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From Wikipedia
Active learning is a form of supervised machine learning in which the learning algorithm is able to interactively query the user (or some other information source) to obtain the desired outputs at new data points. In statistics literature it is sometimes also called optimal experimental design.
There are situations in which unlabeled data is abundant but labeling data is expensive. In such a scenario the learning algorithm can actively query the user/teacher for labels. This type of iterative supervised learning is called active learning. Since the learner chooses the examples, the number of examples to learn a concept can often be much lower than the number required in normal supervised learning. With this approach there is a risk that the algorithm might focus on unimportant or even invalid examples.
Active learning can be especially useful in biological research problems such as Protein engineering where a few proteins have been discovered with a certain interesting function and one wishes to determine which of many possible mutants to make next that will have a similar function.
Definitions
Let T be the total set of all data under consideration. For example, in a protein engineering problem, T would include all proteins that are known to have a certain interesting activity and all additional proteins that one might want to test for that activity.
During each iteration, i, T is broken up into three subsets
 \mathbf{T}_{K,i}: Data points where the label is known.
 \mathbf{T}_{U,i}: Data points where the label is unknown.
 \mathbf{T}_{C,i}: A subset of T_{U,i} that is chosen to be labeled.
Most of the current research in active learning involves the best method to chose the data points for T_{C,i}.
Minimum Marginal Hyperplane
Some active learning algorithms are built upon Support vector machines (SVMs) and exploit the structure of the SVM to determine which data points to label. Such methods usually calculate the margin, W, of each unlabeled datum in T_{U,i} and treat W as an ndimensional distance from that datum to separating hyperplane.
Minimum Marginal Hyperplane methods assume that the data with the smallest W are those that the SVM is most uncertain about and therefore should be placed in T_{C,i} to be labeled. Other similar methods, such as Maximum Marginal Hyperplane, choose data with the largest W. Tradeoff methods choose a mix of the smallest and largest Ws.
Maximum Curiosity
Another active learning method, that typically learns a data set with fewer examples than Minimum Marginal Hyperplane but is more computationally intensive and only works for discrete classifiers is Maximum Curiosity.
Maximum curiosity takes each unlabeled datum in T_{U,i} and assumes all possible labels that datum might have. This datum with each assumed class is added to T_{K,i} and then the new T_{K,i} is crossvalidated. It is assumed that when the datum is paired up with its correct label, the crossvalidated accuracy (or correlation coefficient) of T_{K,i} will most improve. The datum with the most improved accuracy is placed in T_{C,i} to be labeled
Visual learning is a teaching and learning style in which ideas, concepts, data and other information are associated with images and techniques. It is one of the three basic types of learning styles in the widelyused Fleming VAK/VARK model that also includes kinesthetic learning and auditory learning.
Theory
First let us place visual learning in it's proper context , learning as a whole .The influential management and systems thinker pioneer Russel Ackoff suggested , the most important contribution of a first rate 21st century education is not content . It is that we acquire the capability to learn and are motivated to do so throughout our lives , we are , by any objective standard , not doing a very good job. In the developed world today , falling global competitiveness is blamed on eduction [Karen Ward HSBC:2011 ] , our schools , our universities , our tried and tested auditory sequential systems are broken , no longer fit for purpose , a relic of the 19th century [Ackoff] . It is through this lens that we should judge the early pioneers attempts to use psychology to better our society .The great promise of learning styles , we can prepare our population so they are better able to internalize , reflect , boil down , apply and synthesize information from many , many different sources over extended time frames . As a society we can do better , we must do better and we will do better
Although learning styles have "enormous popularity" and both children and adults express personal preferences, there is no evidence that identifying a student's learning style produces better outcomes, and there is significant evidence that the widespread "meshing hypothesis" (that a student will learn best if taught in a method deemed appropriate for the student's learning style) is invalid. Welldesigned studies "flatly contradict the popular meshing hypothesis".
