- A Bayesian network is a graphical model that depicts probabilistic relationships among variables. It represents a joint probability distribution over variables in a directed acyclic graph with conditional probability tables.
- A Bayesian network consists of a directed acyclic graph whose nodes represent variables and edges represent probabilistic dependencies, along with conditional probability distributions that quantify the relationships.
- Inference using a Bayesian network allows computing probabilities like P(X|evidence) by taking into account the graph structure and probability tables.
In this presentation is given an introduction to Bayesian networks and basic probability theory. Graphical explanation of Bayes' theorem, random variable, conditional and joint probability. Spam classifier, medical diagnosis, fault prediction. The main software for Bayesian Networks are presented.
What is the Expectation Maximization (EM) Algorithm?Kazuki Yoshida
Review of Do and Batzoglou. "What is the expectation maximization algorith?" Nat. Biotechnol. 2008;26:897. Also covers the Data Augmentation and Stan implementation. Resources at https://github.com/kaz-yos/em_da_repo
In this presentation is given an introduction to Bayesian networks and basic probability theory. Graphical explanation of Bayes' theorem, random variable, conditional and joint probability. Spam classifier, medical diagnosis, fault prediction. The main software for Bayesian Networks are presented.
What is the Expectation Maximization (EM) Algorithm?Kazuki Yoshida
Review of Do and Batzoglou. "What is the expectation maximization algorith?" Nat. Biotechnol. 2008;26:897. Also covers the Data Augmentation and Stan implementation. Resources at https://github.com/kaz-yos/em_da_repo
Introduction to Statistical Machine Learningmahutte
This course provides a broad introduction to the methods and practice
of statistical machine learning, which is concerned with the development
of algorithms and techniques that learn from observed data by
constructing stochastic models that can be used for making predictions
and decisions. Topics covered include Bayesian inference and maximum
likelihood modeling; regression, classi¯cation, density estimation,
clustering, principal component analysis; parametric, semi-parametric,
and non-parametric models; basis functions, neural networks, kernel
methods, and graphical models; deterministic and stochastic
optimization; over¯tting, regularization, and validation.
Ensemble Learning is a technique that creates multiple models and then combines them to produce improved results.
Ensemble learning usually produces more accurate solutions than a single model would.
Uncertainty & Probability
Baye's rule
Choosing Hypotheses- Maximum a posteriori
Maximum Likelihood - Baye's concept learning
Maximum Likelihood of real valued function
Bayes optimal Classifier
Joint distributions
Naive Bayes Classifier
In this tutorial, we will learn the the following topics -
+ Voting Classifiers
+ Bagging and Pasting
+ Random Patches and Random Subspaces
+ Random Forests
+ Boosting
+ Stacking
Introduction to Statistical Machine Learningmahutte
This course provides a broad introduction to the methods and practice
of statistical machine learning, which is concerned with the development
of algorithms and techniques that learn from observed data by
constructing stochastic models that can be used for making predictions
and decisions. Topics covered include Bayesian inference and maximum
likelihood modeling; regression, classi¯cation, density estimation,
clustering, principal component analysis; parametric, semi-parametric,
and non-parametric models; basis functions, neural networks, kernel
methods, and graphical models; deterministic and stochastic
optimization; over¯tting, regularization, and validation.
Ensemble Learning is a technique that creates multiple models and then combines them to produce improved results.
Ensemble learning usually produces more accurate solutions than a single model would.
Uncertainty & Probability
Baye's rule
Choosing Hypotheses- Maximum a posteriori
Maximum Likelihood - Baye's concept learning
Maximum Likelihood of real valued function
Bayes optimal Classifier
Joint distributions
Naive Bayes Classifier
In this tutorial, we will learn the the following topics -
+ Voting Classifiers
+ Bagging and Pasting
+ Random Patches and Random Subspaces
+ Random Forests
+ Boosting
+ Stacking
A Study on Comparison of Bayesian Network Structure Learning Algorithms for S...Jae-seong Yoo
A Study on Comparison of Bayesian Network Structure Learning Algorithms for Selecting Appropriate Models with BNDataGenerator in R
Reference : Jae-seong Yoo, (2014), "A Study on Comparison of Bayesian Network Structure Learning Algorithms for Selecting Appropriate Models", M.S. thesis, Department of Statistics, Korea University, Seoul.
