Package 'pvclass' reference manual

Title:	P-Values for Classification
Description:	Computes nonparametric p-values for the potential class memberships of new observations as well as cross-validated p-values for the training data. The p-values are based on permutation tests applied to an estimated Bayesian likelihood ratio, using a plug-in statistic for the Gaussian model, 'k nearest neighbors', 'weighted nearest neighbors' or 'penalized logistic regression'. Additionally, it provides graphical displays and quantitative analyses of the p-values.
Authors:	Niki Zumbrunnen <[email protected]>, Lutz Duembgen <[email protected]>.
Maintainer:	Niki Zumbrunnen <[email protected]>
License:	GPL (>= 2)
Version:	1.4
Built:	2024-10-27 06:27:11 UTC
Source:	CRAN

P-Values for Classification

Description

Computes nonparametric p-values for the potential class memberships of new observations as well as cross-validated p-values for the training data. The p-values are based on permutation tests applied to an estimated Bayesian likelihood ratio, using a plug-in statistic for the Gaussian model, 'k nearest neighbors', 'weighted nearest neighbors' or 'penalized logistic regression'.
Additionally, it provides graphical displays and quantitative analyses of the p-values.

Details

Use cvpvs to compute cross-validated p-values, pvs to classify new observations and analyze.pvs to analyze the p-values.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

cv <- cvpvs(X,Y)
analyze.pvs(cv,Y)

pv <- pvs(NewX, X, Y, method = 'k', k = 10)
analyze.pvs(pv)
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

cv <- cvpvs(X,Y)
analyze.pvs(cv,Y)

pv <- pvs(NewX, X, Y, method = 'k', k = 10)
analyze.pvs(pv)

Analyze P-Values

Description

Graphical displays and quantitative analyses of a matrix of p-values.

Usage

 analyze.pvs(pv, Y = NULL, alpha = 0.05, roc = TRUE, pvplot = TRUE, cex = 1) analyze.pvs(pv, Y = NULL, alpha = 0.05, roc = TRUE, pvplot = TRUE, cex = 1)

Arguments

`pv`	matrix with p-values, e.g. output of `cvpvs` or `pvs`.
`Y`	optional. Vector indicating the classes which the observations belong to.
`alpha`	test level, i.e. 1 - confidence level.
`roc`	logical. If `TRUE` and `Y` is not `NULL`, ROC curves are plotted.
`pvplot`	logical. If `TRUE` or `Y` is `NULL`, the p-values are displayed graphically.
`cex`	A numerical value giving the amount by which plotting text should be magnified relative to the default.

Details

Displays the p-values graphically, i.e. it plots for each p-value a rectangle. The area of this rectangle is proportional to the the p-value. The rectangle is drawn blue if the p-value is greater than alpha and red otherwise.
If Y is not NULL, i.e. the class memberships of the observations are known (e.g. cross-validated p-values), then additionally it plots the empirical ROC curves and prints some empirical conditional inclusion probabilities $I(b,\theta)$ and/or pattern probabilities $P(b,S)$ . Precisely, $I(b,\theta)$ is the proportion of training observations of class $b$ whose p-value for class $\theta$ is greater than $\alpha$ , while $P(b,S)$ is the proportion of training observations of class $b$ such that the $(1 - \alpha)$ -prediction region equals $S$ .

Value

`T`	Table containing empirical conditional inclusion and/or pattern probabilities for each class $b$ . In case of $L = 2$ or $L=3$ classes, all patterns $S$ are considered. In case of $L > 3$ , all inclusion probabilities and some special patters $S$ are considered.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

cv <- cvpvs(X,Y)
analyze.pvs(cv,Y)

pv <- pvs(NewX, X, Y, method = 'k', k = 10)
analyze.pvs(pv)
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

cv <- cvpvs(X,Y)
analyze.pvs(cv,Y)

pv <- pvs(NewX, X, Y, method = 'k', k = 10)
analyze.pvs(pv)

Medical Dataset

Description

This data set collected by Dr. Bürk at the university hospital in Lübeck contains data of 21556 surgeries in a certain time period (end of the nineties). Besides the mortality and the morbidity it contains 21 variables describing the condition of the patient and the surgery.