The studies flat contradiction fails by confusing practice and theory ; for deep background see [Linda Silverman , Thomas G West , Stephen Heppel] . The popular meshing hypothesis as implemented by the study designers is much too simplistic in both application and conception . If learning styles are to become a true science of attention proper screening has to be introduced , differentiated materials need to be prepared and communicated in multiple mediums so the learning channels need to overlapped in the correct order . In short a scientific approach .
Visual learning techniques
Creating graphic organizers  Students create graphic organizers such as diagrams, webs, and concept maps by selecting symbols to represent ideas and information. To show the relationships between ideas, students link the symbols and add words to further clarify meaning.
By representing information spatially and with images, students are able to focus on meaning, reorganize and group similar ideas easily, make better use of their visual memory.
In a study entitled Graphic Organizers: A Review of Scientifically Based Research, The Institute for the Advancement of Research in Education at AEL evaluated 29 studies and concluded that visual learning improves student performance in the following areas:
 Critical ThinkingGraphic organizers link verbal and visual information to help students make connections, understand relationships and recall related details.
 Retention
 According to research, students better remember information when it's represented and learned both visually and verbally.
 Comprehension
 Students better comprehend new ideas when they are connected to prior knowledge.
 Organization
 Students can use diagrams to display large amounts of information in ways that are easy to understand and help reveal relationships and patterns.
Visualising data  When working with data, students build data literacy as they collect and explore information in a dynamic inquiry process, using tables and plots to visually investigate, manipulate and analyze data. As students explore the way data moves through various plot types, such as Venn, stack, pie and axis, they formulate questions and discover meaning from the visual representation.
Tips For Students Who Are Visual Learners
The following are some suggested techniques for students who are visual learners, which can be used to make learning and education more effective.
Study Habits
 Understand the big picture, and have it in front of you as you examine smaller details.
 When trying to learn or memorize a piece of information, close your eyes and try to visualize it. If using flashcards, limit the information on each card so it can be easily recalled in your mind.
 Try to find alternate materials to study from; videos, PowerPoint presentations, maps, etc.
Learning During Lectures
 Avoid visual distractions. Looking out the window or at the person in front of you will not help you learn the material.
 Make illustrations as you take notes. Draw pictures to help you visualize information. Graphs, maps, and images are helpful in retaining information.
 After class, review and organize your notes. This will help you to sort out the information in a way that is meaningful to you and further solidify the material.
Learning From Textbooks
 Preview the chapter by looking through titles, graphs, charts and other visual aids. This will help you obtain the 'big picture' of what you will be learning.
 Use highlighters to emphasize pieces of the material that are especially important. Colorcoding is often useful as well.
 Take notes or make illustrations in the margins, or, if it is a textbook you shouldn't be writing in, put them in a separate notebook.
Test Taking
 Think of visual cues used in learning to recall the information for a test. One way to do this is to sit in the same place every time you are in class, then make sure to get the same seat on test day. The visual cues your mind picks up while learning can help you recall information when they are seen again.
 If you find that timed tests are difficult for you or that you feel anxiety when taking tests with a time limit, discuss it with your instructor. Teachers give tests to gather an accurate assessment of the students' progress.
Teaching Visual Learners/ Instructor Course Design
There are some elements of design that can be incorporated into any course that will help ensure learning success:
Simplicity
Distance Education course creators sometimes become victims of the "more is better" concept. This is not the best case when developing a course site. Including everything you have or can find on a topic can overwhelm and confuse students. Improper use of fonts, colors, and graphics can also serve as a distraction and hamper the effectiveness of your course. Another common problem in Blackboard courses is the use of too many buttons or links on the course menu. Keeping the content, menu, color and font variations to a minimum can help keep your site design simple.
Consistency
Consistency can greatly reduce the time initially required to navigate your course site. Consistency across pages can reduce the load on cognitive processing and prevent cognitive overload. If learning to use a course is a quick and painless process, learners are motivated to continue. Consistencies should include: colo
Informal learning is semistructured and occurs in a variety of places, such as learning at home, work, and through daily interactions and shared relationships among members of society. For many learners this includes language acquisition, cultural norms and manners. Informal learning for young people is an ongoing process that also occurs in a variety of places, such as out of school time, as well as in youth programs and at community centers.
