| Type: | Package |
| Title: | Determinantal Point Process Mixture Models |
| Version: | 0.1.1 |
| Date: | 2019-12-20 |
| Author: | Yanxun Xu [aut], Peter Mueller [aut], Donatello Telesca [aut], David J. H. Shih [aut, cre] |
| Maintainer: | David J. H. Shih <djh.shih@gmail.com> |
| Description: | Multivariate Gaussian mixture model with a determinant point process prior to promote the discovery of parsimonious components from observed data. See Xu, Mueller, Telesca (2016) <doi:10.1111/biom.12482>. |
| URL: | https://bitbucket.org/djhshih/dppmix |
| BugReports: | https://bitbucket.org/djhshih/dppmix/issues |
| Imports: | stats, mvtnorm |
| License: | GPL (≥ 3) |
| RoxygenNote: | 7.0.2 |
| NeedsCompilation: | no |
| Packaged: | 2020-01-10 16:51:51 UTC; davids |
| Repository: | CRAN |
| Date/Publication: | 2020-01-14 10:00:07 UTC |
Density function for Gamma-Poisson distribution.
Description
Data follow the Poisson distribution parameterized by a mean parameter that follows a gamma distribution.
Usage
dgammapois(x, a, b = 1, log = FALSE)
Arguments
x |
vector of x values |
a |
shape parameter for gamma distribution on mean parameter |
b |
rate parameter for gamma distribution on mean parameter |
log |
whether to return the density in log scale |
Value
density values
Fit a determinantal point process multivariate normal mixture model.
Description
Discover clusters in multidimensional data using a multivariate normal mixture model with a determinantal point process prior.
Usage
dppmix_mvnorm(
X,
hparams = NULL,
store = NULL,
control = NULL,
fixed = NULL,
verbose = TRUE
)
Arguments
X |
|
hparams |
a list of hyperparameter values:
|
store |
a vector of character strings specifying additional vars of
interest; a value of |
control |
a list of control parameters:
|
fixed |
a list of fixed parameter values |
verbose |
whether to emit verbose message |
Details
A determinantal point process (DPP) prior is a repulsive prior. Compare to mixture models using independent priors, a DPP mixutre model will often discover a parsimonious set of mixture components (clusters).
Model fitting is done by sampling parameters from the posterior distribution using a reversible jump Markov chain Monte Carlo sampling approach.
Given X = [x_i], where each x_i is a D-dimensional real vector,
we seek the posterior distribution the latent variable z = [z_i], where
each z_i is an integer representing cluster membership.
x_i \mid z_i \sim Normal(\mu_k, \Sigma_k)
z_i \sim Categorical(w)
w \sim Dirichlet([\delta ... \delta])
\mu_k \sim DPP(C)
where C is the covariance function that evaluates the distances among the
data points:
C(x_1, x_2) = exp( - \sum_d \frac{ (x_1 - x_2)^2 }{ \theta^2 } )
We also define \Sigma_k = E_k \Lambda_k E_k^\top, where E_k is an
orthonormal matrix whose column represents eigenvectors.
We further assume that E_k = E is fixed across all cluster components
so that E can be estimated as the eigenvectors of the covariance matrix of
the data matrix X. Finally, we put a prior on the entries of the
\Lambda_k diagonal matrix:
\lambda_{kd}^{-1} \sim Gamma( a_0, b_0 )
Hence, the hyperameters of the model include:
delta, a0, b0, theta, as well as sampling hyperparameter
sigma_pro_mu, which controls the spread of the Gaussian
proposal distribution for the random-walk Metropolis-Hastings update of
the \mu parameter.
The parameters (and their dimensions) in the model include:
K, z (N x 1), w (K x 1), lambda (K x J),
mu (K x J), Sigma (J x J x K).
If any parameter is fixed, then K must be fixed as well.
Value
a dppmix_mcmc object containing posterior samples of
the parameters
References
Yanxun Xu, Peter Mueller, Donatello Telesca. Bayesian Inference for Latent Biologic Structure with Determinantal Point Processes. Biometrics. 2016;72(3):955-64.
Examples
set.seed(1)
ns <- c(3, 3)
means <- list(c(-6, -3), c(0, 4))
d <- rmvnorm_clusters(ns, means)
mcmc <- dppmix_mvnorm(d$X, verbose=FALSE)
res <- estimate(mcmc)
table(d$cl, res$z)
Estimate parameter.
Description
Estimate parameter from fitted model.
Usage
estimate(object, pars, ...)
Arguments
object |
fitted model |
pars |
names of parameters to estimate |
... |
other parameters to pass |
Random generator for the Bernoulli distribution.
Description
Random generator for the Bernoulli distribution.
Usage
rbern(n, prob)
Arguments
n |
number of samples to generate |
prob |
event probability |
Value
an integer vector of 0 (non-event) and 1 (event)
Generate a random binary vector.
Description
Generate a random binary vector.
Usage
rbvec(n, prob, e.min = 0)
Arguments
n |
size of binary vector |
prob |
event probability (not accounting for minimum event constraint) |
e.min |
minimum number of events |
Value
an integer vector of 0 and 1
Random generator for the Dirichlet distribution.
Description
Random generator for the Dirichlet distribution.
Usage
rdirichlet(n, alpha)
Arguments
n |
number of vectors to generate |
alpha |
vector of parameters of the Dirichlet distribution |
Value
a matrix in which each row vector is Dirichlet distributed
Generate random multivarate clusters
Description
Generate random multivarate clusters
Usage
rmvnorm_clusters(ns, means)
Arguments
ns |
number of data points in each cluster |
means |
centers of each cluster |
Value
list containing matrix X and labels cl
Examples
ns <- c(5, 8, 7)
means <- list(c(-6, 1), c(-1, -1), c(0, 4))
d <- rmvnorm_clusters(ns, means)