Usage

data(buerk)data(buerk)

Format

A data frame with 21556 observations on the following 23 variables.

age: Age in years
sex: Sex (1 = female, 0 = male)
asa: ASA-Score (American Society of Anesthesiologists), describes the physical condition on an ordinal scale:
1 = A normal healthy patient
2 = A patient with mild systemic disease
3 = A patient with severe systemic disease
4 = A patient with severe systemic disease that is a constant threat to life
5 = A moribund patient who is not expected to survive without the operation
6 = A declared brain-dead patient whose organs are being removed for donor purposes
rf_cer: Risk factor: cerebral (1 = yes, 0 = no)
rf_car: Risk factor: cardiovascular (1 = yes, 0 = no)
rf_pul: Risk factor: pulmonary (1 = yes, 0 = no)
rf_ren: Risk factor: renal (1 = yes, 0 = no)
rf_hep: Risk factor: hepatic (1 = yes, 0 = no)
rf_imu: Risk factor: immunological (1 = yes, 0 = no)
rf_metab: Risk factor: metabolic (1 = yes, 0 = no)
rf_noc: Risk factor: uncooperative, unreliable (1 = yes, 0 = no)
e_malig: Etiology: malignant (1 = yes, 0 = no)
e_vascu: Etiology: vascular (1 = yes, 0 = no)
antibio: Antibiotics therapy (1 = yes, 0 = no)
op: Surgery indicated (1 = yes, 0 = no)
opacute: Emergency operation (1 = yes, 0 = no)
optime: Surgery time in minutes
opsepsis: Septic surgery (1 = yes, 0 = no)
opskill: Expirienced surgeond, i.e. senior physician (1 = yes, 0 = no)
blood: Blood transfusion necessary (1 = yes, 0 = no)
icu: Intensive care necessary (1 = yes, 0 = no)
mortal: Mortality (1 = yes, 0 = no)
morb: Morbidity (1 = yes, 0 = no)

Source

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Cross-Validated P-Values

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data.

Usage

cvpvs(X, Y, method = c('gaussian','knn','wnn', 'logreg'), ...)
cvpvs(X, Y, method = c('gaussian','knn','wnn', 'logreg'), ...)

Arguments

`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`method`	one of the following methods: 'gaussian': plug-in statistic for the standard Gaussian model, 'knn': k nearest neighbors, 'wnn': weighted nearest neighbors, 'logreg': multicategory logistic regression with $l1$ -penalization.
`...`	further arguments depending on the method (see `cvpvs.gaussian,` `cvpvs.knn, cvpvs.wnn, cvpvs.logreg`).

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using a plug-in statistic for the Gaussian model, 'k nearest neighbors', 'weighted nearest neighbors' or multicategory logistic regression with $l1$ -penalization (see cvpvs.gaussian, cvpvs.knn, cvpvs.wnn, cvpvs.logreg) with estimated prior probabilities $N(b)/n$ . Here $N(b)$ is the number of observations of class $b$ and $n$ is the total number of observations.

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[,1:4]
Y <- iris[,5]

cvpvs(X,Y,method='k',k=10,distance='d')
X <- iris[,1:4]
Y <- iris[,5]

cvpvs(X,Y,method='k',k=10,distance='d')

Cross-Validated P-Values (Gaussian)

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on a plug-in statistic for the standard Gaussian model. The latter means that the conditional distribution of $X$ , given $Y=y$ , is Gaussian with mean depending on $y$ and a global covariance matrix.

Usage

cvpvs.gaussian(X, Y, cova = c('standard', 'M', 'sym'))
cvpvs.gaussian(X, Y, cova = c('standard', 'M', 'sym'))

Arguments

`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using a plug-in statistic for the standard Gaussian model with estimated prior probabilities $N(b)/n$ . Here $N(b)$ is the number of observations of class $b$ and $n$ is the total number of observations.

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.gaussian(X, Y, cova = 'standard')
X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.gaussian(X, Y, cova = 'standard')

Cross-Validated P-Values (k Nearest Neighbors)

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'k nearest neighbors'.