In the context of corporate training and education, the term informal learning is widely used to describe the many forms of learning that takes place independently from instructorled programs: books, selfstudy programs, performance support materials and systems, coaching, communities of practice, and expert directories.
Characterizations
Informal learning can be characterized as follows:
 It often takes place outside educational establishments standing out from normal life and professional practice;
 It does not necessarily follow a specified curriculum and is not often professionally organized but rather originates accidentally, sporadically, in association with certain occasions, from changing practical requirements;
 It is not necessarily planned pedagogically conscious, systematically according to subjects, test and qualificationoriented, but rather unconsciously incidental, holistically problemrelated, and related to situationmanagement and fitness for life;
 It is experienced directly in its "natural" function of everyday life.
History
In international discussions, the concept of informal learning, already used by John Dewey at an early stage and later on by Malcolm Knowles, experienced a renaissance, especially in the context of development policy. At first, informal learning was only delimited from formal school learning and nonformal learning in courses (Coombs/Achmed 1974). Marsick and Watkins take up this approach and go one step further in their definition. They, too, begin with the organizational form of learning and call those learning processes informal which are nonformal or not formally organized and are not financed by institutions (Watkins/Marsick, p. 12 et sec.). An example for a wider approach is Livingstone's definition which is oriented towards autodidactic and selfdirected learning and places special emphasis on the selfdefinition of the learning process by the learner (Livingstone 1999, p. 68 et seq.).
Another perspective
Merriam and others (2007) state: "Informal learning, Schugurensky (2000) suggests, has its own internal forms that are important to distinguish in studying the phenomenon. He proposes three forms: selfdirected learning, incidental learning, and socialization, or tacit learning. These differ among themselves in terms of intentionality and awareness at the time of the learning experience. Selfdirected learning, for example, is intentional and conscious; incidental learning, which Marsick and Watkins (1990) describe as an accidental byproduct of doing something else, is unintentional but after the experience she or he becomes aware that some learning has taken place; and finally, socialization or tacit learning is neither intentional nor conscious (although we can become aware of this learning later through 'retrospective recognition') (Marsick & Watkins, 1990, p. 6)" (p. 36).
Formal and nonformal education
To fully understand informal learning it is useful to define the terms "formal" and "nonformal" education. Merriam, Caffarella, and Baumgartner (2007), state: "Formal education is highly institutionalized, bureaucratic, curriculum driven, and formally recognized with grades, diplomas, or certificates" (p. 29). Merriam and others (2007), also state: "The term nonformal has been used most often to describe organized learning outside of the formal education system. These offerings tend to be shortterm, voluntary, and have few if any prerequisites. However they typically have a curriculum and often a facilitator" (p. 30).Nonformal learning can also include learning in the formal arena when concepts are adapted to the unique needs of individual students (Burlin, 2009).
Research and data
Merriam and others (2007) state: "studies of informal learning, especially those asking about adults' selfdirected learning projects, reveal that upwards of 90 percent of adults are engaged in hundreds of hours of informal learning. It has also been estimated that the great majority (upwards of 70 percent) of learning in the workplace is informal (Kim, Collins, Hagedorn, Williamson, & Chapman, 2004), although billions of dollars each year are spent by business and industry on formal training programs" (p. 35â€“36). vb
Informal learning experiences
Informal knowledge is information that has not been externalized or captured and exists only inside someone's head. To get at the knowledge, you must locate and talk to that person. Examples of such informal knowledge transfer include instant messaging, a spontaneous meeting on the Internet, a phone call to someone who has information you need, a live onetimeonly sales meeting introducing a new product, a chatroom in real time, a chance meeting by the water cooler, a scheduled Webbased meeting with a realtime agenda, a tech walking you through a repair process, or a meeting with your assigned mentor or manager.
