Dirichlet_Process_Mixture_Model_For_RNA_data

This repository contains the code to estimate the models in the paper On the inference of RNA life cycle kinetic rates from sequencing data by latent Dirichlet Process Mixture Models.

The code is written in R and C++ and to run it the package OdePackRT1 is needed, that can be installed by the source archive in the directory R PACKAGE. Notice that you need to have OPENMP installed.

The posterior sample from the model can be obtained launching the code PosteriorSamples.R. The following variables must be specified

  NAME      = ""
  DIR       = ".../Dirichlet_Process_Mixture_Model_For_RNA_data/"
  Nthreads  =
  DoClust   =

where NAME is the name of the output files, DIR is the directory where this repository is downloaded, Nthreads is the number of cores that should be used for the computations, and DoClust is TRUE if the mixture model is used, FALSE if not. The results are stored in the file NAME.Rdata in the directory OUT.

The model output is a list of 18 elements

• MinK parameter \beta in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of parameters. The first 3 columns are the parameters of the k_1, k_2 and k_3 of the first gene. The next three the one of the second...
• VarK parameter \sigma^2 in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of parameters. The first 3 columns are the parameters of the k_1, k_2 and k_3 of the first gene. The next three the one of the second...
• MeanK parameter \mu in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of parameters. The first 3 columns are the parameters of the k_1, k_2 and k_3 of the first gene. The next three the one of the second...
• EtaK1 parameter \eta_1 in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of parameters. The first 3 columns are the parameters of the k_1, k_2 and k_3 of the first gene. The next three the one of the second...
• EtaK2 parameter \eta_2 in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of parameters. The first 3 columns are the parameters of the k_1, k_2 and k_3 of the first gene. The next three the one of the second...
• Y the estimated ODEs. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the NumberTimeNumberGene3. The first 3 columns are the ODEs of the first time point for the first gene, the next three are the second time point of the first gene ... row 34, 35, 36 contains the first time point of the secong gene, ...
• Y0 the estimated first time points of the ODEs. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to NumberGene*3. The first 3 columns are the first time point of the ODEs of the first gene, the next three the ones of the second, ...
• Beta0 regressive parameter \beta_{j,0} in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to 3
• Beta1 regressive parameter \beta_{j,1} in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to 3
• SF_1 parameter \rho_{1}(t) in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of time points
• SF_2 parameter \rho_{2}(t) in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of time points
• SF_3 parameter \rho_{3}(t) in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of time points
• ModelOutput_11 Mixture model output for the shape parameters of the first kinetic rates
• ModelOutput_12 Mixture model output for the starting level of the first kinetic rates
• ModelOutput_21 Mixture model output for the shape parameters of the second kinetic rates
• ModelOutput_22 Mixture model output for the starting level of the second kinetic rates
• ModelOutput_31 Mixture model output for the shape parameters of the third kinetic rates
• ModelOutput_32 Mixture model output for the starting level of the third kinetic rates

Each Mixture model output is composed of a list of 2 elements, where PostK is the MAP estimator of the number of clusters for each gene, and ModelOutput is a list of 150 elements, where the k-th element contains the posterior samples of the iterations where the number of clusters is k. ModelOutput[[k]] is a list of two elements

• LikelihoodParameters
  • st parameter z in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to the number of genes
  • MAP MAP estimator of the number of clusters for each gene
  • pi parameter pi in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to k
  • DPpar parameter \zeta in the paper.
• Clustering
  • Beta parameter \Zeta (mean of the normal distribution) in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to k (if it is the cluster object of the starting level) or k*4 (if it is the cluster object of the shape parameters). The first 1 or 4 elements, are related to the first cluster, the second 1 or 4 to the second, ...
  • Sigma parameter \Omega (covariance matrix of the normal distribution) in the paper. A matrix with number of rows equal to the number of posterior samples, and number of columns equal to k (if it is the cluster object of the starting level) or k*4^2 (if it is the cluster object of the shape parameters). The first 1 or 4^2 elements, are related to the first cluster, the second 1 or 4^2 to the second, ...