Bayes Nets Meetup Sept 29th 2016 - Bayesian Network Modelling by Marco ScutariBayes Nets meetup London
A talk given at the Bayes Nets meetup on Sept 29th 2016 by Dr Marco Scutari from the University of Oxford. Title of the talk was Bayesian Network Modelling with examples in Genetics and Systems Biology, with case studies.
Spark with Azure HDInsight - Tampa Bay Data Science - Adnan Masood, PhDAdnan Masood
Spark is a unified framework for big data analytics. Spark provides one integrated API for use by developers, data scientists, and analysts to perform diverse tasks that would have previously required separate processing engines such as batch analytics, stream processing and statistical modeling. Spark supports a wide range of popular languages including Python, R, Scala, SQL, and Java. Spark can read from diverse data sources and scale to thousands of nodes.
In this presentation we discuss Microsoft HDInsight offering of Spark. Azure HDInsight, Microsoft’s managed Hadoop and Spark cloud service that runs the Hortonworks Data Platform. Spark for Azure HDInsight offers customers an enterprise-ready Spark solution that’s fully managed, secured, and highly available and made simpler for users with compelling and interactive experiences.
Data science with Windows Azure - A Brief IntroductionAdnan Masood
Data Science with Windows Azure is an introduction to HDInsight and Hadoop offerings from Microsoft Machine Learning and Big Data Cloud based platform. This was presented at Microsoft Data Science Group – Tampa Analytics Professionals.
Restructuring Technical Debt - A Software and System Quality ApproachAdnan Masood
Agile Software Architecture based overview of the technical debt metaphor … idea is that developers sometimes accept compromises in a system in one dimension (e.g., modularity) to meet an urgent demand in some other dimension (e.g., a deadline), and that such compromises incur a "debt": on which "interest" has to be paid and which the "principal" should be repaid at some point for the long-term health of the project. (ACM)
System Quality Attributes for Software ArchitectureAdnan Masood
Software Quality Attributes are the benchmarks that describe system’s intended behavior. These slides go through an overview of what some of these attributes are and how to evaluate them.
Web API or WCF - An Architectural ComparisonAdnan Masood
ASP.NET Web API is a framework that makes it easy to build HTTP services that reach a broad range of clients, including browsers and mobile devices. The new ASP.NET Web API is a continuation of the previous WCF Web API projection. WCF was originally created to enable SOAP-based services and other related bindings. However, for simpler RESTful or RPCish services (think clients like jQuery) ASP.NET Web API is a good choice.
In this meeting we discussed what do you need to understand as an architect to implement your service oriented architecture using WCF or ASP.NET web API. With code samples, we will elaborate on WCF Web API’s transition to ASP.NET Web API and respective constructs such as Service vs. Web API controller, Operation vs. Action, URI templates vs ASP.NET Routing, Message handlers, Formatters and Operation handlers vs Filters, model binders. WebApi offers support for modern HTTP programming model with full support for ASP.NET Routing, content negotiation and custom formatters, model binding and validation, filters, query composition, is easy to unit test and offers improved Inversion of Control (IoC) via DependencyResolver.
You will walk away with a sample set of services that run on Silverlight, Windows Forms, WPF, Windows Phone and ASP.NET.
SOLID Principles of Refactoring Presentation - Inland Empire User GroupAdnan Masood
Abstract: SOLID is a mnemonic acronym coined by Robert C. Martin (aka Uncle Bob) referring to a collection of design principles of object-oriented programming and design. By using these principles, developers are much more likely to create a system that more maintainable and extensible. SOLID can be used to remove code smells by refactoring. In this session, you will learn about the following SOLID principles with code examples demonstrating the corresponding refactoring.