Usage

cvpvs.knn(X, Y, k = NULL, distance = c('euclidean', 'ddeuclidean',
          'mahalanobis'), cova = c('standard', 'M', 'sym'))
cvpvs.knn(X, Y, k = NULL, distance = c('euclidean', 'ddeuclidean',
          'mahalanobis'), cova = c('standard', 'M', 'sym'))

Arguments

`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`k`	number of nearest neighbors. If `k` is a vector or `k = NULL`, the program searches for the best `k`. For more information see section 'Details'.
`distance`	the distance measure: "euclidean": fixed Euclidean distance, "ddeuclidean": data driven Euclidean distance (component-wise standardization), "mahalanobis": Mahalanobis distance.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'k nearest neighbors' with estimated prior probabilities $N(b)/n$ . Here $N(b)$ is the number of observations of class $b$ and $n$ is the total number of observations.
If k is a vector, the program searches for the best k. To determine the best k for the p-value PV[i,b], the class label of the training observation $X[i,]$ is set temporarily to b and then for all training observations with Y[j] != b the proportion of the k nearest neighbors of X[j,] belonging to class b is computed. Then the k which minimizes the sum of these values is chosen.
If k = NULL, it is set to 2:ceiling(length(Y)/2).

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
If k is a vector or NULL, PV has an attribute "opt.k", which is a matrix and opt.k[i,b] is the best k for observation X[i,] and class b (see section 'Details'). opt.k[i,b] is used to compute the p-value for observation X[i,] and class b.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.knn(X, Y, k = c(5, 10, 15))
X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.knn(X, Y, k = c(5, 10, 15))

Cross-Validated P-Values (Penalized Multicategory Logistic Regression)

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'penalized logistic regression'.

Usage

cvpvs.logreg(X, Y, tau.o=10, find.tau=FALSE, delta=2, tau.max=80, tau.min=1,
             pen.method = c("vectors", "simple", "none"), progress = TRUE)
cvpvs.logreg(X, Y, tau.o=10, find.tau=FALSE, delta=2, tau.max=80, tau.min=1,
             pen.method = c("vectors", "simple", "none"), progress = TRUE)

Arguments

`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`tau.o`	the penalty parameter (see section 'Details' below).
`find.tau`	logical. If TRUE the program searches for the best `tau`. For more information see section 'Details'.
`delta`	factor for the penalty parameter. Should be greater than 1. Only needed if `find.tau == TRUE`.
`tau.max`	maximal penalty parameter considered. Only needed if `find.tau == TRUE`.
`tau.min`	minimal penalty parameter considered. Only needed if `find.tau == TRUE`.
`pen.method`	the method of penalization (see section 'Details' below).
`progress`	optional parameter for reporting the status of the computations.

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that Y[i] equals b, based on the remaining training observations.
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'penalized logistic regression'. This means, the conditional probability of $Y = y$ , given $X = x$ , is assumed to be proportional to $exp(a_y + b_y^T x)$ . The parameters $a_y$ , $b_y$ are estimated via penalized maximum log-likelihood. The penalization is either a weighted sum of the euclidean norms of the vectors $(b_1[j],b_2[j],\ldots,b_L[j])$ (pen.method=='vectors') or a weighted sum of all moduli $|b_y[j]|$ (pen.method=='simple'). The weights are given by tau.o times the sample standard deviation (within groups) of the $j$ -th components of the feature vectors. In case of pen.method=='none', no penalization is used, but this option may be unstable.
If find.tau == TRUE, the program searches for the best penalty parameter. To determine the best parameter tau for the p-value PV[i,b], the class label of the training observation X[i,] is set temporarily to b and then for all training observations with Y[j] != b the estimated probability of X[j,] belonging to class b is computed. Then the tau which minimizes the sum of these values is chosen. First, tau.o is compared with tau.o*delta. If tau.o*delta is better, it is compared with tau.o*delta^2, etc. The maximal parameter considered is tau.max. If tau.o is better than tau.o*delta, it is compared with tau.o*delta^-1, etc. The minimal parameter considered is tau.min.

