL_FEST
Name = Technozion
Trained model
of POS
Tagging and
NER
detection
Organize (year = 2018, qualifier = grand)
Technozion 2018 | Workshop on Artificial Intelligence 6
 Reasoning is a technique that allows to discover the unknown
 Instead of coding static rules, discover correlations/patterns through statistical means and act
 Provides more level of abstraction
 More resilient to changes
 Examples:
 Geospatial: health risk associated to a place (say, breakout of an epidemic) can be associated to
location of an individual
 Temporal: risk of fraud can be associated to the transactions in a timeframe
 Collaborative:
 Similarity of customers could influence similar buying pattern
Ability to reason
Technozion 2018 | Workshop on Artificial Intelligence 7
 Learning allows AI solution to improve over time
 Assisted learning: the most common form of learning that happens today, where a machine is
presented with defined inputs and outputs in a sample set of data and then reverse engineers
the algorithm in between.
 It is important to design for a feedback loop for such learning to work effectively
 Example:
 Classification algorithms
 Relevancy ranking
 Unassisted learning: when a machine is presented with a set of documents or data and then
figures things out on its own. This can be done with even a very small number files.
 Reinforcement learning: when a machine is presented with a set goal and then cut loose to do
what it needs to do  including adjustments and rework  until it finds ways to most effectively
reach that goal.
Ability to learn
Technozion 2018 | Workshop on Artificial Intelligence 8
 Narrow / Weak AI - is an application of artificial intelligence technologies to enable a high
functioning system that replicates and perhaps surpasses human intelligence for a dedicated
purpose.
 Robotic Process Automation (RPA)
 Voice based mobile assistant (play music, book appointment, set alarm etc.)
 Domain specific advisors (Q&A / dialogue, ranked information retrieval)
 Data mining, pattern recognition and help to take decision
 Artificial General Intelligence / Strong AI - is the representation of generalized human
cognitive abilities in software so that, faced with an unfamiliar task, the AI system could find a
solution. An AGI system could perform any task that a human is capable of.
 On contrary to the AI of today, where huge amount of training data is needed to take the software
through a learning process; it would try by itself and fail - thereby generate its own data to learn
until it can achieve desired result.
Types of Artificial Intelligence
Technozion 2018 | Workshop on Artificial Intelligence 9
 What is meant by AI software
 The science behind the engineering
 How can we infuse AI in industry solution
 Some of the typical Industry use cases
 Some leading AI tools
Content
Technozion 2018 | Workshop on Artificial Intelligence 10
 Natural Language Processing
 Regular expression based deterministic rules
 N-gram for calculate probabilistic language model
 Text classification
 Information extraction
 Information retrieval
 Computer Vision
 Machine Learning
 Prediction through regression
 Classification
 Deep learning
 Automation (RPA)
 Handling of Big Data
 Cloud computing
Major scientific elements behind AI
Technozion 2018 | Workshop on Artificial Intelligence 11
 Accuracy = (TP + TN) / {whole set}
 Accuracy will not work well where correct set is
much smaller than not correct set
 Precision (P) = % of selected items that are
correct. i.e. TP / (TP + FP)
 Recall (R) = % of correct items that are selected,
i.e. TP / (TP + FN)
 A combined measure that assesses the precision
and recall tradeoff is F measure, where F is the
weighted harmonic mean.
