| Title: | Methods for Changepoint Detection |
|---|---|
| Description: | Implements various mainstream and specialised changepoint methods for finding single and multiple changepoints within data. Many popular non-parametric and frequentist methods are included. The cpt.mean(), cpt.var(), cpt.meanvar() functions should be your first point of call. |
| Authors: | Rebecca Killick [aut, cre], Kaylea Haynes [ctb], Harjit Hullait [ctb], Idris Eckley [ths], Paul Fearnhead [ctb, ths], Robin Long [ctb], Jamie Lee [ctr] |
| Maintainer: | Rebecca Killick <[email protected]> |
| License: | GPL |
| Version: | 2.3 |
| Built: | 2024-11-03 21:16:03 UTC |
| Source: | https://github.com/rkillick/changepoint |
Implements various mainstream and specialised changepoint methods for finding single and multiple changepoints within data. Many popular non-parametric and frequentist methods are included. Users should start by looking at the documentation for cpt.mean(), cpt.var() and cpt.meanvar().
| Package: | changepoint |
| Type: | Package |
| Version: | 2.3 |
| Date: | 2024-11-02 |
| License: | GPL |
| LazyLoad: | yes |
Rebecca Killick <[email protected]>, with contributions from Kaylea Haynes, Harjit Hullait, Paul Fearnhead, Robin Long and Jamie Lee.
Maintainer: Rebecca Killick <[email protected]>
Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39–54
# change in variance set.seed(1) x=c(rnorm(100,0,1),rnorm(100,0,10)) ansvar=cpt.var(x) plot(ansvar) print(ansvar) # identifies 1 changepoint at 100 # change in mean y=c(rnorm(100,0,1),rnorm(100,5,1)) ansmean=cpt.mean(y) plot(ansmean,cpt.col='blue') print(ansmean) # change in mean and variance z=c(rnorm(100,0,1),rnorm(100,2,10)) ansmeanvar=cpt.meanvar(z) plot(ansmeanvar,cpt.width=3) print(ansmeanvar)# change in variance set.seed(1) x=c(rnorm(100,0,1),rnorm(100,0,10)) ansvar=cpt.var(x) plot(ansvar) print(ansvar) # identifies 1 changepoint at 100 # change in mean y=c(rnorm(100,0,1),rnorm(100,5,1)) ansmean=cpt.mean(y) plot(ansmean,cpt.col='blue') print(ansmean) # change in mean and variance z=c(rnorm(100,0,1),rnorm(100,2,10)) ansmeanvar=cpt.meanvar(z) plot(ansmeanvar,cpt.width=3) print(ansmeanvar)
Implements the Binary Segmentation method for identifying changepoints in a given set of summary statistics for a specified cost function and penalty.
This function is called by cpt.mean, cpt.var and cpt.meanvar when method="BinSeg". This is not intended for use by regular users of the package. It is exported for developers to call directly for speed increases or to fit alternative cost functions.
WARNING: No checks on arguments are performed!
BINSEG(sumstat, pen = 0, cost_func = "norm.mean", shape = 1, minseglen = 2, Q=5)BINSEG(sumstat, pen = 0, cost_func = "norm.mean", shape = 1, minseglen = 2, Q=5)
sumstat |
A matrix containing the summary statistics of data within which you wish to find a changepoint. Currently assumes 3 columns and uses the number of rows as the length of the data +1 (initial value of 0). |
pen |
Default choice is 0, this should be evaluated elsewhere and a numerical value entered. This should be positive - this isn't checked but results are meaningless if it isn't. |
cost_func |
The friendly name of the cost function to be called in C. If using your own cost function, this must be the name of the C function to use. |
shape |
Only required for cost_func="Gamma",default is 1. Must be a positive value, this isn't checked. |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes), default is 2. No checks are performed on the input value so it could be larger than feasible to have changes in the data. |
Q |
The maximum number of changepoints to search for (positive integer). No checks are performed and so a number larger than allowed can be input. |
This function is used as a wrapper function to implement the Binary Segmentation algorithm in C. It simply creates the necessary worker vectors, ensures all inputs are the correct type, and passes everything to the C function.
This function is exported for developer use only. It does not perform any checks on inputs (other than type coersion) and is simply a wrapper function for the C code.
A list is returned with elements:
cps |
2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row in the order identified. |
cpts |
Ordered list of optimal number of changepoints ending with n. |
op.cpts |
The optimal number changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
Rebecca Killick
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
cpt.mean,cpt.meanvar,plot-methods,cpt
#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.
This function helps to input all the necessary information into the correct format for cpt and cpt.range classes.
This function is called by cpt.mean, cpt.var and cpt.meanvar when class=TRUE. This is not intended for use by regular users of the package. It is exported for developers to call directly for speed and convenience.