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ , based on the remaining training observations.
If find.tau == TRUE, PV has an attribute "tau.opt", which is a matrix and tau.opt[i,b] is the best tau for observation X[i,] and class b (see section 'Details'). tau.opt[i,b] is used to compute the p-value for observation X[i,] and class b.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

## Not run: 
X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.logreg(X, Y, tau.o=1, pen.method="vectors",progress=TRUE)

## End(Not run)

# A bigger data example: Buerk's hospital data.
## Not run: 
data(buerk)
X.raw <- as.matrix(buerk[,1:21])
Y.raw <- buerk[,22]
n0.raw <- sum(1 - Y.raw)
n1 <- sum(Y.raw)
n0 <- 3*n1

X0 <- X.raw[Y.raw==0,]
X1 <- X.raw[Y.raw==1,]

tmpi0 <- sample(1:n0.raw,size=n0,replace=FALSE)
tmpi1 <- sample(1:n1    ,size=n1,replace=FALSE)

X <- rbind(X0[tmpi0,],X1)
Y <- c(rep(1,n0),rep(2,n1))

str(X)
str(Y)

PV <- cvpvs.logreg(X,Y,
	tau.o=5,pen.method="v",progress=TRUE)

analyze.pvs(Y=Y,pv=PV,pvplot=FALSE)

## End(Not run)

## Not run: 
X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.logreg(X, Y, tau.o=1, pen.method="vectors",progress=TRUE)

## End(Not run)

# A bigger data example: Buerk's hospital data.
## Not run: 
data(buerk)
X.raw <- as.matrix(buerk[,1:21])
Y.raw <- buerk[,22]
n0.raw <- sum(1 - Y.raw)
n1 <- sum(Y.raw)
n0 <- 3*n1

X0 <- X.raw[Y.raw==0,]
X1 <- X.raw[Y.raw==1,]

tmpi0 <- sample(1:n0.raw,size=n0,replace=FALSE)
tmpi1 <- sample(1:n1    ,size=n1,replace=FALSE)

X <- rbind(X0[tmpi0,],X1)
Y <- c(rep(1,n0),rep(2,n1))

str(X)
str(Y)

PV <- cvpvs.logreg(X,Y,
	tau.o=5,pen.method="v",progress=TRUE)

analyze.pvs(Y=Y,pv=PV,pvplot=FALSE)

## End(Not run)

Cross-Validated P-Values (Weighted Nearest Neighbors)

Description

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'weighted nearest-neighbors'.

Usage

cvpvs.wnn(X, Y, wtype = c('linear', 'exponential'), W = NULL,
          tau = 0.3, distance = c('euclidean', 'ddeuclidean',
          'mahalanobis'), cova = c('standard', 'M', 'sym'))
cvpvs.wnn(X, Y, wtype = c('linear', 'exponential'), W = NULL,
          tau = 0.3, distance = c('euclidean', 'ddeuclidean',
          'mahalanobis'), cova = c('standard', 'M', 'sym'))

Arguments

`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`wtype`	type of the weight function (see section 'Details' below).
`W`	vector of the (decreasing) weights (see section 'Details' below).
`tau`	parameter of the weight function. If `tau` is a vector or `tau = NULL`, the program searches for the best `tau`. For more information see section 'Details'.
`distance`	the distance measure: "euclidean": fixed Euclidean distance, "ddeuclidean": data driven Euclidean distance (component-wise standardization), "mahalanobis": Mahalanobis distance.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that Y[i] equals b.
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'weighted nearest neighbors' with estimated prior probabilities $N(b)/n$ . Here $N(b)$ is the number of observations of class $b$ and $n$ is the total number of observations.
The (decreasing) weights for the observations can be either indicated with a $n$ dimensional vector W or (if W = NULL) one of the following weight functions can be used:
linear:

$W_i = \max(1-\frac{i}{n}/\tau,0),$

exponential:

$W_i = (1-\frac{i}{n})^\tau.$

If tau is a vector, the program searches for the best tau. To determine the best tau for the p-value PV[i,b], the class label of the training observation $X[i,]$ is set temporarily to b and then for all training observations with Y[j] != b the sum of the weights of the observations belonging to class b is computed. Then the tau which minimizes the sum of these values is chosen.
If W = NULL and tau = NULL, tau is set to seq(0.1,0.9,0.1) if wtype = "l" and to c(1,5,10,20) if wtype = "e".