Experience indicates that almost all real learning for performance is informal (The Institute for Research on Learning, 2000, Menlo Park), and the people from whom we learn informally are usually present in real time. We all need that kind of access to an expert who can answer our questions and with whom we can play with the learning, practice, make mistakes, and practice some more. It
Machine learning, a branch of artificial intelligence, is a scientific discipline that is concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases. A learner can take advantage of examples (data) to capture characteristics of interest of their unknown underlying probability distribution. Data can be seen as examples that illustrate relations between observed variables. A major focus of machine learning research is to automatically learn to recognize complex patterns and make intelligent decisions based on data; the difficulty lies in the fact that the set of all possible behaviors given all possible inputs is too large to be covered by the set of observed examples (training data). Hence the learner must generalize from the given examples, so as to be able to produce a useful output in new cases. Machine learning, like all subjects in artificial intelligence, requires crossdisciplinary proficiency in several areas, such as probability theory, statistics, pattern recognition, cognitive science, data mining, adaptive control, computational neuroscience and theoretical computer science.
Definition
A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.
Generalization
The core objective of a learner is to generalize from its experience. The training examples from its experience come from some generally unknown probability distribution and the learner has to extract from them something more general, something about that distribution, that allows it to produce useful answers in new cases.
Human interaction
Some machine learning systems attempt to eliminate the need for human intuition in data analysis, while others adopt a collaborative approach between human and machine. Human intuition cannot, however, be entirely eliminated, since the system's designer must specify how the data is to be represented and what mechanisms will be used to search for a characterization of the data.
Algorithm types
Machine learning algorithms are organized into a taxonomy, based on the desired outcome of the algorithm.
 Supervised learninggenerates a function that maps inputs to desired outputs. For example, in aclassification problem, the learner approximates a function mapping a vector into classes by looking at inputoutput examples of the function.
 Unsupervised learningmodels a set of inputs, like clustering.
 Semisupervised learningcombines both labeled and unlabeled examples to generate an appropriate function or classifier.
 Reinforcement learninglearns how to act given an observation of the world. Every action has some impact in the environment, and the environment provides feedback in the form of rewards that guides the learning algorithm.
 Transductiontries to predict new outputs based on training inputs, training outputs, and test inputs.
 Learning to learnlearns its owninductive bias based on previous experience.
Theory
The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory. Because training sets are finite and the future is uncertain, learning theory usually does not yield absolute guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common.
In addition to performance bounds, computational learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results. Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.
There are many similarities between machine learning theory and statistics, although they use different terms.
Approaches
Decision tree learning
Decision tree learning uses a decision tree as a predictive model which maps observations about an item to conclusions about the item's target value.
Association rule learning
Association rule learning is a method for discovering interesting relations between variables in large databases.
Artificial neural networks
An artificial neural network (ANN), usually called "neural network" (NN), is a mathematical model or computational model that tries to simulate the structure and/or functional aspects of biological neural networks. It consists of an interconnected group of artificial neurons and processes information using a
From Encyclopedia