WARNING: No checks on arguments are performed!
class_input(data, cpttype, method, test.stat, penalty, pen.value, minseglen, param.estimates, out=list(), Q=NA, shape=NA)class_input(data, cpttype, method, test.stat, penalty, pen.value, minseglen, param.estimates, out=list(), Q=NA, shape=NA)
data |
Data used in changepoint analysis, see |
cpttype |
Type of changepoint analysis performed as a text string, e.g. "Mean", "Mean and Variance". |
method |
Method used as a text string, see |
test.stat |
The assumed test statistic / distribution of the data as a text string. , see |
penalty |
Penalty used as a text string, see |
pen.value |
Numerical penalty value used in the analysis (positive). |
minseglen |
Minimum segment length used in the analysis (positive integer). |
param.estimates |
Logical. If TRUE then parameter estimates are calculated. If FALSE no parameter estimates are calculated and the slot is blank in the returned object. |
out |
List of output from |
Q |
The value of |
shape |
Value of the assumed known shape parameter required when test.stat="Gamma". |
This function takes all the input required for the cpt or cpt.range classes and enters it into the object.
This function is exported for developer use only. It does not perform any checks on inputs and is simply a convenience function for converting the output of the worker functions into a nice format for the cpt and cpt.range classes.
An object of class cpt or cpt.range as appropriate filled with the given attributes.
Rebecca Killick
cpt.var,cpt.mean,plot-methods,cpt
#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.
Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.
cpt.mean(data,penalty="MBIC",pen.value=0,method="PELT",Q=5,test.stat="Normal",class=TRUE, param.estimates=TRUE,minseglen=1)cpt.mean(data,penalty="MBIC",pen.value=0,method="PELT",Q=5,test.stat="Normal",class=TRUE, param.estimates=TRUE,minseglen=1)
data |
A vector, ts object or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset. |
penalty |
Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Asymptotic", "Manual" and "CROPS" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. If CROPS is specified, the penalty range is contained in the pen.value parameter; note this is a vector of length 2 which contains the minimum and maximum penalty value. Note CROPS can only be used if the method is "PELT". The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter. |
pen.value |
The theoretical type I error e.g.0.05 when using the Asymptotic penalty. A vector of length 2 (min,max) if using the CROPS penalty. The value of the penalty when using the Manual penalty option - this can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint, diffparam=difference in number of alternatve and null parameters. |
method |
Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg". Default is "PELT" (from 2.3). |
Q |
The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method. |
test.stat |
The assumed test statistic / distribution of the data. Currently only "Normal" and "CUSUM" supported. |
class |
Logical. If TRUE then an object of class |
param.estimates |
Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned. |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes), default is the minimum allowed by theory. |
This function is used to find changes in mean for data using the test statistic specfified in the test.stat parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods. A changepoint is denoted as the last observation of the segment / regime.
If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are returned. For class=FALSE the structure is as follows.
If data is a vector (single dataset) then a vector/list is returned depending on the value of method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of method.
If method is AMOC then a vector (one dataset) or matrix (multiple datasets) is returned, the columns are:
cpt |
The most probable location of a changepoint if a change was identified or NA if no changepoint. |
p value |
The p-value of the identified changepoint. |
If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. This always ends with n. If the penalty is CROPS then a list is returned with elements:
cpt.out |
A data frame containing the value of the penalty value where the number of segmentations changes, the number of segmentations and the value of the cost at that penalty value. |
changepoints |
The optimal changepoint for the different penalty values starting with the lowest penalty value |
If method is SegNeigh then a list is returned with elements:
cps |
Matrix containing the changepoint positions for 1,...,Q changepoints. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
like |
Value of the -2*log(likelihood ratio) + penalty for the optimal number of changepoints selected. |
If method is BinSeg then a list is returned with elements:
cps |
2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
Rebecca Killick
Change in Normal mean: Hinkley, D. V. (1970) Inference About the Change-Point in a Sequence of Random Variables, Biometrika 57, 1–17
CUSUM Test: M. Csorgo, L. Horvath (1997) Limit Theorems in Change-Point Analysis, Wiley
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39–54
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
cpt.var,cpt.meanvar,plot-methods,cpt
# Example of a change in mean at 100 in simulated normal data set.seed(1) x=c(rnorm(100,0,1),rnorm(100,10,1)) cpt.mean(x,penalty="SIC",method="AMOC",class=FALSE) # returns 100 to show that the null hypothesis #was rejected and the change in mean is at 100 and the confidence level is 1. ans=cpt.mean(x,penalty="Asymptotic",pen.value=0.01,method="AMOC") cpts(ans)# returns 100 to show that the null hypothesis was rejected, the change in mean is at 100 #and we are 99% confident of this result cpt.mean(x,penalty="Manual",pen.value=0.8,method="AMOC",test.stat="CUSUM") # returns 101 as the changepoint location # Example of multiple changes in mean at 50,100,150 in simulated normal data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) cpt.mean(x,penalty="Manual",pen.value="2*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal number of changepoints is 3, locations are 50,100,150. # Example of using the CROPS penalty in data set above set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) out=cpt.mean(x, pen.value = c(4,1500),penalty = "CROPS",method = "PELT") cpts.full(out) # returns 7 segmentations for penalty values between 4 and 1500. # We find segmentations with 7, 5, 4, 3, 2, 1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 3 changepoints, 50,100,150 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in mean and the second row has #no change in mean set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) y=rnorm(200,0,1) z=rbind(x,y) cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list #that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second #has no changes in variance ans=cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.# Example of a change in mean at 100 in simulated normal data set.seed(1) x=c(rnorm(100,0,1),rnorm(100,10,1)) cpt.mean(x,penalty="SIC",method="AMOC",class=FALSE) # returns 100 to show that the null hypothesis #was rejected and the change in mean is at 100 and the confidence level is 1. ans=cpt.mean(x,penalty="Asymptotic",pen.value=0.01,method="AMOC") cpts(ans)# returns 100 to show that the null hypothesis was rejected, the change in mean is at 100 #and we are 99% confident of this result cpt.mean(x,penalty="Manual",pen.value=0.8,method="AMOC",test.stat="CUSUM") # returns 101 as the changepoint location # Example of multiple changes in mean at 50,100,150 in simulated normal data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) cpt.mean(x,penalty="Manual",pen.value="2*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal number of changepoints is 3, locations are 50,100,150. # Example of using the CROPS penalty in data set above set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) out=cpt.mean(x, pen.value = c(4,1500),penalty = "CROPS",method = "PELT") cpts.full(out) # returns 7 segmentations for penalty values between 4 and 1500. # We find segmentations with 7, 5, 4, 3, 2, 1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 3 changepoints, 50,100,150 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in mean and the second row has #no change in mean set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1)) y=rnorm(200,0,1) z=rbind(x,y) cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list #that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second #has no changes in variance ans=cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.
Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.
cpt.meanvar(data,penalty="MBIC",pen.value=0,method="PELT",Q=5,test.stat="Normal", class=TRUE,param.estimates=TRUE,shape=1,minseglen=2)cpt.meanvar(data,penalty="MBIC",pen.value=0,method="PELT",Q=5,test.stat="Normal", class=TRUE,param.estimates=TRUE,shape=1,minseglen=2)
data |
A vector, ts object or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset. |
penalty |
Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Asymptotic", "Manual" and "CROPS" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. If CROPS is specified, the penalty range is contained in the pen.value parameter; note this is a vector of length 2 which contains the minimum and maximum penalty value. Note CROPS can only be used if the method is "PELT". The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter. |
pen.value |
The theoretical type I error e.g.0.05 when using the Asymptotic penalty. A vector of length 2 (min,max) if using the CROPS penalty. The value of the penalty when using the Manual penalty option - this can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint, diffparam=difference in number of alternatve and null parameters. |
method |
Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg". Default is "PELT" (from 2.3). |
Q |
The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method. |
test.stat |
The assumed test statistic / distribution of the data. Currently only "Normal", "Gamma", "Exponential" and "Poisson" are supported. |
class |
Logical. If TRUE then an object of class |
param.estimates |
Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned. |
shape |
Value of the assumed known shape parameter required when test.stat="Gamma". |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes), default is the minimum allowed by theory. |
This function is used to find changes in mean and variance for data using the test statistic specified in the test.stat parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods. A changepoint is denoted as the last observation of the segment / regime.
If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are returned. For class=FALSE the structure is as follows.
If data is a vector (single dataset) then a vector/list is returned depending on the value of method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of method.
If method is AMOC then a vector (one dataset) or matrix (multiple datasets) is returned, the columns are:
cpt |
The most probable location of a changepoint if a change was identified or NA if no changepoint. |
p value |
The p-value of the identified changepoint. |
If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. This always ends with n. If the penalty is CROPS then a list is returned with elements:
cpt.out |
A data frame containing the value of the penalty value where the number of segmentations changes, the number of segmentations and the value of the cost at that penalty value. |
changepoints |
The optimal changepoints for the different penalty values starting with the lowest penalty value |
If method is SegNeigh then a list is returned with elements:
cps |
Matrix containing the changepoint positions for 1,...,Q changepoints. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
like |
Value of the -2*log(likelihood ratio) + penalty for the optimal number of changepoints selected. |
If method is BinSeg then a list is returned with elements:
cps |
2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
Rebecca Killick
Change in Normal mean and variance: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Gamma shape parameter: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Exponential model: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
Change in Poisson model: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39–54
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
cpt.var,cpt.mean,plot-methods,cpt
# Example of a change in scale parameter (mean and variance) at 100 in simulated gamma data set.seed(1) x=c(rgamma(100,shape=1,rate=1),rgamma(100,shape=1,rate=5)) cpt.meanvar(x,penalty="SIC",method="AMOC",test.stat="Gamma",class=FALSE,shape=1) # returns 97 to #show that the null hypothesis was rejected and the change in scale parameter is at 97 ans=cpt.meanvar(x,penalty="AIC",method="AMOC",test.stat="Gamma",shape=1) cpts(ans) # returns 97 to show that the null hypothesis was rejected, the change in scale parameter is at 97 # Example of multiple changes in mean and variance at 50,100,150 in simulated normal data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) cpt.meanvar(x,penalty="Manual",pen.value="4*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal number of changepoints is 4, locations are 50,100,150,152. # Example of using the CROPS penalty in the above example set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) out=cpt.meanvar(x,pen.value=c(2*log(length(x)),100*log(length(x))),penalty="CROPS",method="PELT") cpts.full(out) # returns 6 segmentations for penalty values between 2log(n) and 100log(n). # We find segmentations with 9, 7, 4, 3, 1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 4 changepoints, 50,100,150,200 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in mean and variance and the #second row has no change in mean or variance set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) y=rnorm(200,0,1) z=rbind(x,y) cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list #that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second #has no changes in mean or variance ans=cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.