The learning method used by our approach is usually known in the artificial intelligence community as learning by observation, imitation learning, learning from demonstration, programming by demonstration, learning by watching or learning by showing. For consistency, learning by observation will be used from here on.
This slide includes :
Types of Machine Learning
Supervised Learning
Brain
Neuron
Design a Learning System
Perspectives
Issues in Machine Learning
Learning Task
Learning as Search
Hypothesis
Version Spaces
Candidate elimination algorithm
linear Discriminant
Perception
Linear Separability
Linear Regression
Unsupervised Learning
Reinforcement Learning
Evolutionary Learning
A Review on Introduction to Reinforcement Learningijtsrd
This paper aims to introduce, review and summarize the basic concepts of reinforcement learning. It will provide an introduction to reinforcement learning in machine learning while covering reinforcement learning workflow, types, methods and algorithms used in it. Shreya Khare | Yogeshchandra Puranik "A Review on Introduction to Reinforcement Learning" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42498.pdf Paper URL: https://www.ijtsrd.comcomputer-science/artificial-intelligence/42498/a-review-on-introduction-to-reinforcement-learning/shreya-khare
This slide includes :
Types of Machine Learning
Supervised Learning
Brain
Neuron
Design a Learning System
Perspectives
Issues in Machine Learning
Learning Task
Learning as Search
Hypothesis
Version Spaces
Candidate elimination algorithm
linear Discriminant
Perception
Linear Separability
Linear Regression
Unsupervised Learning
Reinforcement Learning
Evolutionary Learning
A Review on Introduction to Reinforcement Learningijtsrd
This paper aims to introduce, review and summarize the basic concepts of reinforcement learning. It will provide an introduction to reinforcement learning in machine learning while covering reinforcement learning workflow, types, methods and algorithms used in it. Shreya Khare | Yogeshchandra Puranik "A Review on Introduction to Reinforcement Learning" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42498.pdf Paper URL: https://www.ijtsrd.comcomputer-science/artificial-intelligence/42498/a-review-on-introduction-to-reinforcement-learning/shreya-khare
Implementation of Naive Bayesian Classifier and Ada-Boost Algorithm Using Mai...ijistjournal
Machine learning [1] is concerned with the design and development of algorithms that allow computers to evolve intelligent behaviors based on empirical data. Weak learner is a learning algorithm with accuracy less than 50%. Adaptive Boosting (Ada-Boost) is a machine learning algorithm may be used to increase accuracy for any weak learning algorithm. This can be achieved by running it on a given weak learner several times, slightly alters data and combines the hypotheses. In this paper, Ada-Boost algorithm is used to increase the accuracy of the weak learner Naïve-Bayesian classifier. The Ada-Boost algorithm iteratively works on the Naïve-Bayesian classifier with normalized weights and it classifies the given input into different classes with some attributes. Maize Expert System is developed to identify the diseases of Maize crop using Ada-Boost algorithm logic as inference mechanism. A separate user interface for the Maize expert system consisting of three different interfaces namely, End-user/farmer, Expert and Admin are presented here. End-user/farmer module may be used for identifying the diseases for the symptoms entered by the farmer. Expert module may be used for adding rules and questions to data set by a domain expert. Admin module may be used for maintenance of the system.
Implementation of Naive Bayesian Classifier and Ada-Boost Algorithm Using Mai...ijistjournal
Machine learning [1] is concerned with the design and development of algorithms that allow computers to evolve intelligent behaviors based on empirical data. Weak learner is a learning algorithm with accuracy less than 50%. Adaptive Boosting (Ada-Boost) is a machine learning algorithm may be used to increase accuracy for any weak learning algorithm. This can be achieved by running it on a given weak learner several times, slightly alters data and combines the hypotheses. In this paper, Ada-Boost algorithm is used to increase the accuracy of the weak learner Naïve-Bayesian classifier. The Ada-Boost algorithm iteratively works on the Naïve-Bayesian classifier with normalized weights and it classifies the given input into different classes with some attributes. Maize Expert System is developed to identify the diseases of Maize crop using Ada-Boost algorithm logic as inference mechanism. A separate user interface for the Maize expert system consisting of three different interfaces namely, End-user/farmer, Expert and Admin are presented here. End-user/farmer module may be used for identifying the diseases for the symptoms entered by the farmer. Expert module may be used for adding rules and questions to data set by a domain expert. Admin module may be used for maintenance of the system.
