# SpiecEasi v1.0.2

## Sparse Inverse Covariance for Ecological Statistical Inference

Estimate networks from the precision matrix of compositional microbial abundance data.

# SpiecEasi

Sparse InversE Covariance estimation for Ecological Association and Statistical Inference

This package will be useful to anybody who wants to infer graphical models for all sorts of compositional data, though primarily intended for microbiome relative abundance data (generated from 16S amplicon sequence data). It also includes a generator for [overdispersed, zero inflated] multivariate, correlated count data. Please see the paper published in PLoS Comp Bio.

One small point on notation: we refer to the method as "SPIEC-EASI" and reserve "SpiecEasi" for this package.

## Installation

I assume that all auxiliary packages are already installed - for example huge, MASS, etc. If you get an unexpected error, you may need to download and install a missing dependency.

From an interactive R session:

library(devtools)
install_github("zdk123/SpiecEasi")
library(SpiecEasi)

## News

The latest SpiecEasi (version 1.0.0 and higher) now uses the pulsar package for stability-based model selection. The methods are similar to previous releases, but contains some additional methods for speeding up computations

The input arguments have changed slightly (but are backwards compatible) but the data structure that is returned from spiec.easi has changed.

The output to spiec.easi-fit models structure can be easily processed using new getter functions. See ?getOptInd for usage.

You can revert to the previous release (0.1.4) to avoid code-breaking changes.

## Basic Usage

Lets simulate some multivariate data under zero-inflated negative binomial model, based on (high depth/count) round 1 of the American gut project, with a sparse network. The basic steps are

1. load the data and normalize counts to to common scale (min depth)
2. fit count margins to the model
3. generate a synthetic network
4. generate some synthetic data
5. clr transformation
6. inverse covariance estimation along a lambda (sparsity) path
7. stability selection using the StARS criterion
8. evaluate performance

Obviously, for real data, skip 1-4.

data(amgut1.filt)
depths <- rowSums(amgut1.filt)
amgut1.filt.n  <- t(apply(amgut1.filt, 1, norm_to_total))
amgut1.filt.cs <- round(amgut1.filt.n * min(depths))

d <- ncol(amgut1.filt.cs)
n <- nrow(amgut1.filt.cs)
e <- d

Synthesize the data

set.seed(10010)
graph <- make_graph('cluster', d, e)
Prec  <- graph2prec(graph)
Cor   <- cov2cor(prec2cov(Prec))

X <- synth_comm_from_counts(amgut1.filt.cs, mar=2, distr='zinegbin', Sigma=Cor, n=n)

the main SPIEC-EASI pipeline: Data transformation, sparse inverse covariance estimation and model selection

se <- spiec.easi(X, method='mb', lambda.min.ratio=1e-2, nlambda=15)
# Applying data transformations...
# Selecting model with pulsar using stars...
# Fitting final estimate with mb...
# done

examine ROC over lambda path and PR over the stars index for the selected graph

huge::huge.roc(se$est$path, graph, verbose=FALSE)
stars.pr(getOptMerge(se), graph, verbose=FALSE)
# stars selected final network under: se.est$refit$stars

The above example does not cover all possible options and parameters. For example, other generative network models are available, the lambda.min.ratio (the scaling factor that determines the minimum sparsity/lambda parameter) shown here might not be right for your dataset, and its possible that you'll want more repetitions (number of subsamples) for StARS.

## Analysis of American Gut data

Now let's apply SpiecEasi directly to the American Gut data. Don't forget that the normalization is performed internally in the spiec.easi function. Also, we should use a larger number of stars repetitions for real data. We can pass in arguments to the inner stars selection function as a list via the parameter pulsar.params. If you have more than one processor available, you can also supply a number to ncores. Also, let's compare results from the MB and glasso methods as well as SparCC (correlation).

se.mb.amgut <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-2,
nlambda=20, pulsar.params=list(rep.num=50))
se.gl.amgut <- spiec.easi(amgut1.filt, method='glasso', lambda.min.ratio=1e-2,
nlambda=20, pulsar.params=list(rep.num=50))
sparcc.amgut <- sparcc(amgut1.filt)
## Define arbitrary threshold for SparCC correlation matrix for the graph
sparcc.graph <- abs(sparcc.amgut$Cor) >= 0.3 diag(sparcc.graph) <- 0 sparcc.graph <- Matrix(sparcc.graph, sparse=TRUE) ## Create igraph objects ig.mb <- adj2igraph(getRefit(se.mb.amgut)) ig.gl <- adj2igraph(getRefit(se.gl.amgut)) ig.sparcc <- adj2igraph(sparcc.graph) Visualize using igraph plotting: library(igraph) ## set size of vertex proportional to clr-mean vsize <- rowMeans(clr(amgut1.filt, 1))+6 am.coord <- layout.fruchterman.reingold(ig.mb) par(mfrow=c(1,3)) plot(ig.mb, layout=am.coord, vertex.size=vsize, vertex.label=NA, main="MB") plot(ig.gl, layout=am.coord, vertex.size=vsize, vertex.label=NA, main="glasso") plot(ig.sparcc, layout=am.coord, vertex.size=vsize, vertex.label=NA, main="sparcc") We can evaluate the weights on edges networks using the terms from the underlying model. SparCC correlations can be used directly, while SpiecEasi networks need to be massaged a bit. Note that since SPIEC-EASI is based on penalized estimators, the edge weights are not directly comparable to SparCC (or Pearson/Spearman correlation coefficients) library(Matrix) secor <- cov2cor(getOptCov(se.gl.amgut)) sebeta <- symBeta(getOptBeta(se.mb.amgut), mode='maxabs') elist.gl <- summary(triu(secor*getRefit(se.gl.amgut), k=1)) elist.mb <- summary(sebeta) elist.sparcc <- summary(sparcc.graph*sparcc.amgut$Cor)