# Example of a change in scale parameter (mean and variance) at 100 in simulated gamma data set.seed(1) x=c(rgamma(100,shape=1,rate=1),rgamma(100,shape=1,rate=5)) cpt.meanvar(x,penalty="SIC",method="AMOC",test.stat="Gamma",class=FALSE,shape=1) # returns 97 to #show that the null hypothesis was rejected and the change in scale parameter is at 97 ans=cpt.meanvar(x,penalty="AIC",method="AMOC",test.stat="Gamma",shape=1) cpts(ans) # returns 97 to show that the null hypothesis was rejected, the change in scale parameter is at 97 # Example of multiple changes in mean and variance at 50,100,150 in simulated normal data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) cpt.meanvar(x,penalty="Manual",pen.value="4*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal number of changepoints is 4, locations are 50,100,150,152. # Example of using the CROPS penalty in the above example set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) out=cpt.meanvar(x,pen.value=c(2*log(length(x)),100*log(length(x))),penalty="CROPS",method="PELT") cpts.full(out) # returns 6 segmentations for penalty values between 2log(n) and 100log(n). # We find segmentations with 9, 7, 4, 3, 1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 4 changepoints, 50,100,150,200 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in mean and variance and the #second row has no change in mean or variance set.seed(1) x=c(rnorm(50,0,1),rnorm(50,5,3),rnorm(50,10,1),rnorm(50,3,10)) y=rnorm(200,0,1) z=rbind(x,y) cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list #that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second #has no changes in mean or variance ans=cpt.meanvar(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.
Calculates the optimal position and (potentially) number of changepoints in regression structure for data using the user specified method.
cpt.reg(data, penalty="MBIC", pen.value=0, method="PELT", test.stat="Normal", class=TRUE, param.estimates=TRUE, shape=0, minseglen=3, tol=1e-07)cpt.reg(data, penalty="MBIC", pen.value=0, method="PELT", test.stat="Normal", class=TRUE, param.estimates=TRUE, shape=0, minseglen=3, tol=1e-07)
data |
A matrix/array or ts object containing the data to fit the models to. Col1: the dependent variable, Col2+: regressors. A check is performed validate (or include if not) that an intercept regressor is included. |
penalty |
Choice of penalty, see |
pen.value |
Additional values to be used in evaluating the penalty. |
method |
Choice changepoint algorithm. Either "AMOC" (at least one changepoint) or "PELT" (pruned exact linear time) method. Default is "PELT". |
test.stat |
Test statistic used for regression fit. Currently only "Normal" is supported which assumes a Normal distribution for the errors and fits using Residual Sum of Squares. |
class |
Logical. If |
param.estimates |
Logical. If |
shape |
Additional parameters used in the cost function. If * * * |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes). Default is set at 3, however checks (and adjustements where applicable) are performed to ensure this is not smaller than the number of regressors. |
tol |
Tolerance for the 'qr' decomposition. Default is 1e-7.
See |
This function is used to find change in linear regression structure for
data. The changes are found using the method supplied wihich can be
single changepoint (AMOC) or multiple changepoints (PELT). A changepoint is
denoted as the last observation of the segment / regime.
If class=TRUE then an object of S4 class "cpt.reg" is returned.
The slot cpts contains the changepoints that are returned. For
class=FALSE the changepoint positions are returned, along with
supplementary information about the fit detailed below. (This info is mainly
used for bug fixing.)
If data is a matrix, then a vector/list/cpt.reg is returned depending
on the of method. If data is a 3D array (multiple data sets,
with total number of data sets = dim1 and each data set of the same size)
then a list is returned where each element is either a vector/list/cpt.reg
corresponding to the fit on each data set in the order they appear in the array.
If method="AMOC" & dist="Normal" then a list is returned with:
cpts: changepoint position.
pen.value: penalty value.
If method="PELT" & dist="Normal" then a list is returned with:
cpts: changepoint positions.
lastchangecpts: index of last changepoint according to optimal sequential fit.
lastchangelike: cost at last changepont according to optimal sequential fit.
ncpts: number of changepoints according to optimal squential fit.