How to measure success
Correct Not correct
Selected TP FP
Not
selected
FN FP
Technozion 2018 | Workshop on Artificial Intelligence 12
 What is meant by AI software
 The science behind the engineering
 How can we infuse AI in industry solution
 Some of the typical Industry use cases
 Some leading AI tools
Content
Technozion 2018 | Workshop on Artificial Intelligence 13
AI for Industry, as of today
Streamlining, standardizing
& improving decision
processes
 Implementing preventive & more targeted actions that
is less subject to human bias
 Predictions on the basis on incomplete information
 Detect individual data records or patterns
Evidences
not mapped
to response
Yielding insights
unattainable by humans
 Feature recognition, identify objects, actions or
characteristics, describe contents
 Enables the collection, processing and analysis of
image data from various sources such as satellite,
aerial images and digital video
Time-
consuming
search
Operational efficiency
 Finds insights and connections, understands the vast
amounts of information available
 Vast amount of qualitative and quantitate data can be
crawled, summarizing the required need
Inaccurate
and slow
analysis
Scaling human expertise
cost-effectively
 Helps governments / orgs to understand public / user
sentiments and preferences better, augmenting human
capacities to formulate effective decisions
 Complex citizen engagement scenarios with different
past histories can be analyzed
Unable to
interact in
natural way
Challenges Example of how Cognitive helps today Value Client Impact
Better insights
Digitize and
streamline
processes
Deploy
disruptive
business
models
Re-invent user
engagement
pattern
Today, AI and associated technologies has tremendous potential to drive revenue and cost
Technozion 2018 | Workshop on Artificial Intelligence 14
 What is meant by AI software
 The science behind the engineering
 How can we infuse AI in industry solution
 Some of the typical Industry use cases
 Some leading AI tools
Content
Technozion 2018 | Workshop on Artificial Intelligence 15
 Accelerate search and discovery - spend less time looking for the information you need and more
time acting on it.
 Enrich interaction - reduce response times, increase the number of transactions, and make every
interaction meaningful and productive through personalized yet consistent experience.
 Anticipate and preempt disruption - constantly monitor the condition of systems that power business
to ensure bigger problems dont disrupt work.
 Recommend with confidence - Teach systems about parameters and nuances to ensure they take
every important factor into account when you make a decision.
 Scale expertise and learning - combining every employees expertise with industrys latest learning,
each of you knows as much as all of you.
 Detect liabilities and mitigate risk - Train systems to understand and keep up with constantly
changing regulations and privacy obligations.
Applicability of AI in Industry
Technozion 2018 | Workshop on Artificial Intelligence 16
How can you contribute
 Domain Perspective
 Domain consulting for AI opportunities
 Risk assessment and Control
 Business process consulting
 Product innovation and modeling
 IT/System Perspective
 Solution / IT System Architecture and Technology Consulting
 Q&A, Dialogue for virtual agents
 Enterprise Search and exploratory analysis
 Human computer interaction
 Cognitive project management, testing
 API / IoT device Integration
 Data Science Perspective
 NLP Pipeline
 Neural Networks / Deep Learning
 Advanced Analytics
 Optimization
 Robotics
Typically if you are from
mathematics / statistics
background. Or the world
of math/stat excites you.
However, often there is
also domain specific
knowledge embedded.
Typically if you are
software geek and
making of an
interconnected, intelligent
and instrumented world
through real life project
excites you
In case you have a strong
domain of interest (e.g.
banking, retail etc.).
Technozion 2018 | Workshop on Artificial Intelligence 17
 What is meant by AI software
 The science behind the engineering
 How can we infuse AI in industry solution
 Some of the typical Industry use cases
 Some leading AI tools
Content
Technozion 2018 | Workshop on Artificial Intelligence 18
IBM Tools towards AI  APIs & Services
Category Name Description
AI assistant Watson Assistant
Creates a conversational AI solution where user can interact with the system in natural language.
The graphical tool helps non-technical domain SMEs to contribute effectively.
Knowledge
Watson Discovery
Stores and indexes the unstructured content to support the ranked retrieval based on relevancy
ranking against query in natural language.
Natural Language Understanding
Applies text analytics to extract meaning (entities, concepts, relationship etc.) of unstructured textual
content and relate the same to enterprise ontology.
Discovery News
Provides aggregated analysis result on news along with evidences. Helps to stay alert for unwanted
business functions.
Knowledge Studio
Allows the domain SMEs annotate the documents as per custom type-system (ontology), apply text
analytics rules and generate custom machine learned model to be used by Natural Language
Understanding or Watson Discovery.
