| Title: | Linear Programming Model for Network Inference |
|---|---|
| Description: | lpNet aims at infering biological networks, in particular signaling and gene networks. For that it takes perturbation data, either steady-state or time-series, as input and generates an LP model which allows the inference of signaling networks. For parameter identification either leave-one-out cross-validation or stratified n-fold cross-validation can be used. |
| Authors: | Bettina Knapp, Marta R. A. Matos, Johanna Mazur, Lars Kaderali |
| Maintainer: | Lars Kaderali <[email protected]> |
| License: | Artistic License 2.0 |
| Version: | 2.37.0 |
| Built: | 2024-06-30 02:40:39 UTC |
| Source: | https://github.com/bioc/lpNet |
lpNet aims at infering biological networks, in particular signaling and gene networks. For that it takes perturbation data, either steady-state or time-series, as input and generates an LP model which allows the inference of signaling networks. For parameter identification either leave-one-out cross-validation or stratified n-fold cross-validation can be used.
| Package: | lpNet |
| Type: | Package |
| Version: | 1.99.2 |
| Date: | 2013-01-11 |
| License: | Artistic License 2.0 |
B. Knapp, M. R. A. Matos, J. Mazur, L. Kaderali
Maintainer: [email protected]
Bettina Knapp and Lars Kaderali, Reconstruction of cellular signal transduction networks using perturbation assays and linear programming, PLoS ONE, 2013.
Marta R. A. Matos, Network inference : extension of linear programming model for time-series data, Master's thesis, Department of Informatics, University of Minho.
Calculate the activation matrix assuming that the signaling is deterministically propagated along the network. For a given network and perturbation experiment the theoretical states of the genes are computed. So, if a gene has been silenced in an experiment, then the state of this gene is assumed to be inactive, otherwise if its inflow (coming from parent nodes) is activating, it is active. Cycles within a network are not resolved, therefore this function can be used only for networks without cycles. This function is also used to generate the network states for time-series data (by generateTimeSeriesNetStates), in which case flag_gen_data is set to true, and the activation matrix is calculated without taking the edges sign into account.
calcActivation(T_nw, b, n, K, flag_gen_data = FALSE)calcActivation(T_nw, b, n, K, flag_gen_data = FALSE)
T_nw |
Adjacency matrix: the network which is used to compute the activities and inactivities. |
b |
Vector of 0/1 values describing the experiments (entry is 0 if gene is inactivated in the respetive experiment and 1 otherwise). The measurements of the genes of each experiment are appended as a long vector. |
n |
Integer: number of genes. |
K |
Integer: number of perturbation experiments. |
flag_gen_data |
Logical: if set to TRUE the edges sign will not be taken into account. It should be TRUE if the function is used to generate the network states for time-series data. |
Matrix of 0/1 values; rows corresponding to genes, columns to experiments. If an entry is 1, it means that the corresponding gene is active in the corresponing experiment and inactive otherwise.
n <- 5 # number of genes K <- 7 # number of perturbations experiments # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1,1,1, # perturbation exp1: gene 1 perturbed, gene 2-5 unperturbed 1,0,1,1,1, # perturbation exp2: gene 2 perturbed, gene 1,3,4,5 unperturbed 1,1,0,1,1, # perturbation exp3.... 1,1,1,0,1, 1,1,1,1,0, 1,0,0,1,1, 1,1,1,1,1) # example network T_nw <- matrix(c(0,1,1,0,0, 0,0,0,-1,0, 0,0,0,1,0, 0,0,0,0,1, 0,0,0,0,0), nrow=n,ncol=n,byrow=TRUE) # compute theoretical activation of genes from example network with given perturbations act_mat <- calcActivation(T_nw, b, n, K)n <- 5 # number of genes K <- 7 # number of perturbations experiments # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1,1,1, # perturbation exp1: gene 1 perturbed, gene 2-5 unperturbed 1,0,1,1,1, # perturbation exp2: gene 2 perturbed, gene 1,3,4,5 unperturbed 1,1,0,1,1, # perturbation exp3.... 1,1,1,0,1, 1,1,1,1,0, 1,0,0,1,1, 1,1,1,1,1) # example network T_nw <- matrix(c(0,1,1,0,0, 0,0,0,-1,0, 0,0,0,1,0, 0,0,0,0,1, 0,0,0,0,0), nrow=n,ncol=n,byrow=TRUE) # compute theoretical activation of genes from example network with given perturbations act_mat <- calcActivation(T_nw, b, n, K)
Calculate the predicted observation of a perturbation experiment. If observations of an experiment are missing this function can be used to determine for a given network the predicted outcome. The missing measurement is predicted from two normal distributions, one for observations coming from active and one coming from inactive genes. The state of the gene is predicted based on the states of its parents.
calcPredictionLOOCV(obs, delta, b, n ,K, adja, baseline, rem_gene, rem_k, rem_t=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, flag_time_series=FALSE) calcPredictionKfoldCV(obs, delta, b, n, K, adja, baseline, rem_entries=NULL, rem_entries_vec=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, flag_time_series=FALSE)calcPredictionLOOCV(obs, delta, b, n ,K, adja, baseline, rem_gene, rem_k, rem_t=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, flag_time_series=FALSE) calcPredictionKfoldCV(obs, delta, b, n, K, adja, baseline, rem_entries=NULL, rem_entries_vec=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, flag_time_series=FALSE)
obs |
Numeric matrix/array: the observation matrix/array. It can have up to 3 dimensions, where dimension 1 are the network nodes, dimension 2 are the perturbation experiments, and dimension 3 are the time points (if considered). |
delta |
Numeric vector defining the thresholds for each gene to determine its observation to be active or inactive. |
b |
Binary vector representing the perturbation experiments (entry is 0 if gene is inactive in the respective experiment and 1 otherwise). |
n |
Number of genes in the observation matrix. |
K |
Number of perturbation experiments. |
adja |
Numeric matrix: the adjacency matrix of the given network. |
baseline |
Vector containing the inferred baseline vectors of each gene. |
rem_gene |
Integer: the index of the gene that is missing. |
rem_k |
Integer: the index of the perturbation experiment that is missing. |
rem_t |
Integer: the index of the time point that is missing. |
rem_entries |
Numeric matrix: each row represents an entry that was removed from the observation matrix, while the 3 columns represent the gene, perturbation experiment and time point, respectively. |
rem_entries_vec |
Numeric vector: contains the entries that were removed in an "absolute form", i.e., if entry (2,1,2) was removed, it will appear in this vector as simply 5. |
active_mu |
Numeric: the average value assumed for observations coming from active nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
active_sd |
Numeric: the variation assumed for observations coming from active nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_mu |
Numeric: the average value assumed for observations coming from inactive nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_sd |
Numeric: the variation assumed for observations coming from inactive nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
mu_type |
Character: can have the following values and meanings:
|
flag_time_series |
Logical: specifies whether steady-state (FALSE) or time series data (TRUE) is used. |
n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) # adjacency matrix adja <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) # define node baseline values baseline <- c(0.75, 0, 0) # define delta value delta <- rep(0.75, n) # define the parameters for the observation generated from the normal distributions mu_type <- "single" active_mu <- 0.9 inactive_mu <- 0.5 active_sd <- inactive_sd <- 0.01 #### kfoldCV # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) # define the observationd to be removed, whose values will be predicted obs[2,4,2] <- NA obs[3,4,3] <- NA rem_entries <- which(is.na(obs), arr.ind=TRUE) rem_entries_vec <- which(is.na(obs)) # compute the predicted observation matrix for the "kfoldCV" calcPredictionKfoldCV(obs=obs, delta=delta, b=b, n=n, K=K, adja=adja, baseline=baseline, rem_entries=rem_entries, rem_entries_vec=rem_entries_vec, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, flag_time_series=TRUE) #### LOOCV # generate random observation matrix obs <- matrix(rnorm(n*K), nrow=n, ncol=K) # define the observationd to be removed rem_k <- 3 rem_gene <- 2 obs[rem_gene, rem_k] <- NA # compute the predicted value calcPredictionLOOCV(obs=obs, delta=delta,b=b, n=n ,K=K, adja=adja, baseline=baseline, rem_gene=rem_gene, rem_k=rem_k, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type)n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) # adjacency matrix adja <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) # define node baseline values baseline <- c(0.75, 0, 0) # define delta value delta <- rep(0.75, n) # define the parameters for the observation generated from the normal distributions mu_type <- "single" active_mu <- 0.9 inactive_mu <- 0.5 active_sd <- inactive_sd <- 0.01 #### kfoldCV # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) # define the observationd to be removed, whose values will be predicted obs[2,4,2] <- NA obs[3,4,3] <- NA rem_entries <- which(is.na(obs), arr.ind=TRUE) rem_entries_vec <- which(is.na(obs)) # compute the predicted observation matrix for the "kfoldCV" calcPredictionKfoldCV(obs=obs, delta=delta, b=b, n=n, K=K, adja=adja, baseline=baseline, rem_entries=rem_entries, rem_entries_vec=rem_entries_vec, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, flag_time_series=TRUE) #### LOOCV # generate random observation matrix obs <- matrix(rnorm(n*K), nrow=n, ncol=K) # define the observationd to be removed rem_k <- 3 rem_gene <- 2 obs[rem_gene, rem_k] <- NA # compute the predicted value calcPredictionLOOCV(obs=obs, delta=delta,b=b, n=n ,K=K, adja=adja, baseline=baseline, rem_gene=rem_gene, rem_k=rem_k, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type)
The penalty parameter lambda can range from zero to infinity and it controls the introduction of slack variables in the network inference lp model. To limit the introduction of slack variables we restrict lambda to be not larger than lambdaMax (=the number of slack variables times the variance of all measurements given). This function computes the range from zero to lambdaMax with a given stepsize that increases exponentially.
calcRangeLambda(obs, delta, delta_type, flag_time_series=FALSE)calcRangeLambda(obs, delta, delta_type, flag_time_series=FALSE)
obs |
Numeric matrix/array: the observation matrix/array. It can have up to 3 dimensions, where dimension 1 are the network nodes, dimension 2 are the perturbation experiments, and dimension 3 are the time points (if considered). |
delta |
Numeric: defines the thresholds for each gene to determine its observation to be active or inactive. This parameter can be either a numeric vector, a matrix, or a 3D array, depending on the specified delta_type. |
delta_type |
Character: can have the following values and meanings:
|
flag_time_series |
Logical: specifies whether steady-state (FALSE) or time series data (TRUE) is used. |
Numeric vector of possible values for lambda.
# generate random observation matrix with 5 experiments and 5 genes obs <- matrix(rnorm(5*5, 1, 0.1), nrow=5, ncol=5) # define delta to be 1 for each gene delta <- rep(1, 5) delta_type <- "perGene" lambda_values <- calcRangeLambda(obs, delta, delta_type)# generate random observation matrix with 5 experiments and 5 genes obs <- matrix(rnorm(5*5, 1, 0.1), nrow=5, ncol=5) # define delta to be 1 for each gene delta <- rep(1, 5) delta_type <- "perGene" lambda_values <- calcRangeLambda(obs, delta, delta_type)
Performs a stratified k-fold cross-validation or a Leave-One-Out cross-validation.
loocv(kfold=NULL, times, obs, delta, lambda, b, n, K, T_=NULL, annot, annot_node, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=FALSE) kfoldCV(kfold, times, obs, delta, lambda, b, n, K, T_=NULL, annot, annot_node, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=FALSE)loocv(kfold=NULL, times, obs, delta, lambda, b, n, K, T_=NULL, annot, annot_node, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=FALSE) kfoldCV(kfold, times, obs, delta, lambda, b, n, K, T_=NULL, annot, annot_node, active_mu, active_sd, inactive_mu, inactive_sd, mu_type, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=FALSE)
kfold |
Integer value of the number "k" in the k-fold cross-calidation. |
times |
Integer: the number of times the cross-validation shall be performed. |
obs |
Numeric matrix/array: the measured observation matrix/array. It can have up to 3 dimensions, where dimension 1 are the network nodes, dimension 2 are the perturbation experiments, and dimension 3 are the time points (if considered). |
delta |
Numeric vector, matrix, or array defining the thresholds to determine an observation active or inactive. |
lambda |
Numeric value defining the penalty parameter lambda. It can range from zero to infinity and it controls the introduction of slack variables in the network inference lp model. |
n |
Integer: number of genes. |
b |
Vector of 0/1 values describing the experiments (entry is 0 if gene is inactivated in the respetive experiment and 1 otherwise). The measurements of the genes of each experiment are appended as a long vector. |
K |
Integer: number of perturbation experiments. |
T_ |
Integer: number of time points in time-series data. |
annot |
Vector of character strings: the annotation of the edges as returned by "getEdgeAnnot". |
annot_node |
Vector of character strings: the annoation of the nodes. |
active_mu |
Numeric: the average value assumed for observations coming from activated nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
active_sd |
Numeric: the variation assumed for observations coming from activated nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_mu |
Numeric: the average value assumed for observations coming from inactivated nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_sd |
Numeric: the variation assumed for observations coming from inactivated nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
mu_type |
Character: can have the following values and meanings:
|
delta_type |
Character: can have the following values and meanings:
|
prior |
Prior knowledge, given as a list of constraints. Each constraint consists of a vector with four entries describing the prior knowledge of one edge. For example the edge between node 1 and 2, called w+_1_2, is defined to be bigger than 1 with constraint c("w+_1_2",1,">",2). The first entry specifies the annotation of the edge (see function "getEdgeAnnot") and the second defines the coefficient of the objective function (see parameter "objective.in" in the "lp" function of the package "lpSolve"). Furthermore, the third, respectively the fourth elements give the direction, respectively the right-hand side of the constraint (see the parameters "const.dir", respectively "const.rhs" in the "lp" function of the package "lpSolve"). |
sourceNode |
Integer vector: indices of the known source nodes. |
sinkNode |
Integer vector: indices of the known sink nodes. |
allint |
Logical: should all variables be integer? Corresponds to an Integer Linear Program (see "lp" function in package "lpSolve"). Default: FALSE. |
allpos |
Logical: should all variables be positive? Corresponds to learning only activating edges. Default: FALSE. |
flag_time_series |
Logical: specifies whether steady-state (FALSE) or time series data (TRUE) is used. |
A list of
MSE |
The mean squared error (MSE) of predicted and observed measurements of the corresponding cross-validation step. |
edges_all |
The learned edge weights for each cross-validation step. |
baseline_all |
The learned baseline weights for each cross-validation step. |
n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points annot_node <- seq(1, n) annot <- getEdgeAnnot(n) # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) # define delta delta <- apply(obs, 1, mean, na.rm=TRUE) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) T_nw <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) colnames(T_nw) <- rownames(T_nw) <- annot_node ## calculate observation matrix with given parameters for the # Gaussian distributions for activation and deactivation active_mu <- 0.95 inactive_mu <- 0.56 active_sd <- inactive_sd <- 0.1 times <- kfold <- 10 # can be increased i.e. to 1000 to produce stable results mu_type <- "single" delta_type <- "perGene" lambda <- 1/10 #### LOOCV loocv(kfold=NULL, times=times, obs=obs, delta=delta, lambda=lambda, b=b, n=n, K=K, T_=T_, annot=annot, annot_node=annot_node, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, delta_type=delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=TRUE) #### K-fold CV kfoldCV(kfold=kfold, times=times, obs=obs, delta=delta, lambda=lambda, b=b, n=n, K=K, T_=T_, annot=annot, annot_node=annot_node, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, delta_type=delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=TRUE)n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points annot_node <- seq(1, n) annot <- getEdgeAnnot(n) # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) # define delta delta <- apply(obs, 1, mean, na.rm=TRUE) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) T_nw <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) colnames(T_nw) <- rownames(T_nw) <- annot_node ## calculate observation matrix with given parameters for the # Gaussian distributions for activation and deactivation active_mu <- 0.95 inactive_mu <- 0.56 active_sd <- inactive_sd <- 0.1 times <- kfold <- 10 # can be increased i.e. to 1000 to produce stable results mu_type <- "single" delta_type <- "perGene" lambda <- 1/10 #### LOOCV loocv(kfold=NULL, times=times, obs=obs, delta=delta, lambda=lambda, b=b, n=n, K=K, T_=T_, annot=annot, annot_node=annot_node, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, delta_type=delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=TRUE) #### K-fold CV kfoldCV(kfold=kfold, times=times, obs=obs, delta=delta, lambda=lambda, b=b, n=n, K=K, T_=T_, annot=annot, annot_node=annot_node, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type, delta_type=delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, allint=FALSE, allpos=FALSE, flag_time_series=TRUE)
This function converts observation data into a linear programming problem.
doILP(obs, delta, lambda, b, n, K, T_=NULL, annot, delta_type, prior=NULL,sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=FALSE)doILP(obs, delta, lambda, b, n, K, T_=NULL, annot, delta_type, prior=NULL,sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=FALSE)
obs |
Numeric matrix/array: the given observation matrix/array. It can have up to 3 dimensions, where dimension 1 are the network nodes, dimension 2 are the perturbation experiments, and dimension 3 are the time points (if considered). |
delta |
Numeric: defining the thresholds for each gene to determine its observation to be active or inactive. This parameter can be either a numeric vector, a matrix, or a 3D array, depending on the specified delta_type. |
lambda |
Numeric value defining the penalty parameter lambda. It can range from zero to infinity and it controls the introduction of slack variables in the network inference lp model. |
b |
Vector of 0/1 values describing the experiments (entry is 0 if gene is inactivated in the respetive experiment and 1 otherwise). The measurements of the genes of each experiment are appended as a long vector. |
n |
Integer: number of genes. |
K |
Integer: number of perturbation experiments. |
T_ |
Integer: number of time points. |
annot |
Vector of character strings: the annotation of the edges as returned by "getEdgeAnnot". |
delta_type |
Character: can have the following values and meanings: - "perGene" - the value of delta depends on the gene; - "perGeneExp" - the value of delta depends on the gene and perturbation experiment; - "perGeneTime" - the value of delta depends on the gene and time point; - "perGeneExpTime" - the value of delta depends on the gene, perturbation experiment, and time point; |
prior |
Prior knowledge, given as a list of constraints. Each constraint consists of a vector with four entries describing the prior knowledge of one edge. For example the edge between node 1 and 2, called w+_1_2, is defined to be bigger than 1 with constraint c("w+_1_2",1,">",2). The first entry specifies the annotation of the edge (see function "getEdgeAnnot") and the second defines the coefficient of the objective function (see parameter "objective.in" in the "lp" function of the package "lpSolve"). Furthermore, the third, respectively the fourth elements give the direction, respectively the right-hand side of the constraint (see the parameters "const.dir", respectively "const.rhs" in the "lp" function of the package "lpSolve"). |
sourceNode |
Integer vector: indices of the known source nodes. |
sinkNode |
Integer vector: indices of the known sink nodes. |
all.int |
Logical: should all variables be integer? Corresponds to an Integer Linear Program (see "lp" function in package "lpSolve"). Default: FALSE. |
all.pos |
Logical: should all variables be positive? Corresponds to learning only activating edges. Default: FALSE. |
flag_time_series |
Logical: specifies whether steady-state (FALSE) or time series data (TRUE) is used. |
An lp object. See "lp.object" in package "lpSolve" for details.
n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE)n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE)
The function returns all gene states for each network state in time-series data. The signalling propagates downstream one edge per time-point. The stopping criteria is when all edges have been active at least once, so that infinite loops are avoided. The number of time points for the data can be defined by the user or not, if not the number of time points will be the same as the number of different network states. If the number of time points is defined by the user, network states will be either repeated or removed, so that there are as many network states as time points.
generateTimeSeriesNetStates(nw_und, b, n, K, T_user=NULL)generateTimeSeriesNetStates(nw_und, b, n, K, T_user=NULL)
nw_und |
Numeric matrix: the adjacency matrix representing the underlying network. |
b |
Vector of 0/1 values describing the experiments (entry is 0 if gene is inactivated in the respetive experiment and 1 otherwise). The measurements of the genes of each experiment are appended as a long vector. |
n |
Integer: number of genes. |
K |
Integer: number of perturbation experiments. |
T_user |
Integer definining the number of time points in the network. |
List containing an array with all nodes states and the number of time points.
n <- 3 # number of genes K <- 4 # number of experiments # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) # adjacency matrix nw_und <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) generateTimeSeriesNetStates(nw_und,b, n, K, T_user=5)n <- 3 # number of genes K <- 4 # number of experiments # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) # adjacency matrix nw_und <- matrix(c(0,1,0, 0,0,1, 0,0,0), nrow=n, ncol=n, byrow=TRUE) generateTimeSeriesNetStates(nw_und,b, n, K, T_user=5)
The function returns the adjacency matrix of the network computed with the "doILP" function.
getAdja(res, n, annot=NULL)getAdja(res, n, annot=NULL)
res |
Result returned by the "doILP" function. |
n |
Integer: the number of nodes of the inferred network. |
annot |
Vector of character strings: the annotation of the edges as returned by "getEdgeAnnot". |
Numeric matrix: the adjacency matrix of the network.
n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) #infer the network res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE) # make the adjacency matrix adja <- getAdja(res, n)n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) #infer the network res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE) # make the adjacency matrix adja <- getAdja(res, n)
The function returns a vector with the baseline values of each node in the network computed with the "doILP" function.
getBaseline(res, n, allpos=FALSE)getBaseline(res, n, allpos=FALSE)
res |
Result returned by the "doILP" or "doILP_timeSeries" function. |
n |
Integer: the number of nodes of the inferred network. |
allpos |
Logical: should all variables be positive? Corresponds to learning only activating edges. Default: FALSE. |
Numeric matrix: the adjacency matrix of the network.
n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) #infer the network res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE) # make the adjacency matrix adja <- getBaseline(res, n)n <- 3 # number of genes K <- 4 # number of experiments T_ <- 4 # number of time points # generate random observation matrix obs <- array(rnorm(n*K*T_), c(n,K,T_)) baseline <- c(0.75, 0, 0) delta <- rep(0.75, n) # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1, # perturbation exp1: gene 1 perturbed, gene 2,3 unperturbed 1,0,1, # perturbation exp2: gene 2 perturbed, gene 1,3 unperturbed 1,1,0, # perturbation exp3.... 1,1,1) delta_type <- "perGene" lambda <- 1/10 annot <- getEdgeAnnot(n) #infer the network res <- doILP(obs, delta, lambda, b, n, K, T_, annot, delta_type, prior=NULL, sourceNode=NULL, sinkNode=NULL, all.int=FALSE, all.pos=FALSE, flag_time_series=TRUE) # make the adjacency matrix adja <- getBaseline(res, n)
The function returns the annotation of the edges needed for the LP. Positive edges are annotated with "w+" and negative with "w-". The given nodes are just enumerated from 1 to n and the edge between node i and j is given by "w+_i_j" for the positive, respectively by "w-_i_j" for the negative edges. The annotation "w_i_^_0" defines the baseline activity of gene i.
getEdgeAnnot(n, allpos)getEdgeAnnot(n, allpos)
n |
Integer: number of genes. |
allpos |
Logical: should all edges be positive? Corresponds to learning only activating edges. Default: FALSE. |
n <- 5 annot <- getEdgeAnnot(n)n <- 5 annot <- getEdgeAnnot(n)
The function generates the observation matrix where active/inactive observations are generated from a normal distribution with the average and variation as given in the parameters. This matrix can either be generated from the activation matrix calculated with calcActivation or from the network states caculated with generateTimeSeriesNetStates.
getObsMat(act_mat=NULL, net_states=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type)getObsMat(act_mat=NULL, net_states=NULL, active_mu, active_sd, inactive_mu, inactive_sd, mu_type)
act_mat |
Matrix of 0/1 values called the activation matrix. Rows correspond to genes, columns to experiments. If an entry is 1, it means that the corresponding gene is active in the corresponing experiment and inactive otherwise. |
net_states |
Array of 0/1 values called the network states. Rows correspond to genes, columns to experiments, and the third dimension corresponds to time points. If an entry is 1, it means that the corresponding gene is active in the corresponing experiment and inactive otherwise. |
active_mu |
Numeric: the average value assumed for observations coming from activated nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
active_sd |
Numeric: the variation assumed for observations coming from activated nodes. The parameter active_mu and active_sd are used for predicting the observations of the normal distribution of activate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_mu |
Numeric: the average value assumed for observations coming from inactivated nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
inactive_sd |
Numeric: the variation assumed for observations coming from inactivated nodes. The parameter inactive_mu and inactive_sd are used for predicting the observations of the normal distribution of inactivate genes. This parameter can be either a numeric, a vector, a matrix, or a 3D array, depending on the specified mu_type. |
mu_type |
Character: can have the following values and meanings:
|
Numeric matrix/array: the observation matrix/array. It can have up to 3 dimensions, where dimension 1 are the network nodes, dimension 2 are the perturbation experiments, and dimension 3 are the time points (if considered).