Rebecca Killick, Simon Taylor
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
cpt.mean,
penalty_decision,
plot-methods,
cpt,
lm.fit
## Trend change set.seed(1) x <- 1:200 beta0 <- rep(c(0,100,50,0),each=50) beta1 <- rep(c(1,-1,0,0.25),each=50) y <- beta0 + beta1*x + rnorm(200) data <- cbind(y,1,x) out <- cpt.reg(data, method="PELT", minseglen=5, penalty="MBIC", test.stat="Normal") cpts(out) ##changepoints param.est(out) ##parameter estimates (rows: beta estimates per segment) plot(out) ##plot of fit ## Seasonal change, period 12 n=100 indicator=rep(1,n) trend=1:n seasonal=cos(2*pi*(1:n -6)/12) # yearly, peak in summer cpt.s = c(rep(0,floor(n/4)), rep(2, floor(n/4)), rep(1, floor(n/4)),rep(0,n-3*floor(n/4))) ##3 Alternating Cpts y=0.1*cpt.s*1:n+cos(2*pi*(1:n -6)/12)+rnorm(n) data=cbind(y,indicator,trend,seasonal) out=cpt.reg(data, minseglen=12) plot(out,cpt.width=3) cpts(out) param.est(out) ## column order of estimates matches the column order of inputs## Trend change set.seed(1) x <- 1:200 beta0 <- rep(c(0,100,50,0),each=50) beta1 <- rep(c(1,-1,0,0.25),each=50) y <- beta0 + beta1*x + rnorm(200) data <- cbind(y,1,x) out <- cpt.reg(data, method="PELT", minseglen=5, penalty="MBIC", test.stat="Normal") cpts(out) ##changepoints param.est(out) ##parameter estimates (rows: beta estimates per segment) plot(out) ##plot of fit ## Seasonal change, period 12 n=100 indicator=rep(1,n) trend=1:n seasonal=cos(2*pi*(1:n -6)/12) # yearly, peak in summer cpt.s = c(rep(0,floor(n/4)), rep(2, floor(n/4)), rep(1, floor(n/4)),rep(0,n-3*floor(n/4))) ##3 Alternating Cpts y=0.1*cpt.s*1:n+cos(2*pi*(1:n -6)/12)+rnorm(n) data=cbind(y,indicator,trend,seasonal) out=cpt.reg(data, minseglen=12) plot(out,cpt.width=3) cpts(out) param.est(out) ## column order of estimates matches the column order of inputs
Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.
cpt.var(data,penalty="MBIC",pen.value=0,know.mean=FALSE,mu=NA,method="PELT",Q=5, test.stat="Normal",class=TRUE,param.estimates=TRUE,minseglen=2)cpt.var(data,penalty="MBIC",pen.value=0,know.mean=FALSE,mu=NA,method="PELT",Q=5, test.stat="Normal",class=TRUE,param.estimates=TRUE,minseglen=2)
data |
A vector, ts object or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset. |
penalty |
Choice of "None", "SIC", "BIC", "MBIC", "AIC", "Hannan-Quinn", "Asymptotic", "Manual" and "CROPS" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. If CROPS is specified, the penalty range is contained in the pen.value parameter; note this is a vector of length 2 which contains the minimum and maximum penalty value. Note CROPS can only be used if the method is "PELT". The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter. |
pen.value |
The theoretical type I error e.g.0.05 when using the Asymptotic penalty. A vector of length 2 (min,max) if using the CROPS penalty. The value of the penalty when using the Manual penalty option - this can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint, diffparam=difference in number of alternatve and null parameters. |
know.mean |
Only required for test.stat="Normal". Logical, if TRUE then the mean is assumed known and mu is taken as its value. If FALSE, and mu=NA (default value) then the mean is estimated via maximum likelihood. If FALSE and the value of mu is supplied, mu is not estimated but is counted as an estimated parameter for decisions. |
mu |
Only required for test.stat="Normal". Numerical value of the true mean of the data. Either single value or vector of length nrow(data). If data is a matrix and mu is a single value, the same mean is used for each row. |
method |
Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg". Default is "PELT" (from 2.3). |
Q |
The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method. |
test.stat |
The assumed test statistic / distribution of the data. Currently only "Normal" and "CSS" supported. |
class |
Logical. If TRUE then an object of class |
param.estimates |
Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned. |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes), default is the minimum allowed by theory. |
This function is used to find changes in variance for data using the test statistic specified in the test.stat parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods. A changepoint is denoted as the last observation of the segment / regime. Note that for the test.stat="CSS" option the preset penalties are log(.) to allow comparison with test.stat="Normal".
If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are returned. For class=FALSE the structure is as follows.
If data is a vector (single dataset) then a vector/list is returned depending on the value of method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of method.