Supervised learning is a paradigm in machine learning, using multiple pairs consisting of an input object and a desired output value to train a model. The training data is analyzed and an inferred function is generated, which can be used for mapping new examples.
In a world of data explosion, the rate of data generation and consumption is on the increasing side,
there comes the buzzword - Big Data.
Big Data is the concept of fast-moving, large-volume data in varying dimensions (sources) and
highly unpredicted sources.
The 4Vs of Big Data
● Volume - Scale of Data
● Velocity - Analysis of Streaming Data
● Variety - Different forms of Data
● Veracity - Uncertainty of Data
With increasing data availability, the new trend in the industry demands not just data collection but making an ample sense of acquired data - thereby, the concept of Data Analytics.
Taking it a step further to further make futuristic prediction and realistic inferences - the concept
of Machine Learning.
A blend of both gives a robust analysis of data for the past, now and the future.
There is a thin line between data analytics and Machine learning which becomes very obvious
when you dig deep.
Presentation on Teaching Quantitative Methods using Excel workbook courseware. -- at the 25th International Conference on Technology in Collegiate Mathematics, Boston, March 21 - 24, 2013. A Pearson Education event.
This slides present the Statistical foundations in verious machine learning techniques. The intended audiance is Statistics Professionals/ students and Data Scientists.
A neural network is a method in artificial intelligence that teaches computers to process data in a way that is inspired by the human brain. It is a type of machine learning process, called deep learning, that uses interconnected nodes or neurons in a layered structure that resembles the human brain.
A public member is visible from anywhere in the system. In class diagram, it is prefixed by the symbol '+'. Private − A private member is visible only from within the class.
Implementation of Naive Bayesian Classifier and Ada-Boost Algorithm Using Mai...ijistjournal
Machine learning [1] is concerned with the design and development of algorithms that allow computers to evolve intelligent behaviors based on empirical data. Weak learner is a learning algorithm with accuracy less than 50%. Adaptive Boosting (Ada-Boost) is a machine learning algorithm may be used to increase accuracy for any weak learning algorithm. This can be achieved by running it on a given weak learner several times, slightly alters data and combines the hypotheses. In this paper, Ada-Boost algorithm is used to increase the accuracy of the weak learner Naïve-Bayesian classifier. The Ada-Boost algorithm iteratively works on the Naïve-Bayesian classifier with normalized weights and it classifies the given input into different classes with some attributes. Maize Expert System is developed to identify the diseases of Maize crop using Ada-Boost algorithm logic as inference mechanism. A separate user interface for the Maize expert system consisting of three different interfaces namely, End-user/farmer, Expert and Admin are presented here. End-user/farmer module may be used for identifying the diseases for the symptoms entered by the farmer. Expert module may be used for adding rules and questions to data set by a domain expert. Admin module may be used for maintenance of the system.
Implementation of Naive Bayesian Classifier and Ada-Boost Algorithm Using Mai...ijistjournal
Machine learning [1] is concerned with the design and development of algorithms that allow computers to evolve intelligent behaviors based on empirical data. Weak learner is a learning algorithm with accuracy less than 50%. Adaptive Boosting (Ada-Boost) is a machine learning algorithm may be used to increase accuracy for any weak learning algorithm. This can be achieved by running it on a given weak learner several times, slightly alters data and combines the hypotheses. In this paper, Ada-Boost algorithm is used to increase the accuracy of the weak learner Naïve-Bayesian classifier. The Ada-Boost algorithm iteratively works on the Naïve-Bayesian classifier with normalized weights and it classifies the given input into different classes with some attributes. Maize Expert System is developed to identify the diseases of Maize crop using Ada-Boost algorithm logic as inference mechanism. A separate user interface for the Maize expert system consisting of three different interfaces namely, End-user/farmer, Expert and Admin are presented here. End-user/farmer module may be used for identifying the diseases for the symptoms entered by the farmer. Expert module may be used for adding rules and questions to data set by a domain expert. Admin module may be used for maintenance of the system.