hist(elist.sparcc[,3], main='', xlab='edge weights')

Lets look at the degree statistics from the networks inferred by each method.

dd.gl     <- degree.distribution(ig.gl)
dd.mb     <- degree.distribution(ig.mb)
dd.sparcc <- degree.distribution(ig.sparcc)

plot(0:(length(dd.sparcc)-1), dd.sparcc, ylim=c(0,.35), type='b',
ylab="Frequency", xlab="Degree", main="Degree Distributions")
points(0:(length(dd.gl)-1), dd.gl, col="red" , type='b')
points(0:(length(dd.mb)-1), dd.mb, col="forestgreen", type='b')
legend("topright", c("MB", "glasso", "sparcc"),
col=c("forestgreen", "red", "black"), pch=1, lty=1)

## Working with phyloseq

SpiecEasi includes some convience wrappers to work directly with phyloseq objects.

library(phyloseq)
## Load round 2 of American gut project
data('amgut2.filt.phy')
se.mb.amgut2 <- spiec.easi(amgut2.filt.phy, method='mb', lambda.min.ratio=1e-2,
nlambda=20, pulsar.params=list(rep.num=50))
plot_network(ig2.mb, amgut2.filt.phy, type='taxa', color="Rank3")

## Cross domain interactions

SpiecEasi now includes a convenience wrapper for dealing with multiple taxa sequenced on the same samples, such as 16S and ITS, as seen in Tipton, Müller, et. al. (2018). It assumes that each taxa is in it's own data matrix and that all samples are in all data matrices in the same order.

Here's an example run from the HMP2 project with 16S and Proteomics data.

library(phyloseq)
data(hmp2)
se.hmp2 <- spiec.easi(list(hmp216S, hmp2prot), method='mb', nlambda=40,
lambda.min.ratio=1e-2, pulsar.params = list(thresh = 0.05))

dtype <- c(rep(1,ntaxa(hmp216S)), rep(2,ntaxa(hmp2prot)))

## pulsar: parallel utilities for model selection

SpiecEasi is now using the pulsar package as the backend for performing model selection. In the default parameter setting, this uses the same StARS procedure as previous versions. As in the previous version of SpiecEasi, we can supply the ncores argument to the pulsar.params list to break up the subsampled computations into parallel tasks. In this example, we set the random seed to make consistent comparison across experiments.

## Default settings ##
pargs1 <- list(rep.num=50, seed=10010)
t1 <- system.time(
se1 <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-3, nlambda=30,
sel.criterion='stars', pulsar.select=TRUE, pulsar.params=pargs1)
)
## Parallel multicore ##
pargs2 <- list(rep.num=50, seed=10010, ncores=4)
t2 <- system.time(
se2 <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-3, nlambda=30,
sel.criterion='stars', pulsar.select=TRUE, pulsar.params=pargs2)
)

We can further speed up StARS using the bounded-StARS ('bstars') method. The B-StARS approach computes network stability across the whole lambda path, but only for the first 2 subsamples. This is used to build an initial estimate of the summary statistic, which in turn gives us a lower/upper bound on the optimal lambda. The remaining subsamples are used to compute the stability over the restricted path. Since denser networks are more computational expensive to compute, this can significantly reduce computational time for datasets with many variables.

t3 <- system.time(
se3 <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-3, nlambda=30,
sel.criterion='bstars', pulsar.select=TRUE, pulsar.params=pargs1)
)
t4 <- system.time(
se4 <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-3, nlambda=30,
sel.criterion='bstars', pulsar.select=TRUE, pulsar.params=pargs2)
)

We can see that in addition to the computational savings, the refit networks are identical.

## serial vs parallel
identical(getRefit(se1), getRefit(se2))
t1[3] > t2[3]
## stars vs bstars
identical(getRefit(se1), getRefit(se3))
t1[3] > t3[3]
identical(getRefit(se2), getRefit(se4))
t2[3] > t4[3]

### Batch Mode

Pulsar gives us the option of running stability selection in batch mode, using the batchtools package. This will be useful to anyone with access to an hpc/distributing computing system. Each subsample will be independently executed using a system-specific cluster function.

