Help for package DOEM

Title:

The Distributed Online Expectation Maximization Algorithms to Solve Parameters of Poisson Mixture Models

Version:

0.0.0.1

Description:

The distributed online expectation maximization algorithms are used to solve parameters of Poisson mixture models. The philosophy of the package is described in Guo, G. (2022) <doi:10.1080/02664763.2022.2053949>.

License:

MIT + file LICENSE

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.1.2

Imports:

stats

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

Packaged:

2022-03-29 14:46:35 UTC; GD

Author:

Qian Wang [aut, cre], Guangbao Guo [aut], Guoqi Qian [aut]

Maintainer:

Qian Wang <waqian0715@163.com>

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2022-03-30 07:20:13 UTC

The DE-OEM algorithm replaces E-step with stochastic step in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Description

The DE-OEM algorithm replaces E-step with stochastic step in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Usage

DE_OEM(y, M, K, seed, alpha0, lambda0, a, b)

Arguments

y

is a vector

M

is the number of subsets

K

is the number of Poisson distribution

seed

is the recommended way to specify seeds

alpha0

is the initial value of the mixing weight

lambda0

is the initial value of the mean

a

represents the power of the reciprocal of the step size

b

indicates that the M-step is not implemented for the first b data points

Value

DE_OEMtime,DE_OEMalpha,DE_OEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0=e/sum(e)
lambda0=c(1.5,2.5,3.5,4.5,5.5)
a=1
b=5
DE_OEM(y,M,K,seed,alpha0,lambda0,a,b)

The DMOEM is an overrelaxation algorithm in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Description

The DMOEM is an overrelaxation algorithm in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Usage

DMOEM(
  y,
  M,
  K,
  seed,
  alpha0,
  lambda0,
  MOEMalpha0,
  MOEMlambda0,
  omega,
  T,
  epsilon
)

Arguments

y

is a data matrix

M

is the number of subsets

K

is the number of Poisson distribution

seed

is the recommended way to specify seeds

alpha0

is the initial value of the mixing weight under the EM algorithm

lambda0

is the initial value of the mean under the EM algorithm

MOEMalpha0

is the initial value of the mixing weight under the monotonically overrelaxed EM algorithm

MOEMlambda0

is the initial value of the mean under the monotonically overrelaxed EM algorithm

omega

is the overrelaxation factor

T

is the number of iterations

epsilon

is the threshold value

Value

DMOEMtime,DMOEMalpha,DMOEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0= MOEMalpha0=e/sum(e)
lambda0= MOEMlambda0=c(1.5,2.5,3.5,4.5,5.5)
omega=0.8
T=10
epsilon=0.005
DMOEM(y,M,K,seed,alpha0,lambda0,MOEMalpha0,MOEMlambda0,omega,T,epsilon)

The DM-OEM algorithm replaces M-step with stochastic step in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Description

The DM-OEM algorithm replaces M-step with stochastic step in distributed manner, which is used to solve the parameter estimation of Poisson mixture model.

Usage

DM_OEM(y, M, K, seed, alpha0, lambda0, a, b)

Arguments

y

is a vector

M

is the number of subsets

K

is the number of Poisson distribution

seed

is the recommended way to specify seeds

alpha0

is the initial value of the mixing weight

lambda0

is the initial value of the mean

a

represents the power of the reciprocal of the step size

b

indicates that the M-step is not implemented for the first b data points

Value

DM_OEMtime,DM_OEMalpha,DM_OEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0=e/sum(e)
lambda0=c(1.5,2.5,3.5,4.5,5.5)
a=1
b=5
DM_OEM(y,M,K,seed,alpha0,lambda0,a,b)

The E-OEM algorithm replaces E-step with stochastic step, which is used to solve the parameter estimation of Poisson mixture model.

Description

The E-OEM algorithm replaces E-step with stochastic step, which is used to solve the parameter estimation of Poisson mixture model.

Usage

E_OEM(y, K, alpha0, lambda0, a, b)

Arguments

y

is a data vector

K

is the number of Poisson distribution

alpha0

is the initial value of the mixing weight

lambda0

is the initial value of the mean

a

represents the power of the reciprocal of the step size

b

indicates that the M-step is not implemented for the first b data points

Value

E_OEMtime,E_OEMalpha,E_OEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0=e/sum(e)
lambda0=c(1.5,2.5,3.5,4.5,5.5)
a=0.75
b=5
E_OEM(y,K,alpha0,lambda0,a,b)

The M-OEM algorithm replaces M-step with stochastic step, which is used to solve the parameter estimation of Poisson mixture model.

Description

The M-OEM algorithm replaces M-step with stochastic step, which is used to solve the parameter estimation of Poisson mixture model.