Value

PV is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
If tau is a vector or NULL (and W = NULL), PV has an attribute "opt.tau", which is a matrix and opt.tau[i,b] is the best tau for observation X[i,] and class b (see section 'Details'). "opt.tau" is used to compute the p-values.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.wnn(X, Y, wtype = 'l', tau = 0.5)
X <- iris[, 1:4]
Y <- iris[, 5]

cvpvs.wnn(X, Y, wtype = 'l', tau = 0.5)

P-Values to Classify New Observations

Description

Computes nonparametric p-values for the potential class memberships of new observations.

Usage

pvs(NewX, X, Y, method = c('gaussian', 'knn', 'wnn', 'logreg'), ...)
pvs(NewX, X, Y, method = c('gaussian', 'knn', 'wnn', 'logreg'), ...)

Arguments

`NewX`	data matrix consisting of one or several new observations (row vectors) to be classified.
`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`method`	one of the following methods: 'gaussian': plug-in statistic for the standard Gaussian model, 'knn': k nearest neighbors, 'wnn': weighted nearest neighbors, 'logreg': multicategory logistic regression with $l1$ -penalization.
`...`	further arguments depending on the method (see `pvs.gaussian, pvs.knn, pvs.wnn, pvs.logreg`).

Details

Value

PV is a matrix containing the p-values. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs(NewX, X, Y, method = 'k', k = 10)
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs(NewX, X, Y, method = 'k', k = 10)

P-Values to Classify New Observations (Gaussian)

Description

Computes nonparametric p-values for the potential class memberships of new observations. The p-values are based on a plug-in statistic for the standard Gaussian model. The latter means that the conditional distribution of $X$ , given $Y=y$ , is Gaussian with mean depending on $y$ and a global covariance matrix.

Usage

pvs.gaussian(NewX, X, Y, cova = c('standard', 'M', 'sym'))
pvs.gaussian(NewX, X, Y, cova = c('standard', 'M', 'sym'))

Arguments

`NewX`	data matrix consisting of one or several new observations (row vectors) to be classified.
`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

Value

PV is a matrix containing the p-values. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.gaussian(NewX, X, Y, cova = 'standard')
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.gaussian(NewX, X, Y, cova = 'standard')

P-Values to Classify New Observations (k Nearest Neighbors)

Description

Computes nonparametric p-values for the potential class memberships of new observations. The p-values are based on 'k nearest neighbors'.

Usage

pvs.knn(NewX, X, Y, k = NULL, distance = c('euclidean', 'ddeuclidean',
        'mahalanobis'), cova = c('standard', 'M', 'sym'))
pvs.knn(NewX, X, Y, k = NULL, distance = c('euclidean', 'ddeuclidean',
        'mahalanobis'), cova = c('standard', 'M', 'sym'))

Arguments

`NewX`	data matrix consisting of one or several new observations (row vectors) to be classified.
`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`k`	number of nearest neighbors. If `k` is a vector or `k = NULL`, the program searches for the best `k`. For more information see section 'Details'.
`distance`	the distance measure: 'euclidean': fixed Euclidean distance, 'ddeuclidean': data driven Euclidean distance (component-wise standardization), 'mahalanobis': Mahalanobis distance.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

Value

PV is a matrix containing the p-values. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
If k is a vector or NULL, PV has an attribute "opt.k", which is a matrix and opt.k[i,b] is the best k for observation NewX[i,] and class b (see section 'Details'). opt.k[i,b] is used to compute the p-value for observation NewX[i,] and class b.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.knn(NewX, X, Y, k = c(5, 10, 15))
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.knn(NewX, X, Y, k = c(5, 10, 15))

P-Values to Classify New Observations (Penalized Multicategory Logistic Regression)

Description

Computes nonparametric p-values for the potential class memberships of new observations. The p-values are based on 'penalized logistic regression'.

