smap: smap: A Segmental Maximum A Posteriori Approach to Array-CGH...
In SMAP: A Segmental Maximum A Posteriori Approach to Array-CGH Copy Number Profiling

Description Usage Arguments Details Value Author(s) References See Also Examples

This function fits a Hidden Markov Model (HMM) to a set of observed microarray intensity ratios and outputs the most plausible state sequence in the HMM through segmental a posteriori maximization.

Briefly, given an HMM with initial parameter settings lambda and a set of observations O, the method alternates maximization of the joint posterior probability of the state sequence Q and lambda given O, p(Q,lambda|O), over Q (using a modified Viterbi algorithm) and lambda (using a gradient descent scheme with individual learning rate adaptation).

smap(x, Obs, sd.min=0.05, mean.sd=0.05,
     max.iters=Inf, gd.max.iters=Inf, tau=0.05,
     eta=0.01, e.change=0.5, e.same=1.2,
     e.min=0.0001, e.max=0.5, adaptive=TRUE,
     overlap=TRUE, distance=TRUE, chrom.wise=FALSE,
     verbose=1, L=5000000)

`x`	An object of class `SMAPHMM-class`.
`Obs`	An object of class `SMAPObservations-class`.
`sd.min`	The minimum allowed standard deviation of state associated Gaussian distributions (numeric).
`mean.sd`	Prior standard deviation of state associated Gaussian means (numeric).
`max.iters`	Maximum number of iterations in the SMAP algorithm (numeric).
`gd.max.iters`	Maximum number of iterations in the gradient descent algorithm per SMAP iteration (numeric).
`tau`	Minimum log probability improvement required in the SMAP and gradient descent optimization (numeric).
`eta`	Initial learning rate in the gradient descent optimization (numeric).
`e.change`	Multiplier for individual learning rate adaptation if the sign of partial derivative changes (numeric). Only used if `adaptive == TRUE`.
`e.same`	Multiplier for individual learning rate adaptation if the sign of partial derivative stays the same (numeric). Only used if `adaptive == TRUE`.
`e.min`	Minimum allowed learning rate (numeric).
`e.max`	Maximum allowed learning rate (numeric).
`adaptive`	If `TRUE`, individual learning rate adaptation according to Algorithm 1 in Bagos et al. (2004) is used in the gradient descent optimization.
`overlap`	If `TRUE`, genomic overlap of clones is considered in the optimization.
`distance`	If `TRUE`, genomic distance between clones is considered in the optimization, in terms of distance based transition probabilities.
`chrom.wise`	If `TRUE`, the observations are analyzed chromosome-wise rather than genome-wise.
`verbose`	Specifies the amount of output produced; 0 means no information and 3 a lot of information (numeric).
`L`	A positive length parameter that controls the convergence of distance based transition probabilities towards 1 / `noStates(x)` (numeric).

sd.min, mean.sd, and eta must all be greater than 0. tau must be greater than 0 if max.iters or gd.max.iters are infinite, and can be 0 otherwise. If adaptive is TRUE, then e.change is required to be in the interval (0,1], e.same must be greater than or equal to 1, and e.max must be greater than 0.

The method returns an object of class SMAPProfile-class or SMAPProfiles-class if chrom.wise is set to FALSE or TRUE, respectively.

Robin Andersson robin.andersson@lcb.uu.se

Andersson, R., Bruder, C. E. G., Piotrowski, A., Menzel, U., Nord, H., Sandgren, J., Hvidsten, T. R., Diaz de Stahl, T., Dumanski, J. P., Komorowski, J., A Segmental Maximum A Posteriori Approach to Array-CGH Copy Number Profiling, submitted

Bagos P. G., Liakopoulos T. D., Hamodrakas, S. J. (2004) Faster Gradient Descent Training of Hidden Markov Models, Using Individual Learning Rate Adaptation. In Paliouras, G., Sakakibara, Y., editors, ICGI, volume 3264 of Lecture Notes in Computer Science, pages 40–52.

SMAPHMM, SMAPObservations

## Load Glioblastoma multiforme data
data(GBM)
observations <- SMAPObservations(value=as.numeric(GBM[,2]),
                                 chromosome=as.character(GBM[,3]),
                                 startPosition=as.numeric(GBM[,4]),
                                 endPosition=as.numeric(GBM[,5]),
                                 name="G24460",
                                 reporterId=as.character(GBM[,1]))
plot(observations, ylim=c(0,2))
## Initiate HMM
init.means <- c(0.4, 0.7, 1, 1.3, 1.6, 3)
init.sds <- rep(0.1, 6)
phi <- cbind(init.means, init.sds)
hmm <- SMAPHMM(6, phi, initTrans=0.02)
hmm
## RUN SMAP:
profile <- smap(hmm, observations, verbose=2)
## genome profile
plot(profile, ylim=c(0,2))
## chromosome 9 profile
ids <- which(chromosome(observations) == "9")
plot(profile[ids], ylim=c(0,2), main="chromosome 9")
## output results for chromosome 9
#cbind(reporterId(observations[ids]), Q(profile[ids]))