SEMml: Nodewise SEM train using Machine Learning (ML)

In SEMdeep: Structural Equation Modeling with Deep Neural Network and Machine Learning

Nodewise SEM train using Machine Learning (ML)

Description

The function converts a graph to a collection of nodewise-based models: each mediator or sink variable can be expressed as a function of its parents. Based on the assumed type of relationship, i.e. linear or non-linear, SEMml() fits a ML model to each node (variable) with non-zero incoming connectivity. The model fitting is performed equation-by equation (r=1,...,R) times, where R is the number of mediators and sink nodes.

Usage

SEMml(
  graph,
  data,
  outcome = NULL,
  algo = "sem",
  thr = NULL,
  nboot = 0,
  ncores = 2,
  verbose = FALSE,
  ...
)

Arguments

graph	An igraph object.
data	A matrix with rows corresponding to subjects, and columns to graph nodes (variables).
outcome	A character vector (as.fctor) of labels for a categorical output (target). If NULL (default), the categorical output (target) will not be considered.
algo	ML method used for nodewise-network predictions. Six algorithms can be specified: algo="sem" (default) for a linear SEM, see SEMrun. algo="tree" for a CART model, see rpart. algo="rf" for a random forest model, see ranger. algo="xgb" for a XGBoost model, see xgboost. algo="nn" for a small neural network model (1 hidden layer and 10 nodes), see nnet. algo="dnn" for a large neural network model (1 hidden layers and 1000 nodes), see dnn.
thr	A numeric value [0-1] indicating the threshold to apply to the variable importance values to color the graph. If thr = NULL (default), the threshold is set to thr = 0.5*max(abs(variable importance values)).
nboot	number of bootstrap samples that will be used to compute cheap (lower, upper) CIs for all input variable weights. As a default, nboot = 0.
ncores	number of cpu cores (default = 2)
verbose	A logical value. If FALSE (default), the processed graph will not be plotted to screen.
...	Currently ignored.

Details

By mapping data onto the input graph, SEMml() creates a set of nodewise-based models based on the directed links, i.e., a set of edges pointing in the same direction, between two nodes in the input graph that are causally relevant to each other. The mediator or sink variables can be characterized in detail as functions of their parents. An ML model (sem, tree, rf, xgb, nn, dnn) can then be fitted to each variable with non-zero inbound connectivity. With R representing the number of mediators and sink nodes in the network, the model fitting process is performed equation-by-equation (r=1,...,R) times.

If boot != 0, the function will implement the cheap bootstrapping proposed by Lam (2002) to generate uncertainties, i.e. 90 for ML parameters. Bootstrapping can be enabled by setting a small number (1 to 10) of bootstrap samples. Note, however, that the computation can be time-consuming for massive MLs, even with cheap bootstrapping!

Value

An S3 object of class "ML" is returned. It is a list of 5 objects:

1. "fit", a list of ML model objects, including: the estimated covariance matrix (Sigma), the estimated model errors (Psi), the fitting indices (fitIdx), and the parameterEstimates, i.e., the variable importance measures (VarImp).

2. "gest", the data.frame of variable importances (parameterEstimates) of outcome levels, if outcome != NULL.

3. "model", a list of all the fitted non-linear nodewise-based models (tree, rf, xgb, nn or dnn).

4. "graph", the induced DAG of the input graph mapped on data variables. The DAG with colored edge/nodes based on the variable importance measures, i.e., if abs(VarImp) > thr will be highlighted in red (VarImp > 0) or blue (VarImp < 0). If the outcome vector is given, nodes with variable importances summed over the outcome levels, i.e. sum(VarImp[outcome levels])) > thr, will be highlighted in pink.

5. "data", input data subset mapping graph nodes.

Using the default algo="sem", the usual output of a linear nodewise-based, SEM, see SEMrun (algo="cggm"), will be returned.

Author(s)

Mario Grassi [e-mail]

References

Grassi M., Palluzzi F., and Tarantino B. (2022). SEMgraph: An R Package for Causal Network Analysis of High-Throughput Data with Structural Equation Models. Bioinformatics, 38 (20), 4829–4830 <https://doi.org/10.1093/bioinformatics/btac567>

Breiman L., Friedman J.H., Olshen R.A., and Stone, C.J. (1984) Classification and Regression Trees. Chapman and Hall/CRC.

Breiman L. (2001). Random Forests, Machine Learning 45(1), 5-32.

Chen T., and Guestrin C. (2016). XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.

Ripley B.D. (1996). Pattern Recognition and Neural Networks. Cambridge University Press.

Lam, H. (2022). Cheap bootstrap for input uncertainty quantification. WSC '22: Proceedings of the Winter Simulation Conference, 2318 - 2329.

Examples

# Load Amyotrophic Lateral Sclerosis (ALS)
ig<- alsData$graph
data<- alsData$exprs
data<- transformData(data)$data
group<- alsData$group

#...with train-test (0.5-0.5) samples
set.seed(123)
train<- sample(1:nrow(data), 0.5*nrow(data))

start<- Sys.time()
# ... tree
res1<- SEMml(ig, data[train, ], algo="tree")

# ... rf
res2<- SEMml(ig, data[train, ], algo="rf")

# ... xgb
res3<- SEMml(ig, data[train, ], algo="xgb")

# ... nn
res4<- SEMml(ig, data[train, ], algo="nn")

end<- Sys.time()
print(end-start)

#visualizaation of the colored dag for algo="nn"
gplot(res4$graph, l="dot", main="nn")

#Comparison of fitting indices (in train data)
res1$fit$fitIdx #tree
res2$fit$fitIdx #rf
res3$fit$fitIdx #xgb
res4$fit$fitIdx #nn

#Comparison of parameter estimates (in train data)
parameterEstimates(res1$fit) #tree
parameterEstimates(res2$fit) #rf
parameterEstimates(res3$fit) #xgb
parameterEstimates(res4$fit) #nn

#Comparison of VarImp (in train data)
table(E(res1$graph)$color) #tree
table(E(res2$graph)$color) #rf
table(E(res3$graph)$color) #xgb
table(E(res4$graph)$color) #nn

#Comparison of AMSE, R2, SRMR (in test data)
print(predict(res1, data[-train, ])$PE) #tree
print(predict(res2, data[-train, ])$PE) #rf
print(predict(res3, data[-train, ])$PE) #xgb
print(predict(res4, data[-train, ])$PE) #nn

#...with a categorical (as.factor) outcome
outcome <- factor(ifelse(group == 0, "control", "case")); table(outcome) 

res5 <- SEMml(ig, data[train, ], outcome[train], algo="tree")
gplot(res5$graph)
table(E(res5$graph)$color)
table(V(res5$graph)$color)

pred <- predict(res5, data[-train, ], outcome[-train], verbose=TRUE)
yhat <- pred$Yhat[ ,levels(outcome)]; head(yhat)
yobs <- outcome[-train]; head(yobs)
classificationReport(yobs, yhat, verbose=TRUE)$stats

SEMdeep documentation built on April 12, 2025, 2:24 a.m.