Usage

pvs.logreg(NewX, X, Y, tau.o = 10, find.tau=FALSE, delta=2, tau.max=80, tau.min=1,
           a0 = NULL, b0 = NULL,
           pen.method = c('vectors', 'simple', 'none'),
           progress = FALSE)
pvs.logreg(NewX, X, Y, tau.o = 10, find.tau=FALSE, delta=2, tau.max=80, tau.min=1,
           a0 = NULL, b0 = NULL,
           pen.method = c('vectors', 'simple', 'none'),
           progress = FALSE)

Arguments

`NewX`	data matrix consisting of one or several new observations (row vectors) to be classified.
`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`tau.o`	the penalty parameter (see section 'Details' below).
`find.tau`	logical. If TRUE the program searches for the best `tau`. For more information see section 'Details'.
`delta`	factor for the penalty parameter. Should be greater than 1. Only needed if `find.tau == TRUE`.
`tau.max`	maximal penalty parameter considered. Only needed if `find.tau == TRUE`.
`tau.min`	minimal penalty parameter considered. Only needed if `find.tau == TRUE`.
`a0`, `b0`	optional starting values for logistic regression.
`pen.method`	the method of penalization (see section 'Details' below).
`progress`	optional parameter for reporting the status of the computations.

Details

Computes nonparametric p-values for the potential class memberships of new observations. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that Y[i] equals b.
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'penalized logistic regression'. This means, the conditional probability of $Y = y$ , given $X = x$ , is assumed to be proportional to $exp(a_y + b_y^T x)$ . The parameters $a_y$ , $b_y$ are estimated via penalized maximum log-likelihood. The penalization is either a weighted sum of the euclidean norms of the vectors $(b_1[j],b_2[j],\ldots,b_L[j])$ (pen.method=='vectors') or a weighted sum of all moduli $|b_{\theta}[j]|$ (pen.method=='simple'). The weights are given by tau.o times the sample standard deviation (within groups) of the $j$ -th components of the feature vectors. In case of pen.method=='none', no penalization is used, but this option may be unstable.
If find.tau == TRUE, the program searches for the best penalty parameter. To determine the best parameter tau for the p-value PV[i,b], the new observation NewX[i,] is added to the training data with class label b and then for all training observations with Y[j] != b the estimated probability of X[j,] belonging to class b is computed. Then the tau which minimizes the sum of these values is chosen. First, tau.o is compared with tau.o*delta. If tau.o*delta is better, it is compared with tau.o*delta^2, etc. The maximal parameter considered is tau.max. If tau.o is better than tau.o*delta, it is compared with tau.o*delta^-1, etc. The minimal parameter considered is tau.min.

Value

PV is a matrix containing the p-values. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
If find.tau == TRUE, PV has an attribute "tau.opt", which is a matrix and tau.opt[i,b] is the best tau for observation NewX[i,] and class b (see section 'Details'). tau.opt[i,b] is used to compute the p-value for observation NewX[i,] and class b.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.logreg(NewX, X, Y, tau.o=1, pen.method="vectors", progress=TRUE)

# A bigger data example: Buerk's hospital data.
## Not run: 
data(buerk)
X.raw <- as.matrix(buerk[,1:21])
Y.raw <- buerk[,22]
n0.raw <- sum(1 - Y.raw)
n1 <- sum(Y.raw)
n0 <- 3*n1

X0 <- X.raw[Y.raw==0,]
X1 <- X.raw[Y.raw==1,]

tmpi0 <- sample(1:n0.raw,size=3*n1,replace=FALSE)
tmpi1 <- sample(1:n1    ,size=  n1,replace=FALSE)

Xtrain <- rbind(X0[tmpi0[1:(n0-100)],],X1[1:(n1-100),])
Ytrain <- c(rep(1,n0-100),rep(2,n1-100))
Xtest <- rbind(X0[tmpi0[(n0-99):n0],],X1[(n1-99):n1,])
Ytest <- c(rep(1,100),rep(2,100))

PV <- pvs.logreg(Xtest,Xtrain,Ytrain,tau.o=2,progress=TRUE)
analyze.pvs(Y=Ytest,pv=PV,pvplot=FALSE)

## End(Not run)
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.logreg(NewX, X, Y, tau.o=1, pen.method="vectors", progress=TRUE)

# A bigger data example: Buerk's hospital data.
## Not run: 
data(buerk)
X.raw <- as.matrix(buerk[,1:21])
Y.raw <- buerk[,22]
n0.raw <- sum(1 - Y.raw)
n1 <- sum(Y.raw)
n0 <- 3*n1

X0 <- X.raw[Y.raw==0,]
X1 <- X.raw[Y.raw==1,]

tmpi0 <- sample(1:n0.raw,size=3*n1,replace=FALSE)
tmpi1 <- sample(1:n1    ,size=  n1,replace=FALSE)

Xtrain <- rbind(X0[tmpi0[1:(n0-100)],],X1[1:(n1-100),])
Ytrain <- c(rep(1,n0-100),rep(2,n1-100))
Xtest <- rbind(X0[tmpi0[(n0-99):n0],],X1[(n1-99):n1,])
Ytest <- c(rep(1,100),rep(2,100))

PV <- pvs.logreg(Xtest,Xtrain,Ytrain,tau.o=2,progress=TRUE)
analyze.pvs(Y=Ytest,pv=PV,pvplot=FALSE)

## End(Not run)

P-Values to Classify New Observations (Weighted Nearest Neighbors)

Description

Computes nonparametric p-values for the potential class memberships of new observations. The p-values are based on 'weighted nearest-neighbors'.

Usage

pvs.wnn(NewX, X, Y, wtype = c('linear', 'exponential'), W = NULL,
        tau = 0.3, distance = c('euclidean', 'ddeuclidean',
        'mahalanobis'), cova = c('standard', 'M', 'sym'))
pvs.wnn(NewX, X, Y, wtype = c('linear', 'exponential'), W = NULL,
        tau = 0.3, distance = c('euclidean', 'ddeuclidean',
        'mahalanobis'), cova = c('standard', 'M', 'sym'))

Arguments

`NewX`	data matrix consisting of one or several new observations (row vectors) to be classified.
`X`	matrix containing training observations, where each observation is a row vector.
`Y`	vector indicating the classes which the training observations belong to.
`wtype`	type of the weight function (see section 'Details' below).
`W`	vector of the (decreasing) weights (see section 'Details' below).
`tau`	parameter of the weight function. If `tau` is a vector or `tau = NULL`, the program searches for the best `tau`. For more information see section 'Details'.
`distance`	the distance measure: 'euclidean': fixed Euclidean distance, 'ddeuclidean': data driven Euclidean distance (component-wise standardization), 'mahalanobis': Mahalanobis distance.
`cova`	estimator for the covariance matrix: 'standard': standard estimator, 'M': M-estimator, 'sym': symmetrized M-estimator.

Details

$W_i = \max(1-\frac{i}{n}/\tau,0),$

exponential:

$W_i = (1-\frac{i}{n})^\tau.$

If tau is a vector, the program searches for the best tau. To determine the best tau for the p-value PV[i,b], the new observation NewX[i,] is added to the training data with class label b and then for all training observations with Y[j] != b the sum of the weights of the observations belonging to class b is computed. Then the tau which minimizes the sum of these values is chosen.
If tau = NULL, it is set to seq(0.1,0.9,0.1) if wtype = "l" and to c(1,5,10,20) if wtype = "e".

Value

PV is a matrix containing the p-values. Precisely, for each new observation NewX[i,] and each class b the number PV[i,b] is a p-value for the null hypothesis that $Y[i] = b$ .
If tau is a vector or NULL (and W = NULL), PV has an attribute "opt.tau", which is a matrix and opt.tau[i,b] is the best tau for observation NewX[i,] and class b (see section 'Details'). opt.tau[i,b] is used to compute the p-value for observation NewX[i,] and class b.

Author(s)

Niki Zumbrunnen [email protected]
Lutz Dümbgen [email protected]
www.imsv.unibe.ch/duembgen/index_ger.html

References

Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04

Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.

Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.

Examples

X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.wnn(NewX, X, Y, wtype = 'l', tau = 0.5)
X <- iris[c(1:49, 51:99, 101:149), 1:4]
Y <- iris[c(1:49, 51:99, 101:149), 5]
NewX <- iris[c(50, 100, 150), 1:4]

pvs.wnn(NewX, X, Y, wtype = 'l', tau = 0.5)

Package 'pvclass'

Help Index

P-Values for Classification

Description

Details

Author(s)

References

Examples

Analyze P-Values

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Medical Dataset

Description

Usage

Format

Source

References

Cross-Validated P-Values

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-Validated P-Values (Gaussian)

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-Validated P-Values (k Nearest Neighbors)

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-Validated P-Values (Penalized Multicategory Logistic Regression)

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-Validated P-Values (Weighted Nearest Neighbors)

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

P-Values to Classify New Observations

Description

Usage

Arguments

Details

Value