Fit the multi-study covariate-augmented overdispersed Poisson factor model via variational inference

Fit the high-dimensional multi-study covariate-augmented overdispersed Poisson factor model via variational inference.

MultiCOAP(
  XcList,
  ZList,
  q = 15,
  qs = rep(2, length(XcList)),
  rank_use = NULL,
  aList = NULL,
  init = c("MSFRVI", "LFM"),
  epsELBO = 1e-05,
  maxIter = 30,
  verbose = TRUE,
  seed = 1
)

Arguments

XcList

a length-M list with each component a count matrix, which is the observed count matrix from each source/study.

ZList

a length-M list with each component a matrix that is the covariate matrix from each study.

q

an optional string, specify the number of study-shared factors; default as 15.

qs

a integer vector with length M, specify the number of study-specifed factors; default as 2.

rank_use

an optional integer, specify the rank of the regression coefficient matrix; default as NULL, which means that rank is the dimension of covariates in Z.

aList

an optional length-M list with each component a vector, the normalization factors of each study; default as full-one vector.

init

an optional string, specify the initialization method, default as "MSFRVI".

epsELBO

an optional positive vlaue, tolerance of relative variation rate of the envidence lower bound value, defualt as '1e-5'.

maxIter

the maximum iteration of the VEM algorithm. The default is 30.

verbose

a logical value, whether output the information in iteration.

seed

an optional integer, specify the random seed for reproducibility in initialization.

Value

return a list including the following components: (1) F, a list composed by the posterior estimation of study-shared factor matrix for each study; (2) H, a list composed by the posterior estimation of study-specified factor matrix for each study; (3) Sf, a list consisting of the posterior estimation of covariance matrix of study-shared factors for each study; (4) Sh, a list consisting of the posterior estimation of covariance matrix of study-specified factors for each study; (5) A, the loading matrix corresponding to study-shared factors; (6) B, a list composed by the loading matrices corresponding to the study-specified factors; (7) bbeta, the estimated regression coefficient matrix; (8) invLambda, the inverse of the estimated variances of error; (9) ELBO: the ELBO value when algorithm stops; (7) ELBO_seq: the sequence of ELBO values. (11) qrlist, the number of factors and rank of regression coefficient matrix used in fitting; (12) time.use, the elapsed time for model fitting.

Details

If init="MSFRVI", it will use the results from multi-study linear factor model as initial values; If init="LFM", it will use the results from linear factor model by combing data from all studies as initials.

References

None

See also

MSFRVI

Examples

seed <- 1; nvec <- c(100,300); p<- 300;
d <- 3; q<- 3; qs <- rep(2,2)
datlist <- gendata_simu_multi2(seed=seed, nvec=nvec, p=p, d=d, q=3, qs=qs)
fit_mcoap <- MultiCOAP(datlist$Xlist, ZList = datlist$Zlist, q=3, qs=qs, rank_use = d)
#> iter = 2, ELBO= -90889.644953, dELBO=0.999958 
#> iter = 3, ELBO= -80088.223117, dELBO=0.118841 
#> iter = 4, ELBO= -75759.764645, dELBO=0.054046 
#> iter = 5, ELBO= -73171.507470, dELBO=0.034164 
#> iter = 6, ELBO= -71962.833715, dELBO=0.016518 
#> iter = 7, ELBO= -74819.780396, dELBO=0.039700 
#> iter = 8, ELBO= -72546.405591, dELBO=0.030385 
#> iter = 9, ELBO= -73387.279677, dELBO=0.011591 
#> iter = 10, ELBO= -78559.045054, dELBO=0.070472 
#> iter = 11, ELBO= -73495.533378, dELBO=0.064455 
#> iter = 12, ELBO= -72182.038358, dELBO=0.017872 
#> iter = 13, ELBO= -71269.814019, dELBO=0.012638 
#> iter = 14, ELBO= -71175.423331, dELBO=0.001324 
#> iter = 15, ELBO= -72042.181646, dELBO=0.012178 
#> iter = 16, ELBO= -73908.999501, dELBO=0.025913 
#> iter = 17, ELBO= -71946.489098, dELBO=0.026553 
#> iter = 18, ELBO= -76495.391328, dELBO=0.063226 
#> iter = 19, ELBO= -73208.440675, dELBO=0.042969 
#> iter = 20, ELBO= -71948.064700, dELBO=0.017216 
#> iter = 21, ELBO= -71825.188285, dELBO=0.001708 
#> iter = 22, ELBO= -71808.429994, dELBO=0.000233 
#> iter = 23, ELBO= -70920.619481, dELBO=0.012364 
#> iter = 24, ELBO= -70799.276626, dELBO=0.001711 
#> iter = 25, ELBO= -72588.783734, dELBO=0.025276 
#> iter = 26, ELBO= -71595.350758, dELBO=0.013686 
#> iter = 27, ELBO= -72507.920086, dELBO=0.012746 
#> iter = 28, ELBO= -71380.723517, dELBO=0.015546 
#> iter = 29, ELBO= -70604.166784, dELBO=0.010879 
#> iter = 30, ELBO= -78083.887857, dELBO=0.105939 
str(fit_mcoap)
#> List of 15
#>  $ F        :List of 2
#>   ..$ : num [1:100, 1:3] -0.139 -0.359 0.283 1.616 0.401 ...
#>   ..$ : num [1:300, 1:3] -2.7231 1.5022 -0.5362 0.0178 -1.2687 ...
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ H        :List of 2
#>   ..$ : num [1:100, 1:2] 1.457 2.779 0.999 -1.02 1.021 ...
#>   ..$ : num [1:300, 1:2] 1.3815 -0.8341 -1.4763 -0.7487 0.0234 ...
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ Sf       :List of 2
#>   ..$ : num [1:3, 1:3] 0.0388 0 0 0 0.0589 ...
#>   ..$ : num [1:3, 1:3] 0.0369 0 0 0 0.0561 ...
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ Sh       :List of 2
#>   ..$ : num [1:2, 1:2] 0.272 0 0 0.4
#>   ..$ : num [1:2, 1:2] 0.106 0 0 0.184
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ A        : num [1:300, 1:3] 0.1509 0.0652 0.0987 -0.3762 -0.0505 ...
#>  $ B        :List of 2
#>   ..$ : num [1:300, 1:2] 0.2 -0.1419 0.0683 0.021 -0.1491 ...
#>   ..$ : num [1:300, 1:2] 0.0116 0.1813 0.2533 -0.0739 0.0174 ...
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ bbeta    : num [1:300, 1:3] 0.289 0.168 0.249 0.249 0.181 ...
#>  $ invLambda: num [1:2, 1] 1.16 1.1
#>  $ Mu_y     :List of 2
#>   ..$ : num [1:100, 1:300] 0.253 0.217 0.331 1.77 0.955 ...
#>   ..$ : num [1:300, 1:300] -0.4728 0.2185 0.0191 0.5416 -0.4073 ...
#>   ..- attr(*, "dim")= int [1:2] 2 1
#>  $ ELBO     : num -78084
#>  $ dELBO    : num -7480
#>  $ ELBO_seq : num [1:30] -2.15e+09 -9.09e+04 -8.01e+04 -7.58e+04 -7.32e+04 ...
#>  $ Lambda   : num [1:2, 1] 0.859 0.905
#>  $ qrlist   :List of 3
#>   ..$ q : num 3
#>   ..$ qs: num [1:2] 2 2
#>   ..$ r : num 3
#>  $ time.use : Named num 0.61
#>   ..- attr(*, "names")= chr "elapsed"