| Title: | Confidence Interval for Matrix Completion via De-Biased Estimator |
| Version: | 1.0.0 |
| Description: | Implements the de-biased estimator for low-rank matrix completion and provides confidence intervals for entries of interest. See: by Chen et al. (2019) <doi:10.1073/pnas.1910053116>, Mai (2021) <doi:10.48550/arXiv.2103.11749>. |
| Imports: | softImpute |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.1 |
| Suggests: | rmarkdown, knitr |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-07-19 11:03:02 UTC; thetm |
| Author: | The Tien Mai [aut, cre] |
| Maintainer: | The Tien Mai <t.t.mai@medisin.uio.no> |
| Repository: | CRAN |
| Date/Publication: | 2021-07-20 07:20:08 UTC |
compute the confidence intervals (CIs) from the de-biased estimator
Description
This function returns a CI for an entries of interest with a significant level alpha
Usage
CI_mc(i, j, alpha = 0.05, missfrac, X.db, est_rank, sigma2 = 1)
Arguments
i |
the row index of the interest entry X_i,j |
j |
the row index of the interest entry X_i,j |
alpha |
confidence level, default is 0.05 |
missfrac |
the missing proportion in the underlying matrix. It is the total of missing entries over total entries. |
X.db |
the de-biased estimated matrix from the 'dbmc' function. |
est_rank |
the (estimated) low-rank of the underlying matrix or the rank of the de-biased estimator. |
sigma2 |
the noise-variance level. |
Value
CI confidence interval.
(i,j) the location of the entry at i-th row and j-th column.
v.ij the estimated variance of the limiting Gaussian distribution.
References
Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.
projection onto observation set
Description
This function returns a matrix where the missing entries are replaced by 0 s.
Usage
P_Omega(a, entri)
Arguments
a |
a matrix. |
entri |
missing entries location. |
Value
Return a matrix whose its missing entries are replaced by 0 s.
de-biased estimator
Description
de-biased low-rank matrix completion estimator
This function compute a de-biased estimator from a rank-r matrix completion using the algorithms from the package "softImpute".
Usage
dbmc(x, ximp, entries_miss, est_rank)
Arguments
x |
the initial matrix with missing entries |
ximp |
an imputed matrix, output from the package "softImpute". |
entries_miss |
the missing indices |
est_rank |
the rank of the matrix x, or the estimated rank from the package "softImpute". |
Value
x.db the de-baised estimation matrix.
References
Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.
Examples
# simulated data
require(softImpute)
n = 100
p = 100
J = 2 # the true low-rank
np = n*p
sig2 = 1
missfrac = 0.5
# xtrue is the underlying matrix that we do not know and want to recover it
xtrue = matrix(rnorm(n*J),n,J)%*%matrix(rnorm(J*p),J,p)
# generating missing entries locations
imiss = sample(np,np*missfrac,replace=FALSE)
# xna is the observed matrix with missing entries
xna = xtrue + matrix(rnorm(np, sd = sig2),nr = n,nc = p)
xna[imiss] = NA
lamda = 2.5*sig2*sqrt(n*p)
# note that we only have xna as our initial data
# first, fit a softImpute method
fit1 = softImpute(xna, type = 'als')
# complete the matrix by a softImpute method
ximp = complete(xna,fit1)
mean((ximp - xtrue)^2);rankMatrix(ximp,.1)[1]
# now, de-biased the softImpute method
x.db = dbmc(x = xna,
ximp = ximp,
entries_miss = imiss,
est_rank = 2)
mean((x.db - xtrue)^2);rankMatrix(x.db,.1)[1]