Over the centuries, people have thought of mathematics, and have defined it, in many different ways. Mathematics is constantly developing, and yet the mathematics of 2,000 years ago in Greece and of 4,000 years ago in Babylonia would look familiar to a student of the twentyfirst century. Mathematics, says the mathematician Asgar Aaboe, is characterized by its permanence and its universality and by its independence of time and cultural setting. Try to think, for a moment, of another field of knowledge that is thus characterized. "In most sciences one generation tears down what another has built and what one has established another undoes. In Mathematics alone each generation builds a new story to the old structure," noted Hermann Henkel in 1884. The mathematician and philosopher Bertrand Russell said that math is "the subject in which we never know what we are talking about nor whether what we are saying is true." Mathematics, in its purest form, is a system that is complete in itself, without worrying about whether it is useful or true. Mathematical truth is not based on experience but on inner consistency within the system. Yet, at the same time, mathematics has many important practical applications in every facet of life, including computers, space exploration, engineering, physics, and economics and commerce. In fact, mathematics and its applications have, throughout history, been inextricably intertwined. For example, mathematicians knew about binary arithmetic , using only the digits 0 and 1, for years before this knowledge became practical in computers to describe switches that are either off (0) or on (1). Gamblers playing games of chance led to the development of the laws of probability . This knowledge in turn led to our ability to predict behaviors of large populations by sampling . The desire to explain the patterns in 100 years of weather data led, in part, to the development of mathematical chaos theory . Therefore, mathematics develops as it is needed as a language to describe the real world, and the language of mathematics in turn leads to practical developments in the real world. Another way to think of mathematics is as a game. When players decide to join in a gameâ€”say a game of cards, a board game, or a baseball gameâ€”they agree to play by the rules. It may not be "fair" or "true" in the real world that a player is "out" if someone touches the player with a ball before the player's foot touches the base, but within the game of baseball, that is the rule, and everyone agrees to abide by it. One of the rules of the game of mathematics is that a particular problem must have the same answer every time. So, if Bill says that 3 divided by 2 is 1Â½, and Maria says that 3 divided by 2 is 1.5, then mathematics asks if these two differentlooking answers really represent the same number (as they do). The form of the answers may differ, but the value of the two answers must be identical if both answers are correct. Another rule of the game of mathematics is consistency. If a new rule is introduced, it must not contradict or lead to different results from any of the rules that went before. These rules of the game explain why division by 0 must be undefined. For example, when checking division by multiplication it is clear that 10 divided by 2 is 5 because 2 Ã— 5 is 10. Suppose 10/0 is defined as 0. Then 0 Ã— 0 must be 10, and that contradicts the rule that 0 times anything is 0. One may believe that 0 divided by 0 is 5 because 0 Ã— 5 is 0, but then 0 divided by 0 is 4, because 0 Ã— 4 is also 0. There is another rule in the game of mathematics that says if 0 divided by 0 is 5 and 0 divided by 0 is 4, then 5 must be equal to 4â€”and that is a contradiction that no mathematician or student will accept. Mathematics depends on its own internal rules to test whether something is valid. This means that validity in mathematics does not depend on authority or opinion. A thirdgrade student and a college professor can disagree about an answer, and they can appeal to the rules of the game to decide who is correct. Whoever can prove the point, using the rules of the game, must be correct, regardless of age, experience, or authority. Mathematics is often called a language. Numbers and symbols are understood without the barrier of translation, and mathematics can be used to describe many aspects of today's world, from airline reservation systems to theories about the shape of space. Yet learning the vocabulary of mathematics is often a challenge and can be confusing. For example, mathematicians speak of the "bottom" of a fraction as the "denominator," which is a pretty frightening word to a beginner. But, like any language, mathematics vocabulary can be learned, just as Spanish speakers learn to say anaranjado, and English speakers learn to say "orange" for the same color. In Islands of Truth (1990), the mathematician Ivars Peterson says that "the understanding of mathematics requires hard, concentrated work. It combines the learning of a new language and the rigor of logical thinking, with little room for error." He goes on to say "I've also learned that mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve." see also Mathematics, New Trends in. Lucia McKay Aaboe, Asger. Episodes from the Early History of Mathematics. New York: Random House, 1964. Denholm, Richard A. Mathematics: Man's Key to Progress. Chicago: Franklin Publications, 1968. Flegg, Graham. Numbers, Their History and Meaning. New York: Barnes & Noble Books, 1983. Peterson, Ivars. Islands of Truth: A Mathematical Mystery Cruise. New York: W. H. Freeman and Company, 1990.