Supervised learning is a paradigm in machine learning, using multiple pairs consisting of an input object and a desired output value to train a model. The training data is analyzed and an inferred function is generated, which can be used for mapping new examples.
In a world of data explosion, the rate of data generation and consumption is on the increasing side,
there comes the buzzword - Big Data.
Big Data is the concept of fast-moving, large-volume data in varying dimensions (sources) and
highly unpredicted sources.
The 4Vs of Big Data
● Volume - Scale of Data
● Velocity - Analysis of Streaming Data
● Variety - Different forms of Data
● Veracity - Uncertainty of Data
With increasing data availability, the new trend in the industry demands not just data collection but making an ample sense of acquired data - thereby, the concept of Data Analytics.
Taking it a step further to further make futuristic prediction and realistic inferences - the concept
of Machine Learning.
A blend of both gives a robust analysis of data for the past, now and the future.
There is a thin line between data analytics and Machine learning which becomes very obvious
when you dig deep.
Presentation on Teaching Quantitative Methods using Excel workbook courseware. -- at the 25th International Conference on Technology in Collegiate Mathematics, Boston, March 21 - 24, 2013. A Pearson Education event.
This slides present the Statistical foundations in verious machine learning techniques. The intended audiance is Statistics Professionals/ students and Data Scientists.
A neural network is a method in artificial intelligence that teaches computers to process data in a way that is inspired by the human brain. It is a type of machine learning process, called deep learning, that uses interconnected nodes or neurons in a layered structure that resembles the human brain.
A public member is visible from anywhere in the system. In class diagram, it is prefixed by the symbol '+'. Private − A private member is visible only from within the class.
the compression of images is an important step before we start the processing of larger images or videos. The compression of images is carried out by an encoder and output a compressed form of an image. In the processes of compression, the mathematical transforms play a vital role.
Supervised learning is a machine learning approach that's defined by its use of labeled datasets. These datasets are designed to train or “supervise” algorithms into classifying data or predicting outcomes accurately.
A web service is either: a service offered by an electronic device to another electronic device, communicating with each other via the Internet, or a server running on a computer device, listening for requests at a particular port over a network, serving web documents.
Entrepreneurship is the ability and readiness to develop, organize and run a business enterprise, along with any of its uncertainties in order to make a profit. The most prominent example of entrepreneurship is the starting of new businesses.
The IoT design approach is an approach to the IoT system development with respect to the peculiarities of the Internet of Things. That term covers all components of IoT architecture from IoT devices and their hardware to applications and user interfaces.
DCOM (Distributed Component Object Model) and CORBA (Common Object Request Broker Architecture) are two popular distributed object models. In this paper, we make architectural comparison of DCOM and CORBA at three different layers: basic programming architecture, remoting architecture, and the wire protocol architecture.
Tweepy is an open source Python package that gives you a very convenient way to access the Twitter API with Python. Tweepy includes a set of classes and methods that represent Twitter's models and API endpoints, and it transparently handles various implementation details, such as: Data encoding and decoding.
DCOM (Distributed Component Object Model) and CORBA (Common Object Request Broker Architecture) are two popular distributed object models. In this paper, we make architectural comparison of DCOM and CORBA at three different layers: basic programming architecture, remoting architecture, and the wire protocol architecture.
Every application has some basic interactive interface for the user. For example, a button, check-box, radio-button, text-field, etc. These together form the components in Swing.
