By Assad Ebrahim, on November 15th, 2010 (7,152 views)
Topic: Data Science
(Statistics and Data Mining II)
Automated decision problems are frequently encountered in statistical data processing and data mining. An heuristic filter or heuristic classifier typically has a limited set of input data from which to arrive at a set of conclusions and make a decision: REJECT, ACCEPT, or UNDETERMINED. In such cases, preprocessing the input data before applying the heuristic classifier can substantially enhance the performance of the decision system.
In this article, I’ll motivate the use of a radartracking algorithm to improve the performance of automated decision making and statistical estimation in data processing. I will illustrate using the website visitation statistics problem.
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By Assad Ebrahim, on February 25th, 2010 (30,313 views)
Topic: Mathematics, Technical
Updated! February 5, 2017
The value of zero raised to the zero power, , has been discussed since the time of Euler in the 18th century (1700s). There are three reasonable choices: 1,0, or “indeterminate”. Despite consensus amongst mathematicians that the correct answer is one, computing platforms seem to have reached a variety of conclusions: Google, R, Octave, Ruby, and Microsoft Calculator choose 1; Hexelon Max and TI36 calculator choose 0; and Maxima and Excel throw an error (indeterminate). In this article, I’ll explain why, for discrete mathematics, the correct answer cannot be anything other than 0^0=1, for reasons that go beyond consistency with the Binomial Theorem (Knuth’s argument).
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By Assad Ebrahim, on February 8th, 2010 (13,830 views)
Topic: Technical
By Assad Ebrahim, on January 31st, 2010 (4,489 views)
Topic: Education, Phenomenology
Good mathematical technique can bring the solution to certain mathematical questions within reach. By a proper formulation (one that is both tractable and that generalizes readily) and the use of mechanical techniques, one can often pass from a single insight to the solution of a family of problems, and in some cases, to the solution of the general question itself. … Good mathematical technique has built within it the mathematical insight of the best of previous generations.
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