From Yahoo Answers
Answers:The technique that works best is the simplest. Get little markers and make her work with them. So, if the problem were to be 8+x=12, make her figure out what the answer would be using scraps of paper or something like that on both sides of an equals sign. Under no circumstances let her use a calculator to do simple math (this would include, multiplication, division, squares, and of course addition and subtraction), that will only slow her down in the long run since she needs to understand where the numbers are coming from more than she needs to save a couple seconds. You can use the same concept with almost all math. Either count things out or draw pictures to get a visual idea of what the numbers are representing. The more she practices with the simpler things, the harder things will get easier. If she likes pictures, for a problem like 2x=16, then help her learn to come up with pictures for herself, for example there were sixteen people walking on the sidewalk in groups of two, how many groups would there be (x)? She can even draw a little stick person representation of that. Another really useful thing is a whiteboard, either a bigish one for her bedroom wall or one small enough to throw in a backpack. That way she can write everything out and manipulate the numbers into something she can understand better as many times as she wants without tracking her mistakes on paper. A whiteboard is more friendly than a piece of paper that has been tortured by an eraser.
Answers:That's a good point, I've never really thought about it. I always think of learning curves relating difficulty to knowledge. I guess the graph in my mind was effort on the yaxis, and knowledge gained on the xaxis. Wiki has some interesting things to say, and explains the reason for the metaphor "steep learning curve" http://en.wikipedia.org/wiki/Learning_curve#Common_terms It initially referred to the fact that you retain the most when you're first learning something, so the amount learned vs time invested is steep at the beginning, but has since come to refer to the amount of investment (time & effort) over the amount gained for that investment.
Answers:You are really going to have to adapt some strategies that help you learn effectively. Difficulties in School for a Visual Learner Having to take action before either seeing or reading about what needs to be done Working in an environment with noise or movement Turning out sounds (not very easy responsive to music) Listening to lectures without visual pictures or graphics to illustrate Working in classrooms with drab colors Working under fluorescent lights (makes it hard to concentrate) Things you can do: A Visual Learner Learns Best By: Taking notes and making lists to read later Reading information to be learned Learning from books, videotapes, filmstrips and printouts Seeing a demonstration THE VISUAL LEARNER WILL NEED TO SEE ALL STUDY MATERIAL. Practice visualizing (mental imagery) or picturing spelling words. Write out everything for frequent and quick visual review. Analyze words by tearing them apart and putting them back together (together together). Use color coding when learning new concepts (x and y axis different color when graphing). Use enlarged paper for graphing, making it easier for the visual learner to plot lines. Use outlines of reading assignments which cover key points and guide your reading. Draw lines around the configuration of printed words and structural word elements. Use charts, maps, timelines, and filmstrips when learning new material. Use notes and flash cards for review of material, vocabulary, and terminology for a specific course. Use a dictionary. All the visual cues are present: syllabication, definitions, configurations, affixes, etc. Use graphic organizers and diagrams. Use videos. Utilize "mapping" techniques and draw pictures symbolizing information. Highlight and underline key concepts. Retype notes  use different fonts, bold print, and underline important concepts and facts. VISUAL LEARNER STRATEGIES MATHEMATICS Use visual cues such as flash cards and concrete items. Use graph paper for organizing math problems. Color code math problems. READING/LITERATURE When learning new vocabulary words, look up their meaning in the dictionary and write down their definition on flash cards. Sit close to the instructor for writing board demonstration, etc. Use sight words, flash cards  then close your eyes and visualize what you have seen. Use charts, graphs, and other visual cues. WRITING/SPELLING Use visual study methods rather than recitation of words. Write each spelling word several times. Trace words with colored marking pens. Visualize words mentally and then reproduce them on paper. SOCIAL SCIENCES Learn new material with visual stimulation (videos, computers, etc.). Use colored pens when taking notes  each color represents a degree of importanceblue notes are main themes, red notes are supporting details, green notes are specific details. FACTS ABOUT THE VISUAL LEARNER Is A Natural At Dressing well, putting clothes together easily Remembering details and colors of what he/she sees Reading, spelling and proof reading Remembering faces of people he/she meets (forgets names); remembers names seen in print Quietly taking in surroundings Creating mental photos Studying/Reading Characteristics Reads for pleasure and relaxation; reads rapidly Can spend long periods of time studying Requires quiet during study Learns to spell words in configurations rather than phonetically
Answers:You can find your answer at the end of the rainbow.
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