Curse of dimensionality, Advanced Statistics

Assignment Help:

The phrase first spoken by one of the witches in Macbeth. Now this is used to describe the exponential rise in the number of possible locations in the multivariate space as dimensionality increases. Thus the single binary variable has the two probable values, a 10-dimensional binary vector has over the thousand possible values and a 20-dimensional binary vector over the million possible values. This implies that sample sizes should be increase exponentially with the dimension in order to maintain the constant average sample size in the cells of space. Another consequence is that, for the multivariate normal distribution, the vast mass of the probability lies far from the centre of it if the dimensionality is large.


Related Discussions:- Curse of dimensionality

Oracle property, Oracle property is a name given to techniques for estimat...

Oracle property is a name given to techniques for estimating the regression parameters in the models fitted to high-dimensional data which have the property that they can correctl

Game theory, This is the branch of mathematics which deals with the theory ...

This is the branch of mathematics which deals with the theory of contests between two or more players under the specified sets of rules. The subject supposes a statistical aspect w

Distribution free methods, The statistical methods for estimation and infer...

The statistical methods for estimation and inference which are based on a function of sample observations, probability distribution of which does not rely upon a complete speci?cat

Explain Genetic algorithms, Genetic algorithms: The optimization events mo...

Genetic algorithms: The optimization events motivated by the biological analogies. The prime idea is to try to mimic the 'survival of the fittest' rule of the genetic mutation in

Normality - reasons for screening data, Normality - Reasons for Screening...

Normality - Reasons for Screening Data Prior to analyzing multivariate normality, one should consider univariate normality Histogram, Normal Q-Qplot (values on x axis

Computer-assisted interviews, Computer-assisted interviews : A method or te...

Computer-assisted interviews : A method or technique of interviewing subjects in which the interviewer reads the question from the computer screen instead of the printed page, and

Statistics HW, we are testing : Ho: µ=40 versus Ha: µ>40 (a= 0.01) Suppose...

we are testing : Ho: µ=40 versus Ha: µ>40 (a= 0.01) Suppose that the test statistic is z0=2.75 based on a sample size of n=25. Assume that data are normal with mean mu and standa

Explain information theory., Information theory: This is the branch of app...

Information theory: This is the branch of applied probability theory applicable to various communication and signal processing problems in the field of engineering and biology. In

Mortality odds ratio, Mortality odds ratio  is the ratio equivalent to the ...

Mortality odds ratio  is the ratio equivalent to the odds ratio used in case-control studies where the equivalent of the cases are deaths from the cause of interest and the equival

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd