FLLat.BIC: Optimal Tuning Parameters for the Fused Lasso Latent Feature

Description

Returns the optimal values of the fused lasso tuning parameters for the Fused Lasso Latent Feature (FLLat) model by minimizing the BIC. Also returns the fitted FLLat model for the optimal values of the tuning parameters.

Usage

FLLat.BIC(Y, J=min(15,floor(ncol(Y)/2)), B="pc", thresh=10^(-4), maxiter=100,
          maxiter.B=1, maxiter.T=1)

Arguments

A matrix of data from an aCGH experiment (usually in the form of log intensity ratios) or some other type of copy number data. Rows correspond to the probes and columns correspond to the samples.

The number of features in the FLLat model. The default is the smaller of either $15$ or the number of samples divided by $2$.

The initial values for the features. Can be one of "pc" (the first J principal components of Y), "rand" (a random selection of J columns of Y), or a user specified matrix of initial values, where rows correspond to the probes and columns correspond to the features. The default is "pc".

thresh

The threshold for determining when the solutions have converged. The default is $10^{-4}$.

maxiter

The maximum number of iterations for the outer loop of the FLLat algorithm. The default is $100$.

maxiter.B

The maximum number of iterations for the inner loop of the FLLat algorithm for estimating the features $B$. The default is $1$. Increasing this may decrease the number of iterations for the outer loop but may still increase total run time.

maxiter.T

The maximum number of iterations for the inner loop of the FLLat algorithm for estimating the weights $\Theta$. The default is $1$. Increasing this may decrease the number of iterations for the outer loop but may still increase total run time.

Value

A list with components:

lam0

The optimal value of $\lambda_0$.

alpha

The optimal value of $\alpha$.

lam1

The optimal value of $\lambda_1$.

lam2

The optimal value of $\lambda_2$.

opt.FLLat

The fitted FLLat model for the optimal values of the tuning parameters.

Details

This function returns the optimal values of the fused lasso tuning parameters, $\lambda_1$ and $\lambda_2$, for the FLLat model. The optimal values are chosen by first re-parameterizing $\lambda_1$ and $\lambda_2$ in terms of $\lambda_0$ and a proportion $\alpha$ such that $\lambda_1=\alpha\lambda_0$ and $\lambda_2=(1-\alpha)\lambda_0$. The values of $\alpha$ are fixed to be $\{0.1, 0.3, 0.5, 0.7, 0.9\}$ and for each value of $\alpha$ we consider a range of $\lambda_0$ values. The optimal values of $\lambda_0$ and $\alpha$ (and consequently $\lambda_1$ and $\lambda_2$) are chosen by minimizing the following BIC-type criterion over this two dimensional grid: $$(SL)\times\log\left(\frac{RSS}{SL}\right) + k_{\alpha,\lambda_0}\log(SL),$$ where $S$ is the number of samples, $L$ is the number probes, $RSS$ denotes the residual sum of squares and $k_{\alpha, \lambda_0}$ denotes the sum over all the features of the number of unique non-zero elements in each estimated feature.

Note that for extremely large data sets, this function may take some time to run.

For more details, please see Nowak and others (2011) and the package vignette.

References

G. Nowak, T. Hastie, J. R. Pollack and R. Tibshirani. A Fused Lasso Latent Feature Model for Analyzing Multi-Sample aCGH Data. Biostatistics, 2011, doi: 10.1093/biostatistics/kxr012

Examples

Run this code

## Load simulated aCGH data.
data(simaCGH)

## Run FLLat.BIC to choose optimal tuning parameters for J = 5 features.
result.bic <- FLLat.BIC(simaCGH,J=5)

## Plot the features for the optimal FLLat model.
plot(result.bic$opt.FLLat)

## Plot a heatmap of the weights for the optimal FLLat model.
plot(result.bic$opt.FLLat,type="weights")

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