S – Single Responsibility Principle – An Object should have only one reason to change.
O – Open/Closed Principle – A software entity(module, library, routine) should be closed to any modification but be open to extension
L – Liskov Substitution Principle – Derived classes should be substitutable for the base classes
I – Interface Segregation Principle – Having more fine grained interfaces over fat interfaces
D – Dependency Inversion Principle – Depending on abstractions, not concrete implementations.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
1. A B RIEF INTRODUCTION
A D N A N M A S O O D
S C I S . N O V A . E D U / ~ A D N A N
A D N A N @ N O V A . E D U
D O C T O R A L C A N D I D A T E
N O V A S O U T H E A S T E R N U N I V E R S I T Y
Bayesian Networks
2. What is a Bayesian Network?
A Bayesian network (BN) is a graphical model for
depicting probabilistic relationships among a set
of variables.
BN Encodes the conditional independence relationships between the
variables in the graph structure.
Provides a compact representation of the joint probability
distribution over the variables
A problem domain is modeled by a list of variables X1, …, Xn
Knowledge about the problem domain is represented by a joint
probability P(X1, …, Xn)
Directed links represent causal direct influences
Each node has a conditional probability table quantifying the effects
from the parents.
No directed cycles
3. Bayesian Network constitutes of..
Directed Acyclic Graph (DAG)
Set of conditional probability tables for each node in
the graph
A
B
C D
4. So BN = (DAG, CPD)
DAG: directed acyclic graph (BN’s structure)
Nodes: random variables (typically binary or discrete,
but methods also exist to handle continuous variables)
Arcs: indicate probabilistic dependencies between
nodes (lack of link signifies conditional independence)
CPD: conditional probability distribution (BN’s
parameters)
Conditional probabilities at each node, usually stored
as a table (conditional probability table, or CPT)
5. So, what is a DAG?
A
B
C D
directed acyclic graphs use
only unidirectional arrows to
show the direction of
causation
Each node in graph represents
a random variable
Follow the general graph
principles such as a node A is a
parent of another node B, if
there is an arrow from node A
to node B.
Informally, an arrow from
node X to node Y means X has
a direct influence on Y
6. Where do all these numbers come from?
There is a set of tables for each node in the network.
Each node Xi has a conditional probability distribution
P(Xi | Parents(Xi)) that quantifies the effect of the parents
on the node
The parameters are the probabilities in these conditional
probability tables (CPTs)A
B
C D
7. The infamous Burglary-Alarm Example
Burglary Earthquake
Alarm
John Calls Mary Calls
P(B)
0.001
P(E)
0.002
B E P(A)
T T 0.95
T F 0.94
F T 0.29
F F 0.001
A P(J)
T 0.90
F 0.05
A P(M)
T 0.70
F 0.01
8. Cont..calculations on the belief network
Using the network in the example, suppose you want
to calculate:
P(A = true, B = true, C = true, D = true)
= P(A = true) * P(B = true | A = true) *
P(C = true | B = true) P( D = true | B = true)
= (0.4)*(0.3)*(0.1)*(0.95)
These numbers are from the
conditional probability tables
This is from the
graph structure
9. So let’s see how you can calculate P(John called)
if there was a burglary?
Inference from effect to cause; Given a burglary,
what is P(J|B)?
Can also calculate P (M|B) = 0.67
85.0
)05.0)(06.0()9.0)(94.0()|(
)05.0)(()9.0)(()|(
94.0)|(
)95.0)(002.0(1)94.0)(998.0(1)|(
)95.0)(()()94.0)(()()|(
?)|(
BJP
APAPBJP
BAP
BAP
EPBPEPBPBAP
BJP
10. Why Bayesian Networks?
Bayesian Probability represents the degree of belief
in that event while Classical Probability (or frequents
approach) deals with true or physical probability of
an event
• Bayesian Network
• Handling of Incomplete Data Sets
• Learning about Causal Networks
• Facilitating the combination of domain knowledge and data
• Efficient and principled approach for avoiding the over fitting
of data
11. What are Belief Computations?
Belief Revision
Model explanatory/diagnostic tasks
Given evidence, what is the most likely hypothesis to explain the
evidence?