If method is AMOC then a vector (one dataset) or matrix (multiple datasets) is returned, the columns are:
cpt |
The most probable location of a changepoint if a change was identified or NA if no changepoint. |
p value |
The p-value of the identified changepoint. |
If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. This always ends with n. If the penalty is CROPS then a list is returned with elements:
cpt.out |
A data frame containing the value of the penalty value where the number of segmentations changes, the number of segmentations and the value of the cost at that penalty value. |
segmentations |
The optimal segmentations for the different penalty values starting with the lowest penalty value |
If method is SegNeigh then a list is returned with elements:
cps |
Matrix containing the changepoint positions for 1,...,Q changepoints. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
like |
Value of the -2*log(likelihood ratio) + penalty for the optimal number of changepoints selected. |
If method is BinSeg then a list is returned with elements:
cps |
2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row. |
op.cpts |
The optimal changepoint locations for the penalty supplied. |
pen |
Penalty used to find the optimal number of changepoints. |
Rebecca Killick
Normal: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser
CSS: C. Inclan, G. C. Tiao (1994) Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance, Journal of the American Statistical Association 89(427), 913–923
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507–512
Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39–54
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
cpt.mean,cpt.meanvar,plot-methods,cpt
# Example of a change in variance at 100 in simulated normal data set.seed(1) x=c(rnorm(100,0,1),rnorm(100,0,10)) cpt.var(x,penalty="SIC",method="AMOC",class=FALSE) # returns 100 to show that the null hypothesis #was rejected and the change in variance is at 100 ans=cpt.var(x,penalty="Asymptotic",pen.value=0.01,method="AMOC") cpts(ans)# returns 100 to show that the null hypothesis was rejected, the change in variance is at #100 and we are 99% confident of this result # Example of multiple changes in variance at 50,100,150 in simulated data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) cpt.var(x,penalty="Manual",pen.value="log(2*log(n))",method="BinSeg",test.stat="CSS",Q=5, class=FALSE) # returns optimal number of changepoints is 4, locations are 50,53,99,150. # Example of using CROPS in the above example set.seed(1) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) out=cpt.var(x,pen.value=c(log(length(x)),100*log(length(x))),penalty="CROPS",method="PELT") cpts.full(out) # returns 7 segmentations for penalty values between log(n) and 100log(n). # We find segmentations with 7, 5, 4,3,2,1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 3 changepoints, 50,100,150 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in variance and the second row #has no change in variance set.seed(10) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) y=rnorm(200,0,1) z=rbind(x,y) cpt.var(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list that #has two elements, the first has 3 changes in variance at 50,100,149 and the second has no changes #in variance ans=cpt.var(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.# Example of a change in variance at 100 in simulated normal data set.seed(1) x=c(rnorm(100,0,1),rnorm(100,0,10)) cpt.var(x,penalty="SIC",method="AMOC",class=FALSE) # returns 100 to show that the null hypothesis #was rejected and the change in variance is at 100 ans=cpt.var(x,penalty="Asymptotic",pen.value=0.01,method="AMOC") cpts(ans)# returns 100 to show that the null hypothesis was rejected, the change in variance is at #100 and we are 99% confident of this result # Example of multiple changes in variance at 50,100,150 in simulated data set.seed(1) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) cpt.var(x,penalty="Manual",pen.value="log(2*log(n))",method="BinSeg",test.stat="CSS",Q=5, class=FALSE) # returns optimal number of changepoints is 4, locations are 50,53,99,150. # Example of using CROPS in the above example set.seed(1) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) out=cpt.var(x,pen.value=c(log(length(x)),100*log(length(x))),penalty="CROPS",method="PELT") cpts.full(out) # returns 7 segmentations for penalty values between log(n) and 100log(n). # We find segmentations with 7, 5, 4,3,2,1 and 0 changepoints. # Note that the empty final row indicates no changepoints. pen.value.full(out) # gives associated penalty transition points # CROPS does not give an optimal set of changepoints thus we may wish to explore further plot(out,diagnostic=TRUE) # looks like the segmentation with 3 changepoints, 50,100,150 is the most appropriate plot(out,ncpts=3) # Example multiple datasets where the first row has multiple changes in variance and the second row #has no change in variance set.seed(10) x=c(rnorm(50,0,1),rnorm(50,0,10),rnorm(50,0,5),rnorm(50,0,1)) y=rnorm(200,0,1) z=rbind(x,y) cpt.var(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list that #has two elements, the first has 3 changes in variance at 50,100,149 and the second has no changes #in variance ans=cpt.var(z,penalty="Asymptotic",pen.value=0.01,method="PELT") cpts(ans[[1]]) # same results as for the SegNeigh method. cpts(ans[[2]]) # same results as for the SegNeigh method.
Uses the function parameters to decide if a proposed changepoint is a true changepoint or due to random variability. Test is conducted using the user specified penalty.
This function is called by cpt.mean, cpt.var and cpt.meanvar when method="AMOC". This is not intended for use by regular users of the package. It is exported for developers to call directly for speed increases or to fit alternative cost functions.
WARNING: No checks on arguments are performed!
decision(tau,null,alt=NA,penalty="MBIC",n=0,diffparam=1,pen.value=0)decision(tau,null,alt=NA,penalty="MBIC",n=0,diffparam=1,pen.value=0)
tau |
A numeric value or vector specifying the proposed changepoint location(s). |
null |
The value of the null test statistic. If tau is a vector, so is null. If the test statistic is already known (i.e. doesn't have null and alternative components), replace the null argument with the test statistic. |
alt |
The value of the alternative test statistic (at tau). If tau is a vector, so is alt. If the test statistic is already known, then it is used in replacement of the null argument and the alternative should not be specified (default NA to account for this) |
penalty |
Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Asymptotic" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter. |
n |
The length of the original data, required to give sensible "no changepoint" output. |
diffparam |
The difference in the number of parameters in the null and alternative hypotheses, required for the SIC, BIC, AIC, Hanna-Quinn and possibly Manual penalties. |
pen.value |
The theoretical type I error e.g.0.05 when using the Asymptotic penalty. The value of the penalty when using the Manual penalty option - this can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint, diffparam=difference in number of alternatve and null parameters. |
This function is used to test whether tau is a true changepoint or not. This test uses the null-alternative as the test statistic and performs the test where the null hypothesis is no change point and the alternative hypothesis is a single changepoint at tau. The test is (null-alt)>=penalty, if TRUE then the changepoint is deemed a true changepoint, if FALSE then n (length of data) is returned.