This requires an external config file which will instruct the batchtools registry how to construct the cluster function which will execute the individual jobs. batch.pulsar has some built in config files that are useful for testing purposes (serial mode, "parallel", "snow", etc), but it is advisable to create your own config file and pass in the absolute path. See the batchtools docs for instructions on how to construct config file and template files (i.e. to interact with a queueing system such as TORQUE or SGE).

## bargs <- list(rep.num=50, seed=10010, conffile="path/to/conf.txt")
bargs <- list(rep.num=50, seed=10010, conffile="parallel")
## See the config file stores:
pulsar::findConfFile('parallel')
# [1] "/usr/local/lib/R/3.4/site-library/pulsar/config/batchtools.conf.parallel.R"

## uncomment line below to turn off batchtools reporting
# options(batchtools.verbose=FALSE)
se5 <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-3, nlambda=30,
sel.criterion='stars', pulsar.select='batch', pulsar.params=bargs)
# Applying data transformations...
# Selecting model with batch.pulsar using stars...
# Fitting final estimate with mb...
# done

## Troubleshooting

A common issue that comes up with when running spiec.easi is coming up with an empty network after running StARS.

For example:

pargs <- list(seed=10010)
se <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=5e-1, nlambda=10, pulsar.params=pargs)
# Warning in pulsar(data = X, fun = match.fun(estFun), fargs = args, seed =
# 10010, : Optimal lambda may be smaller than the supplied values
getOptInd(se)
# [1] 1
sum(getRefit(se))/2
# [1] 0

As the warning indicates, the network stability could not be determined from the lambda path. Looking at the stability along the lambda path, se$select$stars\$summary, we can see that the maximum value of the StARS summary statistic never crosses the default threshold (0.05).

This problem we can fix by lowering lambda.min.ratio to explore denser networks.

se <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-1, nlambda=10, pulsar.params=pargs)

We have now fit a network, but since we have only a rough, discrete sampling of networks along the lambda path, we should check how far we are from the target stability threshold (0.05).

getStability(se)
# [1] 0.03518685
sum(getRefit(se))/2
# [1] 158

To get closer to the mark, we should bump up nlambda to more finely sample of the lambda path, which gives a denser network.

se <- spiec.easi(amgut1.filt, method='mb', lambda.min.ratio=1e-1, nlambda=100, pulsar.params=pargs)
getStability(se)
# [1] 0.04798275
sum(getRefit(se))/2
# [1] 206

## Functions in SpiecEasi

 Name Description cov2prec Covariance matrix to its matrix inverse (Precision matrix) graph2prec Convert a symmetric graph (extension of R matrix class) adj2igraph Adjacency to igraph norm_to_total Total Sum Normalize prec2cov Precision matrix (inverse covariance) to a covariance matrix hmp2 Human Microbiome Project 2 alr Additive log-ratio functions clr Centered log-ratio functions symBeta sym beta pulsar.params pulsar params neff N_effective: Compute the exponential of the shannon entropy. linearizes shannon entropy, for a better diveristy metric (effective number of species) as.data.frame.graph s3 method for graph to other data types cor2cov Convert a symmetric correlation matrix to a covariance matrix given the standard deviation rmvpois Generate multivariate poisson data, with counts approximately correlated according to Sigma rmvzinegbin Generate multivariate, negative binomial data, with counts approximately correlated according to Sigma as.matrix.graph s3 method for graph to other data types synth_comm_from_counts synth_comm_from_counts pval.sparccboot SparCC p-vals norm_pseudo Normalize w/ Pseudocount qqdplot deprecated?? make_graph Procedure to generate graph topologies for Gaussian Graphical Models multi.spiec.easi multi domain SPIEC-EASI sparccboot Bootstrap SparCC rzipois Draw samples from a zero-inflated poisson distribution rmvzipois Generate multivariate, Zero-inflated poisson data, with counts approximately correlated according to Sigma AGP American Gut Project SpiecEasi-package SpiecEasi: Sparse Inverse Covariance for Ecological Statistical Inference sparseiCov Sparse/penalized estimators of covariance matrices getOptInd get StARS-optimal network qqdplot_comm qq-plot for theoretical vs observed communities get_comm_params Get the parameters for the OTUs (along mar) of each community rmvnegbin Generate multivariate, Zero-inflated negative binomial data, with counts approximately correlated according to Sigma rmvnorm Draw samples from multivariate, correlated normal distribution with counts correlated according to Sigma spiec.easi SPIEC-EASI pipeline shannon compute the shannon entropy from a vector (normalized internally) stars.roc stars.roc, stars.pr sparcc sparcc wrapper fitdistr Fit parameters of a marginal distribution to some data vector No Results!

## Details

 Encoding UTF-8 biocViews License GPL (>= 2) LazyData true RoxygenNote 6.1.0
 depends , R (>= 3.3.0) suggests batchtools , boot , igraph , parallel , phyloseq , testthat imports graphics , grDevices , huge , MASS , Matrix , methods , pulsar (>= 0.3.4) , stats , VGAM Contributors Christian Mueller, Emily Miraldi, Richard Bonneau, Laura Tipton