Language
Language Translator
Applies neural machine translation to translate with ease and at a great speed. Provision are there to
feed in users own custom model.
Natural Language Classifier
Provides provision to train a custom model to understand the intent behind supplied text and return
a corresponding classification, along with a confidence score.
Empathy
Personality Insight
Uses linguistic analytics to infer individuals' personality characteristics, including Big Five, Needs, and
Values, from digital communications such as email, blogs, tweets, and forum posts
Tone Analyzer
Helps to support conversations so as to respond to customers appropriately and at scale. Identifies
if customers are satisfied or frustrated, and if agents are polite and sympathetic.
Vision Visual Recognition Allows to train custom models and identify / classify images.
Speech
Speech to text Converts speech to texts.
Text to speech Converts texts to audio output.
Technozion 2018 | Workshop on Artificial Intelligence 19
IBM Tools towards AI  Data Life Cycle Management
Category Name Description
Data (Life
cycle
Management)
Watson Studio
The tool to build and train AI models, and prepare and analyze data  all in one integrated
environment.
Watson Knowledge Catalog
Helps in curating structured and unstructured data. Do data profiling, classification to
prepare, shape, join data as per requirement. Also, provides a collaboration platform for a
team to work on the data.
Watson Machine Learning
Build and monitor machine learning and deep learning models through easy visualization.
Integrates well with Watson Studio and Watson Knowledge Catalog.
Technozion 2018 | Workshop on Artificial Intelligence 20
Typical architecture using Watson APIs & services
DISCOVER
Y
NLUPERSONALIT
Y INSIGHT
WATSON
ASSISTANT
TONE
ANALYZE
R
VISUAL
RECOGNITIO
N
TEXT TO
SPEECH
SPEECH TO
TEXT
LANGUAGE
TRANSLATO
R
NLC DOCUMENT
CONVERSIO
N
WATSON
KNOWLEDGE
STUDIO
IBMcloud
environment
Developmen
t service
Runtime Watson
Services
Client
environment
1. Domain SMEs train
Watson through browser
based IDE
2. Develops Machine
learned model and push
the same to Watson
tools and/or services
3. Depending upon
performance train again.> >
Watson Developer Cloud SDK
Finance HR IT Corp
Affairs
Others
Enterprise Applications
access Watson Services
(SaaS) through SSL using
specific authentication
credentials
There are various utility
services that are useful for
building cognitive functions
within enterprise processes.
There are other analytics (e.g.
data science experience) and
infrastructure services (e.g.
secured gateway) which are
not shown here, but could be
useful.
Bulk data movement SDK
On-premise text analytics,
data mining, and other
machine learning capabilities
as needed.
Technozion 2018 | Workshop on Artificial Intelligence 21
Q&A

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Workshop on AI - introductory lecture

  • 1. Workshop on Artificial Intelligence - Introduction Technozion 2018 Subhendu Dey
  • 2. Technozion 2018 | Workshop on Artificial Intelligence 2 What is meant by AI software The science behind the engineering How can we infuse AI in industry solution Some of the typical Industry use cases Some leading AI tools Content
  • 3. Technozion 2018 | Workshop on Artificial Intelligence 3 What is Artificially Intelligent Software A branch of computer science dealing with the simulation of intelligent behavior in computers. The capability of a machine to imitate intelligent human behavior. Artificial intelligence (AI), the ability of a digital computer or computer-controlled robot to perform tasks commonly associated with intelligent beings. The term is frequently applied to the project of developing systems endowed with the intellectual processes characteristic of humans, such as the ability to reason, discover meaning, generalize, or learn from past experience. By AI we mean anything that makes machines act more intelligently. Our work includes basic and applied research in machine learning, deep question answering, search and planning, knowledge representation, and cognitive architectures.