Also called abductive reasoning
Example: Given some evidence variables, find the state of all other
variables that maximize the probability. E.g.: We know John Calls,
but not Mary. What is the most likely state? Only consider
assignments where J=T and M=F, and maximize.
Belief Updating
Queries
Given evidence, what is the probability of some other random
variable occurring?
12. What is conditional independence?
The Markov condition says that given its parents (P1, P2), a
node (X) is conditionally independent of its non-descendants
(ND1, ND2)
X
P1 P2
C1 C2
ND2ND1
13. What is D-Separation?
A variable a is d-separated from b by a set of variables
E if there does not exist a d-connecting path between a
and b such that
None of its linear or diverging nodes is in E
For each of the converging nodes, either it or one of its
descendants is in E.
Intuition:
The influence between a and b must propagate through a d-
connecting path
If a and b are d-separated by E, then they are
conditionally independent of each other given E:
P(a, b | E) = P(a | E) x P(b | E)
14. Construction of a Belief Network
Procedure for constructing BN:
Choose a set of variables describing the application
domain
Choose an ordering of variables
Start with empty network and add variables to the
network one by one according to the ordering
To add i-th variable Xi:
Determine pa(Xi) of variables already in the network (X1, …, Xi – 1)
such that
P(Xi | X1, …, Xi – 1) = P(Xi | pa(Xi))
(domain knowledge is needed there)
Draw an arc from each variable in pa(Xi) to Xi
15. What is Inference in BN?
Using a Bayesian network to compute probabilities is
called inference
In general, inference involves queries of the form:
P( X | E )
where X is the query variable and E is the evidence
variable.
16. Representing causality in Bayesian Networks
A causal Bayesian network, or simply causal
networks, is a Bayesian network whose arcs are
interpreted as indicating cause-effect relationships
Build a causal network:
Choose a set of variables that describes the domain
Draw an arc to a variable from each of its direct causes
(Domain knowledge required)
Visit Africa
Tuberculosis
X-Ray
Smoking
Lung Cancer
Bronchitis
Dyspnea
Tuberculosis or
Lung Cancer
17. Limitations of Bayesian Networks
• Typically require initial knowledge of many
probabilities…quality and extent of prior knowledge
play an important role
• Significant computational cost(NP hard task)
• Unanticipated probability of an event is not taken
care of.
18. Summary
Bayesian methods provide sound theory and framework for
implementation of classifiers
Bayesian networks a natural way to represent conditional independence
information. Qualitative info in links, quantitative in tables.
NP-complete or NP-hard to compute exact values; typical to make
simplifying assumptions or approximate methods.
Many Bayesian tools and systems exist
Bayesian Networks: an efficient and effective representation of the joint
probability distribution of a set of random variables
Efficient:
Local models
Independence (d-separation)
Effective:
Algorithms take advantage of structure to
Compute posterior probabilities
Compute most probable instantiation
Decision making
20. References and Further Reading
Bayesian Networks without Tears by Eugene Charniak
http://www.cs.ubc.ca/~murphyk/Bayes/Charniak_91.
pdf
Russel, S. and Norvig, P. (1995). Artificial
Intelligence, A Modern Approach. Prentice Hall.
Weiss, S. and Kulikowski, C. (1991). Computer Systems
That Learn. Morgan Kaufman.
Heckerman, D. (1996). A Tutorial on Learning with
Bayesian Networks. Microsoft Technical Report
MSR-TR-95-06.
Internet Resources on Bayesian Networks and
Machine Learning:
http://www.cs.orst.edu/~wangxi/resource.html