Distributed firewall is an mechanisms to enforce a network domain security policy through the use of policy language.
Security policy is defined centrally.
A multiprocessor system consists of multiple processing units connected via some interconnection network plus the software needed to make the processing units work together.
The traveling salesman problem (TSP) is an algorithmic problem tasked with finding the shortest route between a set of points and locations that must be visited.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
1. Nadar saraswathi college of arts &
science, theni.
Department of cs & it
ARTIFICIAL INTELLIGENCE
PRESENTED BY
G.KAVIYA
M.SC(IT)
TOPIC:LEARNING FROM
OBSERVATION
3. LEARNING:
Learning is Agent’s percepts should be used for
acting.
It also used for improving the agents ability to act
in the future.
Learning takes places as the agents observes, its
interactions with the world and its own decision making
processes.
4. FORMS OF LEARNING:
Learning Agent can be thought of as containing
a Performance Element, that decides, what actions to take,
and a Learning Elements that modifies the performance
elements to take better decisions.
Three major issues in learning element design
Which components the performance element are to be
learned.
What feedback is available to learn these components.
What representation is used for the components.
5. Components of Agents are;
A direct mapping from conditions on
the current state to actions.
A means to infer relevant properties of
the world from the percept sequence.
Information about the way the world
evolves and about the results of the
possible action the agent can take.
Utility information indicating the
desirability of world states.
Action value information indicating the
desirability of action.
Goals the describe classes of the state
whose achievement maximizes the
agent’s utility.
6. Classified into three categories:
Supervised Learning.
Unsupervised Learning.
Reinforcement Learning.
7. Supervised Learning:
The Learning here is performed with the
help of teacher. Let us take the example of the learning
process of the small child.
The child doesn’t know how to read/write.
He/she is being taught by the parents at home and by the
teacher in school.
The children are recognize the alphabet,
numerals, etc. Their and every action is supervised by a
teacher.
8. Continue;
Actually, a child works on
the basis of the output that
he/she has to produce. All
these real-time events
involve supervised learning
methodology.
Similarly, in ANNs
following the supervised
learning, each input vector
requires a corresponding
target vector, which
represents the desired
outputs.
The input vector
along with the target vector
is called training pair.
9. Continue;
In this type of training, a
supervisor or teacher is
required for error
minimization. Hence, the
network trained by this
method is said to be using
supervised training
methodology.
In supervised learning, It is
assumed that the correct
“target” output values are
known for each input pattern.
The input vector is
presented to the network,
Which result is an output
vector. The output vector is the
actual output vector. Then the
actual output vector is
compared with the desired
output vector.
If there exists a difference
between the two output
vectors then an error signal is
generated by the network. This
error signal is used for
adjustment of weights until the
actual output matches the
desired output.
10. Un Supervised Learning:
The learning here is
performed without the help of
teacher. Consider, learning
process of a tadpole, it learns
by itself, that is, a child fish
learns to swim by itself, it is not
taught by its mother.
Thus, Its learning process
is independent and is not
supervised by a teacher.
In ANNs following
unsupervised learning, the
input vectors of similar type
are grouped without the use of.
11. Reinforcement Learning:
The learning process is
similar to supervised learning.
In the case of supervised
learning the correct target
output values are known for
each input pattern.
But, In some cases, Less
information might be available.
For example, the network
might be told that its actual
output is only “50% correct “or
so. Thus, Here only critic
information is available, not the
exact information.
The learning information
based on the critic information
is called reinforcement learning
and the feedback sent is called
reinforcement signal.
12. ENSEMBLE OF LEARNING:
Learn multiple
alternative definitions of
a concept using different
training data or different
learning algorithms.
Combine decisions
of multiple definitions,
eg. Using weighted
voting.
13. VALUE OF ENSEMBLES
When combing multiple independent and diverse
decisions each of which is at least more accurate than random
guessing, random errors cancel each other out, correct decisions
are reinforcement.
Generate a group of base-learners which when
combined has higher accuracy.