If the test statistic is already known then it replaces the null value and the alternative is not required (default NA). In this case the test is null>=penalty, if TRUE then the changepoint is deemed a true changepoint, if FALSE then n (length of data) is returned.
This function is exported for developer use only. It does not perform any checks on inputs and is included for convenience and speed for those who are developing their own cost functions.
A list is returned with two elements, cpt and pen.
cpt |
If tau is a single value then a single value is returned: Either the value of the true changepoint location or n (length of data) if no changepoint is found. If tau is a vector of length m then a vector of length m is returned:Each element is either the value of the true changepoint location or n (length of data) if no changepoint is found. The first element is for the first value of tau and the final element is for the final value of tau. |
pen |
The numeric value of the penalty used for the test(s). |
Rebecca Killick
SIC/BIC: Schwarz, G. (1978) Estimating the Dimension of a Model, The Annals of Statistics 6(2), 461–464
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
AIC: Akaike, H. (1974) A new look at the statistical model identification, Automatic Control, IEEE Transactions on 19(6), 716–723
Hannan-Quinn: Hannan, E. J. and B. G. Quinn (1979) The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society, B 41, 190–195
# Example of finding a change out=c(100,765.1905,435.6529) # tau, null, alt decision(out[1],out[2],out[3],penalty="SIC",n=200,diffparam=1) # returns 100 as a true changepoint # Example of no change found out=c(53,-22.47768,-24.39894) # tau, null, alt decision(out[1],out[2],out[3],penalty="Manual",n=200,diffparam=1,pen.value="2*log(n)")# Example of finding a change out=c(100,765.1905,435.6529) # tau, null, alt decision(out[1],out[2],out[3],penalty="SIC",n=200,diffparam=1) # returns 100 as a true changepoint # Example of no change found out=c(53,-22.47768,-24.39894) # tau, null, alt decision(out[1],out[2],out[3],penalty="Manual",n=200,diffparam=1,pen.value="2*log(n)")
This dataset gives the daily returns of the UK FTSE 100 index from 2nd April 1984 until the 13th September 2012.
ftse100ftse100
A matrix of dimension 7187 x 2 where the first column is the Date and the second column is the Daily Return.
Yahoo! Finance
This dataset gives the G+C content in 3kb windows along the Human Chromosome from 10Mb to 33Mb (no missing data).
HC1HC1
A vector of length 23553.
http://www.ncbi.nlm.nih.gov/mapview/map_search.cgi?taxid=9606&build=previous
This dataset is taken from Lai W, Johnson MJ, Kucherlapati R, Park PJ, Bioinformatics , 2005. The paper states that the original source of the data is from Bredel et al. (2005). The data is Chromosome 13 in GBM31.
Lai2005fig3Lai2005fig3
A matrix of dimensions 797 x 5. The columns are Spot, CH, POS.start, POS.end, GBM31.
http://compbio.med.harvard.edu/Supplements/Bioinformatics05b/Profiles/Chrom_13_GBM31.xls
This dataset is taken from Lai W, Johnson MJ, Kucherlapati R, Park PJ, Bioinformatics , 2005. The paper states that the original source of the data is from Bredel et al. (2005). The data is an excerpt of chromosome 7 in GBM29 from 40 to 65 Mb.
Lai2005fig4Lai2005fig4
A matrix of dimensions 193 x 5. The columns are Spot, CH, POS.start, POS.end, GBM31.
http://compbio.med.harvard.edu/Supplements/Bioinformatics05b/Profiles/Chrom_7_from40_to65Mb_GBM29.xls
Generic function
ncpts(object)ncpts(object)
object |
Depending on the class of |
Generic Function
Depends on the class of object, see individual methods
Rebecca Killick
x=new("cpt") # new cpt object ncpts(x) # returns the number of changepoints (i.e. length of the cpts slot in x minus 1)x=new("cpt") # new cpt object ncpts(x) # returns the number of changepoints (i.e. length of the cpts slot in x minus 1)
Generic function
nseg(object,...)nseg(object,...)
object |
Depending on the class of |
... |
Other optional arguments used by some methods. |
Generic Function
Depends on the class of object, see individual methods
Rebecca Killick
x=new("cpt") # new cpt object nseg(x) # returns the number of segments (i.e. length of the cpts slot)x=new("cpt") # new cpt object nseg(x) # returns the number of segments (i.e. length of the cpts slot)
Implements the PELT method for identifying changepoints in a given set of summary statistics for a specified cost function and penalty.
This function is called by cpt.mean, cpt.var and cpt.meanvar when method="PELT". This is not intended for use by regular users of the package. It is exported for developers to call directly for speed increases or to fit alternative cost functions.
WARNING: No checks on arguments are performed!
