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

Explain literature controls, Literature controls : The patients with the di...

Literature controls : The patients with the disease of interest who have received, in the past, one of two treatments under the investigation, and for whom the results have been pu

Data reduction, The method of summarizing the large amounts of data by form...

The method of summarizing the large amounts of data by forming the frequency distributions, scatter diagrams, histograms, etc., and calculating statistics like means variances and

Principal components analysis, Principal components analysis is a process ...

Principal components analysis is a process for analysing multivariate data which transforms original variables into the new ones which are uncorrelated and account for decreasing

Tests for heteroscedasticity, Lagrange Multiplier (LM) test The Null Hy...

Lagrange Multiplier (LM) test The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β 1

Conditional logistic regression, Conditional logistic regression : The form...

Conditional logistic regression : The form of logistic regression designed to work with the clustered data, such as data including matched pairs of the subjects, in which subject-s

Locally weighted regression, Locally weighted regression  is the method of ...

Locally weighted regression  is the method of regression analysis in which the polynomials of degree one (linear) or two (quadratic) are used to approximate regression function in

Regression to the mean, Regression to the mean is the procedure first note...

Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten

Length-biased data, Length-biased data is a data which arise when the prob...

Length-biased data is a data which arise when the probability that an item is sampled is proportional to its own length. A main example of this situation occurs in the renewal the

Blinding, Blinding : A procedure used in clinical trials to get rid of the ...

Blinding : A procedure used in clinical trials to get rid of the possible bias which might be introduced if the patient and/or the doctor knew which treatment the patient is receiv

Cycle hunt analysis, The procedure for clustering variables in the multivar...

The procedure for clustering variables in the multivariate data, which forms the clusters by performing one or other of the below written three operations: * combining two varia

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