  • 4. Technozion 2018 | Workshop on Artificial Intelligence 4 Artificial Intelligence (AI) is the specialized branch of computer science that helps develop software systems endowed with the intellectual characteristic of humans, such as the ability to understand and extract meaning from unstructured data, reason, generalize, and/or learn from past experience. Often AI enabled software uses foundational technologies like natural language processing, computer vision, machine/deep learning, robotics and others to provide manifestation of intellectual characteristics in the form of deep question answering, search and planning, knowledge representation, process automation and decisioning. AI Characteristics The Science behind Manifestation What is Artificially Intelligent Software contd.
  • 5. Technozion 2018 | Workshop on Artificial Intelligence 5 Ability to extract meaning out of source data Connect to disparate sources and ability to read data in varied mode, volume and frequency Text analytics to understand unstructured data Identify named entities and relationship, through deterministic rules, machine learned models Related the same to the enterprise ontology Image classification and annotation Classify image Identify parts of image Draw correlation between parts of image Add correlation within enterprise knowledge Ability to extract, understand and relate NITW is organizing Technozion this year in a grand way NITW = NNP NITW is of type Engineering Institute Technozion = NNP Technozion is of type Technical Fest ORG INSTITUTE ENGINEERING_INSTITUTE Name = NITW Syn = NIT Warangal EVENT PRIVATE_EVENT COLLEGE_EVENT TECHNICAL_FEST Name = Technozion Trained model of POS Tagging and NER detection Organize (year = 2018, qualifier = grand)
  • 6. Technozion 2018 | Workshop on Artificial Intelligence 6 Reasoning is a technique that allows to discover the unknown Instead of coding static rules, discover correlations/patterns through statistical means and act Provides more level of abstraction More resilient to changes Examples: Geospatial: health risk associated to a place (say, breakout of an epidemic) can be associated to location of an individual Temporal: risk of fraud can be associated to the transactions in a timeframe Collaborative: Similarity of customers could influence similar buying pattern Ability to reason
  • 7. Technozion 2018 | Workshop on Artificial Intelligence 7 Learning allows AI solution to improve over time Assisted learning: the most common form of learning that happens today, where a machine is presented with defined inputs and outputs in a sample set of data and then reverse engineers the algorithm in between. It is important to design for a feedback loop for such learning to work effectively Example: Classification algorithms Relevancy ranking Unassisted learning: when a machine is presented with a set of documents or data and then figures things out on its own. This can be done with even a very small number files. Reinforcement learning: when a machine is presented with a set goal and then cut loose to do what it needs to do including adjustments and rework until it finds ways to most effectively reach that goal. Ability to learn
  • 8. Technozion 2018 | Workshop on Artificial Intelligence 8 Narrow / Weak AI - is an application of artificial intelligence technologies to enable a high functioning system that replicates and perhaps surpasses human intelligence for a dedicated purpose. Robotic Process Automation (RPA) Voice based mobile assistant (play music, book appointment, set alarm etc.) Domain specific advisors (Q&A / dialogue, ranked information retrieval) Data mining, pattern recognition and help to take decision Artificial General Intelligence / Strong AI - is the representation of generalized human cognitive abilities in software so that, faced with an unfamiliar task, the AI system could find a solution. An AGI system could perform any task that a human is capable of. On contrary to the AI of today, where huge amount of training data is needed to take the software through a learning process; it would try by itself and fail - thereby generate its own data to learn until it can achieve desired result. Types of Artificial Intelligence
  • 9. Technozion 2018 | Workshop on Artificial Intelligence 9 What is meant by AI software The science behind the engineering How can we infuse AI in industry solution Some of the typical Industry use cases Some leading AI tools Content
  • 10. Technozion 2018 | Workshop on Artificial Intelligence 10 Natural Language Processing Regular expression based deterministic rules N-gram for calculate probabilistic language model Text classification Information extraction Information retrieval Computer Vision Machine Learning Prediction through regression Classification Deep learning Automation (RPA) Handling of Big Data Cloud computing Major scientific elements behind AI
  • 11. Technozion 2018 | Workshop on Artificial Intelligence 11 Accuracy = (TP + TN) / {whole set} Accuracy will not work well where correct set is much smaller than not correct set Precision (P) = % of selected items that are correct. i.e. TP / (TP + FP) Recall (R) = % of correct items that are selected, i.e. TP / (TP + FN) A combined measure that assesses the precision and recall tradeoff is F measure, where F is the weighted harmonic mean. How to measure success Correct Not correct Selected TP FP Not selected FN FP
  • 12. Technozion 2018 | Workshop on Artificial Intelligence 12 What is meant by AI software The science behind the engineering How can we infuse AI in industry solution Some of the typical Industry use cases Some leading AI tools Content
  • 13. Technozion 2018 | Workshop on Artificial Intelligence 13 AI for Industry, as of today Streamlining, standardizing & improving decision processes Implementing preventive & more targeted actions that is less subject to human bias Predictions on the basis on incomplete information Detect individual data records or patterns Evidences not mapped to response Yielding insights unattainable by humans Feature recognition, identify objects, actions or characteristics, describe contents Enables the collection, processing and analysis of image data from various sources such as satellite, aerial images and digital video Time- consuming search Operational efficiency Finds insights and connections, understands the vast amounts of information available Vast amount of qualitative and quantitate data can be crawled, summarizing the required need Inaccurate and slow analysis Scaling human expertise cost-effectively Helps governments / orgs to understand public / user sentiments and preferences better, augmenting human capacities to formulate effective decisions Complex citizen engagement scenarios with different past histories can be analyzed Unable to interact in natural way Challenges Example of how Cognitive helps today Value Client Impact Better insights Digitize and streamline processes Deploy disruptive business models Re-invent user engagement pattern Today, AI and associated technologies has tremendous potential to drive revenue and cost
  • 14. Technozion 2018 | Workshop on Artificial Intelligence 14 What is meant by AI software The science behind the engineering How can we infuse AI in industry solution Some of the typical Industry use cases Some leading AI tools Content
  • 15. Technozion 2018 | Workshop on Artificial Intelligence 15 Accelerate search and discovery - spend less time looking for the information you need and more time acting on it. Enrich interaction - reduce response times, increase the number of transactions, and make every interaction meaningful and productive through personalized yet consistent experience. Anticipate and preempt disruption - constantly monitor the condition of systems that power business to ensure bigger problems dont disrupt work. Recommend with confidence - Teach systems about parameters and nuances to ensure they take every important factor into account when you make a decision. Scale expertise and learning - combining every employees expertise with industrys latest learning, each of you knows as much as all of you. Detect liabilities and mitigate risk - Train systems to understand and keep up with constantly changing regulations and privacy obligations. Applicability of AI in Industry
  • 16. Technozion 2018 | Workshop on Artificial Intelligence 16 How can you contribute Domain Perspective Domain consulting for AI opportunities Risk assessment and Control Business process consulting Product innovation and modeling IT/System Perspective Solution / IT System Architecture and Technology Consulting Q&A, Dialogue for virtual agents Enterprise Search and exploratory analysis Human computer interaction Cognitive project management, testing API / IoT device Integration Data Science Perspective NLP Pipeline Neural Networks / Deep Learning Advanced Analytics Optimization Robotics Typically if you are from mathematics / statistics background. Or the world of math/stat excites you. However, often there is also domain specific knowledge embedded. Typically if you are software geek and making of an interconnected, intelligent and instrumented world through real life project excites you In case you have a strong domain of interest (e.g. banking, retail etc.).