PELT(sumstat, pen = 0, cost_func = "norm.mean", shape = 1, minseglen = 1)PELT(sumstat, pen = 0, cost_func = "norm.mean", shape = 1, minseglen = 1)
sumstat |
A matrix containing the summary statistics of data within which you wish to find a changepoint. Currently assumes 3 columns and uses the number of rows as the length of the data +1 (initial value of 0). |
pen |
Default choice is 0, this should be evaluated elsewhere and a numerical value entered. This should be positive - this isn't checked but results are meaningless if it isn't. |
cost_func |
The friendly name of the cost function to be called in C. If using your own cost function, this must be the name of the C function to use. |
shape |
Only required for cost_func="Gamma",default is 1. Must be a positive value, this isn't checked. |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes), default is 1. No checks are performed on the input value so it could be larger than feasible to have changes in the data. |
This function is used as a wrapper function to implement the PELT algorithm in C. It simply creates the necessary worker vectors, ensures all inputs are the correct type, and passes everything to the C function.
This function is exported for developer use only. It does not perform any checks on inputs (other than type coersion) and is simply a wrapper function for the C code.
A list is returned with elements:
lastchangecpts |
Vector of length n containing the last changepoint prior to each timepoint. |
cpts |
Ordered list of optimal number of changepoints ending with n. |
lastchangelike |
Vector of lenght n containing the likelihood of the optimal segmentation up to each timepoint. |
ncpts |
Number of changes identified. |
Rebecca Killick
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
CROPS: Haynes K, Eckley IA, Fearnhead P (2014) Efficient penalty search for multiple changepoint problems (in submission), arXiv:1412.3617
cpt.mean,cpt.meanvar,plot-methods,cpt
#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.#This function should only be used by developers, see its use in cpt.mean, cpt.var and cpt.meanvar.
Evaluates the arguments to give a numeric value for the penalty.
This function is called by cpt.mean, cpt.var and cpt.meanvar. This is not intended for use by regular users of the package. It is exported for developers to call directly for speed increases or to fit alternative cost functions.
WARNING: No checks on arguments are performed!
penalty_decision(penalty, pen.value, n, diffparam, asymcheck, method)penalty_decision(penalty, pen.value, n, diffparam, asymcheck, method)
penalty |
Choice of "None", "SIC", "BIC", "MBIC", AIC", "Hannan-Quinn", "Asymptotic" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the pen.value parameter. The predefined penalties listed DO count the changepoint as a parameter, postfix a 0 e.g."SIC0" to NOT count the changepoint as a parameter. |
pen.value |
The theoretical type I error e.g.0.05 when using the Asymptotic penalty. The value of the penalty when using the Manual penalty option - this can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=null likelihood, alt=alternative likelihood, tau=proposed changepoint, diffparam=difference in number of alternatve and null parameters. |
n |
The length of the original data, required to give sensible "no changepoint" output. |
diffparam |
The difference in the number of parameters (degrees of freedom) when a change is added, required for the SIC, BIC, AIC, Hanna-Quinn and possibly Manual penalties. Do NOT include the changepoint when calculating this number as this is automatically added. |
asymcheck |
A text string which translates to the asymptotic formula for a specific cost function. Currently implemented values are: |
method |
Method used as a text string, see |
This function takes the text string input and converts it to a numerical value for the specific length of data specified by n.
This function is exported for developer use only. It does not perform any checks on inputs and is included for convenience and speed for those who are developing their own cost functions.
The numeric value of the penalty.
Rebecca Killick
SIC/BIC: Schwarz, G. (1978) Estimating the Dimension of a Model, The Annals of Statistics 6(2), 461–464
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
AIC: Akaike, H. (1974) A new look at the statistical model identification, Automatic Control, IEEE Transactions on 19(6), 716–723
Hannan-Quinn: Hannan, E. J. and B. G. Quinn (1979) The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society, B 41, 190–195
# Example of finding a change out=c(100,765.1905,435.6529) # tau, null, alt decision(out[1],out[2],out[3],penalty="SIC",n=200,diffparam=1) # returns 100 as a true changepoint # Example of no change found out=c(53,-22.47768,-24.39894) # tau, null, alt decision(out[1],out[2],out[3],penalty="Manual",n=200,diffparam=1,pen.value="2*log(n)")# Example of finding a change out=c(100,765.1905,435.6529) # tau, null, alt decision(out[1],out[2],out[3],penalty="SIC",n=200,diffparam=1) # returns 100 as a true changepoint # Example of no change found out=c(53,-22.47768,-24.39894) # tau, null, alt decision(out[1],out[2],out[3],penalty="Manual",n=200,diffparam=1,pen.value="2*log(n)")
Generic function
seg.len(object,...)seg.len(object,...)
object |
Depending on the class of |
... |
Other optional arguments used by some methods. |
Generic Function
Depends on the class of object, see individual methods
Rebecca Killick
x=new("cpt") # new cpt object seg.len(x) # returns the length of each segment in the data (i.e. no. of obs between changepoints)x=new("cpt") # new cpt object seg.len(x) # returns the length of each segment in the data (i.e. no. of obs between changepoints)
This dataset gives the significant wave heights from buoy c44137 obtained from the Fisheries and Oceans Canada, East Scotian Slop. The data are taken at hourly intervals from January 2005 until September 2012.
wave.c44137wave.c44137
A vector of length 63651.
http://www.meds-sdmm.dfo-mpo.gc.ca/isdm-gdsi/waves-vagues/search-recherche/list-liste/data-donnees-eng.asp?medsid=C44137