Different learners use different;
Algorithm.
Hyperparameters.
Representations/Modalities/Views.
Training sets.
Subproblems.
15. BOOSTING:
Also uses voting/averaging but models are
weighted according to their performance.
Iterative procedure: new models are influenced
by performance of previously built ones.
* New model is encouraged to become
expert for instances classified incorrectly by earlier
models.
* Intuitive justification: models should be
experts that complement each other.
There are several variants of this algorithm.
16. Continue;
STRONG LEARNER:
Objective of machine learning.
o Take labeled data for training.
o Produce a classifier which can be
arbitrarily accurate.
o Strong learners are very difficult to
construct.
WEAKER LEARNER:
o Take labeled data for training.
o Produce a classifier which is more
accurate than random guessing.
o Constructing weaker learners is
relatively easy.
17. ADAPTIVE BOOSTING:
Each rectangle corresponds to an example, with
weight proportional to its height.
Crosses corresponds to misclassified examples.
Size of decision tree indicates the weight of that
classifier in the final ensemble.
Using Different Data Distribution
* Start with uniform weighting.
* During each step of learning.
Increase weights of the examples which are not
correctly learned by the weak learner.
Decrease weights of the examples which are
correctly learned by the weak learner.
18. Continue;
IDEA:
focus on difficult example which
are not correctly classified in the
previous steps
WEIGHTED VOTING:
construct strong classifier by
weighted voting of the weak classifier.
IDEA:
Better weak classifier gets a
larger weight.
Iteratively add weak classifiers
Increase accuracy of the
combined classifier through
minimization of a cost function.
19. COMPUTATIONAL LEARNING
THEORY
Computational learning theory characterize. The difficulty of
several types of machine learning problem.
Capabilities of several types of ML algorithm.
CLT seeks answer, question such as;
a) “under what conditions is successful learning possible and
impossible?”
b) “under what conditions is a particular learning algorithm
assured of learning successfully?” it means that, what kind of
task are learnable, what kind of data is required for
learnability.
20. Various issues are:
Sample complexity:
How many training examples are needed for a
learner to converge (with high probability) to a successful
hypothesis?
Computational complexity:
How much computational effort is needed for a
learner to converge to a successful hypothesis?
Mistake bound:
How many training examples will the learner
misclassify before converging to a successful hypothesis?
21. (PAC) Probably Learning an Approximately
Correct hypothesis:-
A particular setting for the learning problem,
called the probably approximately correct(PAC) learning
model.
This model of learning is based on following
points:
1. Specifying problem setting that defines PAC
model.
2. How many training examples are required.
3. How much computational are required in order
to learn various classes of target functions within PAC
22. Problem setting:-
X : Set of all the instance (eg: set of people)
each described by attributes <age, height>.
C : Target concept the leaner need to learn.
C: X{0,1}
L : Learner have to learn “people who are
skiers”
C(x) =1 : positive training example
C(x) =0 : negative training example
Error of a hypothesis: True error, denoted by errorD
(h), of hypothesis h w.r.t target concept c and
distribution D is probability that h will misclassify an
instance drawn at random according to D.
errorD (h) = pr [c(x) not equal to h(x)]
XED
23. PAC Learnability:
No of training examples needed to learn a
hypothesis h, for which
errorD (h) = 0.
For these two difficulties, following measures can be
taken:-
1. No requirement of zero error hypothesis for learner L. So
a bound to error can be set by constant E, that can be made small.
2.Not necessary that learner succeed for every sequence of
randomly drawn training example. So learner probably learn a
hypothesis that is approximately correct.
Bounded by same constant S which is,
24. Definition:
Consider a concept class define over a set of instance
X of kngtn n and a learner L using hypothesis space H.
C is PAC learnable by L using H if for all CEC.
distribution D over X
E such that 0<E<1/2 and
S such that 0<S<1/2
Learner L will with Probably at least (1-8)
output a hypothesis nEH such that
errorD (n) <= E.