  • 17. Technozion 2018 | Workshop on Artificial Intelligence 17 What is meant by AI software The science behind the engineering How can we infuse AI in industry solution Some of the typical Industry use cases Some leading AI tools Content
  • 18. Technozion 2018 | Workshop on Artificial Intelligence 18 IBM Tools towards AI APIs & Services Category Name Description AI assistant Watson Assistant Creates a conversational AI solution where user can interact with the system in natural language. The graphical tool helps non-technical domain SMEs to contribute effectively. Knowledge Watson Discovery Stores and indexes the unstructured content to support the ranked retrieval based on relevancy ranking against query in natural language. Natural Language Understanding Applies text analytics to extract meaning (entities, concepts, relationship etc.) of unstructured textual content and relate the same to enterprise ontology. Discovery News Provides aggregated analysis result on news along with evidences. Helps to stay alert for unwanted business functions. Knowledge Studio Allows the domain SMEs annotate the documents as per custom type-system (ontology), apply text analytics rules and generate custom machine learned model to be used by Natural Language Understanding or Watson Discovery. Language Language Translator Applies neural machine translation to translate with ease and at a great speed. Provision are there to feed in users own custom model. Natural Language Classifier Provides provision to train a custom model to understand the intent behind supplied text and return a corresponding classification, along with a confidence score. Empathy Personality Insight Uses linguistic analytics to infer individuals' personality characteristics, including Big Five, Needs, and Values, from digital communications such as email, blogs, tweets, and forum posts Tone Analyzer Helps to support conversations so as to respond to customers appropriately and at scale. Identifies if customers are satisfied or frustrated, and if agents are polite and sympathetic. Vision Visual Recognition Allows to train custom models and identify / classify images. Speech Speech to text Converts speech to texts. Text to speech Converts texts to audio output.
  • 19. Technozion 2018 | Workshop on Artificial Intelligence 19 IBM Tools towards AI Data Life Cycle Management Category Name Description Data (Life cycle Management) Watson Studio The tool to build and train AI models, and prepare and analyze data all in one integrated environment. Watson Knowledge Catalog Helps in curating structured and unstructured data. Do data profiling, classification to prepare, shape, join data as per requirement. Also, provides a collaboration platform for a team to work on the data. Watson Machine Learning Build and monitor machine learning and deep learning models through easy visualization. Integrates well with Watson Studio and Watson Knowledge Catalog.
  • 20. Technozion 2018 | Workshop on Artificial Intelligence 20 Typical architecture using Watson APIs & services DISCOVER Y NLUPERSONALIT Y INSIGHT WATSON ASSISTANT TONE ANALYZE R VISUAL RECOGNITIO N TEXT TO SPEECH SPEECH TO TEXT LANGUAGE TRANSLATO R NLC DOCUMENT CONVERSIO N WATSON KNOWLEDGE STUDIO IBMcloud environment Developmen t service Runtime Watson Services Client environment 1. Domain SMEs train Watson through browser based IDE 2. Develops Machine learned model and push the same to Watson tools and/or services 3. Depending upon performance train again.> > Watson Developer Cloud SDK Finance HR IT Corp Affairs Others Enterprise Applications access Watson Services (SaaS) through SSL using specific authentication credentials There are various utility services that are useful for building cognitive functions within enterprise processes. There are other analytics (e.g. data science experience) and infrastructure services (e.g. secured gateway) which are not shown here, but could be useful. Bulk data movement SDK On-premise text analytics, data mining, and other machine learning capabilities as needed.
  • 21. Technozion 2018 | Workshop on Artificial Intelligence 21 Q&A

Editor's Notes

  • #7: There are four basic forms of logic: Deductive - inference leads fro true propositions to true propositions. In deduction. Inductive - In induction we can infer from cases to generalizations, which get conformation from premises. abductive - In abduction one can infer causes from effect, thus going backward from "conclusions to premisses. Abduction is also called diagnosis. metaphoric inference.. In metaphoric inference 油we transfer knowledge from 油one area to another area, say we study economy in terms of evolution theory.油
  • #11: P(A|B) = P(A,B) / P(B) chain rule P(A,B) = P(B) P(A|B) P(A,B,C) = P(A) P(B|A) P(C|A,B)