Usage

M_OEM(y, K, alpha0, lambda0, a, b)

Arguments

y

is a data vector

K

is the number of Poisson distribution

alpha0

is the initial value of the mixing weight

lambda0

is the initial value of the mean

a

represents the power of the reciprocal of the step size

b

indicates that the M-step is not implemented for the first b data points

Value

M_OEMtime,M_OEMalpha,M_OEMlambda

Examples

library(stats)
set.seed(637351)
K=5 
alpha1=c(rep(1/K,K)) 
lambda1=c(1,2,3,4,5) 
n=300 
U=sample(c(1:n),n,replace=FALSE)
y= c(rep(0,n)) 
for(i in 1:n){
if(U[i]<=0.2*n){
y[i] = rpois(1,lambda1[1])} 
else if(U[i]>0.2*n & U[i]<=0.4*n){
y[i] = rpois(1,lambda1[2])} 
else if(U[i]>0.4*n & U[i]<=0.6*n){
y[i] = rpois(1,lambda1[3])} 
else if(U[i]>0.6*n & U[i]<=0.8*n){
y[i] = rpois(1,lambda1[4])}
else if(U[i]>0.8*n ){
y[i] = rpois(1,lambda1[5])} 
}
M=5
seed=637351
set.seed(123) 
e=sample(c(1:n),K)
alpha0=e/sum(e)
lambda0=c(1.5,2.5,3.5,4.5,5.5)
a=0.75
b=5
M_OEM(y,K,alpha0,lambda0,a,b)

PeMSD3

Description

The PeMSD3 data

Usage

data("PeMSD3")

Format

A data frame with 26208 observations on the following 12 variables.

X315836: a numeric vector
X315837: a numeric vector
X315838: a numeric vector
X315841: a numeric vector
X315842: a numeric vector
X315839: a numeric vector
X315843: a numeric vector
X315846: a numeric vector
X315847: a numeric vector
X317895: a numeric vector
X315849: a numeric vector
X315850: a numeric vector

Details

It is the traffic data of Sacramento in California, the United States.

Source

Song, C., Lin, Y., Guo, S., Wan, H. Spatial-temporal synchronous graph convolutional networks: a new framework for spatial-temporal network data forecasting[C]. Proceedings of the AAAI Conference on Artificial Intelligence, 34(1), 914-921.

References

Examples

data(PeMSD3)
## maybe str(PeMSD3) ; plot(PeMSD3) ...

PeMSD7

Description

The PeMSD7 data

Usage

data("PeMSD7")

Format

A data frame with 17568 observations on the following 20 variables.

X773656: a numeric vector
X760074: a numeric vector
X760080: a numeric vector
X716414: a numeric vector
X760101: a numeric vector
X760112: a numeric vector
X716419: a numeric vector
X716421: a numeric vector
X716424: a numeric vector
X765476: a numeric vector
X760167: a numeric vector
X716427: a numeric vector
X716431: a numeric vector
X716433: a numeric vector
X760187: a numeric vector
X760196: a numeric vector
X716440: a numeric vector
X760226: a numeric vector
X760236: a numeric vector
X716449: a numeric vector

Details

It is the traffic data of Los Angeles in California, the United States.

Source

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

References

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

Examples

data(PeMSD7)
## maybe str(PeMSD7) ; plot(PeMSD7) ...

PeMSD7 on weekend

Description

The weekend data in PeMSD7

Usage

data("PeMSD7_weekend")

Format

A data frame with 5184 observations on the following 20 variables.

X773656: a numeric vector
X760074: a numeric vector
X760080: a numeric vector
X716414: a numeric vector
X760101: a numeric vector
X760112: a numeric vector
X716419: a numeric vector
X716421: a numeric vector
X716424: a numeric vector
X765476: a numeric vector
X760167: a numeric vector
X716427: a numeric vector
X716431: a numeric vector
X716433: a numeric vector
X760187: a numeric vector
X760196: a numeric vector
X716440: a numeric vector
X760226: a numeric vector
X760236: a numeric vector
X716449: a numeric vector

Details

The weekend data set only records traffic flow data on weekends.

Source

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

References

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

Examples

data(PeMSD7_weekend)
## maybe str(PeMSD7_weekend) ; plot(PeMSD7_weekend) ...

PeMSD7 on workday

Description

The workday data in PeMSD7

Usage

data("PeMSD7_workday")

Format

A data frame with 12384 observations on the following 20 variables.

X773656: a numeric vector
X760074: a numeric vector
X760080: a numeric vector
X716414: a numeric vector
X760101: a numeric vector
X760112: a numeric vector
X716419: a numeric vector
X716421: a numeric vector
X716424: a numeric vector
X765476: a numeric vector
X760167: a numeric vector
X716427: a numeric vector
X716431: a numeric vector
X716433: a numeric vector
X760187: a numeric vector
X760196: a numeric vector
X716440: a numeric vector
X760226: a numeric vector
X760236: a numeric vector
X716449: a numeric vector

Details

The workday data set only records traffic flow data on workdays.

Source

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

References

Xu, D., Wei, C., Peng, P., Xuan, Q., Guo, H. Ge-gan: a novel deep learning framework for road traffic state estimation[J]. Transportation Research Part C Emerging Technologies, 2020, 117, 102635.

Examples

data(PeMSD7_workday)
## maybe str(PeMSD7_workday) ; plot(PeMSD7_workday) ...