n <- 5 # number of genes K <- 7 # number of knockdowns # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1,1,1, # perturbation exp1: gene 1 perturbed, gene 2-5 unperturbed 1,0,1,1,1, # perturbation exp2: gene 2 perturbed, gene 1,3,4,5 unperturbed 1,1,0,1,1, # perturbation exp3.... 1,1,1,0,1, 1,1,1,1,0, 1,0,0,1,1, 1,1,1,1,1) T_nw <- matrix(c(0,1,1,0,0, 0,0,0,-1,0, 0,0,0,1,0, 0,0,0,0,1, 0,0,0,0,0), nrow=n, ncol=n, byrow=TRUE) act_mat <- calcActivation(T_nw, b, n, K) # define the parameters for the observation generated from the normal distribution active_mu <- 0.9 inactive_mu <- 0.5 active_sd <- inactive_sd <- 0.1 mu_type <- "single" # compute the observations matrix getObsMat(act_mat=act_mat, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type)n <- 5 # number of genes K <- 7 # number of knockdowns # perturbation vector, entry is 0 if gene is inactivated and 1 otherwise b <- c(0,1,1,1,1, # perturbation exp1: gene 1 perturbed, gene 2-5 unperturbed 1,0,1,1,1, # perturbation exp2: gene 2 perturbed, gene 1,3,4,5 unperturbed 1,1,0,1,1, # perturbation exp3.... 1,1,1,0,1, 1,1,1,1,0, 1,0,0,1,1, 1,1,1,1,1) T_nw <- matrix(c(0,1,1,0,0, 0,0,0,-1,0, 0,0,0,1,0, 0,0,0,0,1, 0,0,0,0,0), nrow=n, ncol=n, byrow=TRUE) act_mat <- calcActivation(T_nw, b, n, K) # define the parameters for the observation generated from the normal distribution active_mu <- 0.9 inactive_mu <- 0.5 active_sd <- inactive_sd <- 0.1 mu_type <- "single" # compute the observations matrix getObsMat(act_mat=act_mat, active_mu=active_mu, active_sd=active_sd, inactive_mu=inactive_mu, inactive_sd=inactive_sd, mu_type=mu_type)
The function computes the adjacency of the edges computed in each step of the "loocv" or the "kfoldCV" function. If the variance of each edge shall be taken into account use "getSampleAdjaMAD", otherwise "getSampleAdja".
getSampleAdjaMAD(edges_all, n, annot_node, method = median, method2 = mad, septype = "->") getSampleAdja(edges_all, n, annot_node, method = median, septype = "->")getSampleAdjaMAD(edges_all, n, annot_node, method = median, method2 = mad, septype = "->") getSampleAdja(edges_all, n, annot_node, method = median, septype = "->")
edges_all |
The inferred edges using the "loocv" or the "kfoldCV" function. |
n |
Integer: the number of nodes. |
annot_node |
Vector of character strings: the annoation of the nodes. |
method |
Character string: the method used to summarize the edges of the individual steps. Default: "median". |
method2 |
Character string: the method used for the computation of the variation of the edges of the individual steps. Default: "mad". |
septype |
Character string: the type of separation of two nodes in the annot string vector. Default: "->". |
Numeric matrix: the adjacency matrix.
# compute random edge weights edges_all <- matrix(rnorm(5*6), nrow=5, ncol=6) # annotation of the edges as returned by "loocv" and kfoldCV colnames(edges_all) <- c("1->2", "1->3", "2->1", "2->3", "3->1", "3->2") # annotation of the nodes annot_node <- c(1,2,3) getSampleAdjaMAD(edges_all, n=3, annot_node, method = "median", method2 = "mad", septype = "->") getSampleAdja(edges_all, n=3, annot_node, method = "median", septype = "->")# compute random edge weights edges_all <- matrix(rnorm(5*6), nrow=5, ncol=6) # annotation of the edges as returned by "loocv" and kfoldCV colnames(edges_all) <- c("1->2", "1->3", "2->1", "2->3", "3->1", "3->2") # annotation of the nodes annot_node <- c(1,2,3) getSampleAdjaMAD(edges_all, n=3, annot_node, method = "median", method2 = "mad", septype = "->") getSampleAdja(edges_all, n=3, annot_node, method = "median", septype = "->")
The function returns the the summarized replicate measuremenst.
summarizeRepl(data,type=median)summarizeRepl(data,type=median)
data |
The data matrix. |
type |
The summarization type which shall be used. Default: median. |
Numeric matrix: the summarized data.
data("SahinRNAi2008") ## process data dataStim <- dat.normalized[dat.normalized[ ,17] == 1, -17] # summarize replicates dataSt <- t(summarizeRepl(dataStim, type=mean))data("SahinRNAi2008") ## process data dataStim <- dat.normalized[dat.normalized[ ,17] == 1, -17] # summarize replicates dataSt <- t(summarizeRepl(dataStim, type=mean))