Spaced repetition: research background. Repetition spacing in learning was in the center of my research over the last ten years (for review see: Wozniak 1990). In this chapter I would like to familiarize the reader with the concept of the optimum spacing of repetitions that will frequently be referred to throughout the dissertation. Research background There has been a great deal of research on how different spacing of repetitions in time affects the strength of memory and how the resulting findings could be applied in the practice of effective learning. It has been predicted, and to a large degree confirmed, that by changing the spacing of repetitions, a substantial gain in the effectiveness of learning might be obtained (e.g., Bjork, 1979; Glenberg, 1979; Glenberg 1980; Clifford, 1981; Dempster, 1987; Bahrick, 1987). However, studies reporting a robust spacing effect in classroom conditions are the exception rather than the rule (Dempster, 1987).
Optimum spacing of repetitions Spacing effect Involuntary habituation. Memory strength and its components. 1. S/R Model of memory 10 years ago we published a paper that delineated a distinction between the two components of long-term memory: stability and retrievability (Wozniak, Gorzelanczyk, Murakowski, 1995). The paper provided the first outline of the so-called S/R Model that makes it easier to build molecular models of long-term memory. Until now, the stability-retrievability distinction has not made a major impact on research in the field. Here we re-emphasize the importance of the S/R Model and sum up the findings of the last decade that refine the S/R Model and highlight its importance in the deconvolution of seemingly contradictory research in the field of memory and learning. 2.
In the literature on memory and learning, we often encounter an ill-defined term: strength of memory (or strength of synaptic connections). Both retrievability and stability of long-term memory can be correlated with a number of molecular or behavioral variables. Now we can obtain the value of k. 4. 5. Maximum Likelihood. Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known likelihood distribution a maximum. The maximum likelihood estimate for a parameter is denoted For a Bernoulli distribution, so maximum likelihood occurs for . If is not known ahead of time, the likelihood function is where or 1, and Rearranging gives so For a normal distribution, and giving Similarly, gives Note that in this case, the maximum likelihood standard deviation is the sample standard deviation, which is a biased estimator for the population standard deviation.
For a weighted normal distribution, The variance of the mean is then But For a Poisson distribution, People.physics.anu.edu.au/~tas110/Teaching/Lectures/L3/Material/Myung03.pdf. 20 rules of formulating knowledge in learning. Knowledge structuring for learning. We will discuss elements that, independently of the repetition spacing algorithm (e.g. as used in SuperMemo), influence the effectiveness of learning. In particular we will see, using examples from a simple knowledge system used in learning microeconomics, how knowledge representation affects the easiness with which knowledge can be retained in the student’s memory. The microeconomics knowledge system has almost entirely been based on the material included in Economics of the firm.
Theory and practice by Arthur A. Thompson, Jr, 1989. Some general concepts of macroeconomics have been added from Macroeconomics by M. Knowledge independent elements of the optimization of self-instruction Before I move toward representation of knowledge, I would only shortly like to list some other principles of effective learning that are representation independent: Knowledge representation issue in learning Components of effective knowledge representation in active recall systems Q: What is production?
Amazon Web Services. ProjectsUsingJUNG – jung. Expectation-maximization (EM) algorithm. Ai.stanford.edu/~chuongdo/papers/em_tutorial.pdf. Www.ee.washington.edu/research/guptalab/publications/EMbookChenGupta2010.pdf. Inside-outside algorithm. In computer science, the inside–outside algorithm is a way of re-estimating production probabilities in a probabilistic context-free grammar. It was introduced James K. Baker in 1979 as a generalization of the forward–backward algorithm for parameter estimation on hidden Markov models to stochastic context-free grammars.
It is used to compute expectations, for example as part of the expectation–maximization algorithm (an unsupervised learning algorithm). Inside and outside probabilities[edit] The inside probability is the total probability of generating words , given the root nonterminal and a grammar The outside probability is the total probability of beginning with the start symbol and generating the nonterminal and all the words outside , given a grammar Computing Inside probabilities[edit] Base Case: General Case: Suppose there is a rule in the grammar, then the probability of generating starting with a subtree rooted at is: is just the sum over all such possible rules: Here the start symbol is J.
File:EM-Gaussian-data.svg. From Wikimedia Commons, the free media repository Summary[edit] Licensing[edit] File history Click on a date/time to view the file as it appeared at that time. You cannot overwrite this file. File usage on other wikis The following other wikis use this file: Fuzzy clustering. Fuzzy clustering is a class of algorithms for cluster analysis in which the allocation of data points to clusters is not "hard" (all-or-nothing) but "fuzzy" in the same sense as fuzzy logic. Explanation of clustering[edit] Data clustering is the process of dividing data elements into classes or clusters so that items in the same class are as similar as possible, and items in different classes are as dissimilar as possible.
Depending on the nature of the data and the purpose for which clustering is being used, different measures of similarity may be used to place items into classes, where the similarity measure controls how the clusters are formed. Some examples of measures that can be used as in clustering include distance, connectivity, and intensity. In hard clustering, data is divided into distinct clusters, where each data element belongs to exactly one cluster.
One of the most widely used fuzzy clustering algorithms is the Fuzzy C-Means (FCM) Algorithm (Bezdek 1981). See also[edit] Cluster analysis. The result of a cluster analysis shown as the coloring of the squares into three clusters. Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics. Besides the term clustering, there are a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology (from Greek βότρυς "grape") and typological analysis.
The subtle differences are often in the usage of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest. Definition[edit] Algorithms[edit] Expectation–maximization algorithm. In statistics, an expectation–maximization (EM) algorithm is an iterative method for finding maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.
EM clustering of Old Faithful eruption data. The random initial model (which due to the different scales of the axes appears to be two very flat and wide spheres) is fit to the observed data. History[edit] The convergence analysis of the Dempster-Laird-Rubin paper was flawed and a correct convergence analysis was published by C.