Localised Co-dependency Analysis

Description

Performs Localised Co-dependency Analysis

Usage

LCA(x,PTLmodel,clique,seed.row,combine.method="Fisher",
adjust.method="BH",comparison.alpha=0.05)

Arguments

Details

Function to evaluate LCD, within the members of clique, for all features in a dataset against the feature represented by seed.row.

Value

List with elements:

Author(s)

Ed Curry e.curry@imperial.ac.uk

Examples

suppressWarnings(RNGversion("3.5.0"))
## create a data matrix

x <- array(runif(1200),dim=c(40,12))

## implant similarity across a 'clique'

clique.cols <- sample(ncol(x),4)
x[,clique.cols] <- x[,clique.cols] + rnorm(nrow(x))

## scale x to (0,1)

x[x<0] <- 0
x[x>1] <- 1

## choose a 'seed' feature and some partner

seed.row <- sample(nrow(x),1)
partner.row <- sample(setdiff(c(1:nrow(x)),seed.row),1)

x[c(seed.row,partner.row),clique.cols] <- x[c(seed.row,partner.row),clique.cols] + 
rep(rnorm(length(clique.cols)),each=2)

## calibrate PTL models to dataset

PTL.fit <- fitPTLmodel(x,nPairs=15)

## evaluate LCD between 'seed' feature and all other features
 
LCA.result <- LCA(x,PTLmodel=PTL.fit,clique=clique.cols,seed.row=seed.row)
## Not run: head(LCA.result$LCD)

Localised Co-Dependency Estimates

Description

Evaluates Statistical Significance of Localised Co-Dependency (LCD)

Usage

LCD(x1,x2,seed.row,PTLmodel)

Arguments

Details

Function to evaluate LCD, between two selected objects, for all features in a dataset against the feature represented by seed.row.

Value

Numeric vector giving p-values for significance estimates of localised co-dependency, with the feature specified by seed.row, of all features in the dataset being analysed.

Author(s)

Ed Curry e.curry@imperial.ac.uk

Polynomial-Tail Laplace

Description

Probability density and distribution functions for Polynomial-Tail Laplace distribution

Usage

dPTL(x,alpha,beta,gamma)
pPTL(q,alpha,beta,gamma)

Arguments

Details

The PTL distribution has density

f(x) = \left\{\begin{array}{cc} 0 & x < -2\\ \displaystyle \frac{\alpha(\frac{x^2}{2}+2x+2) + \beta(e^{\frac{x}{\beta}}-e^{\frac{-2}{\beta}}) + \gamma(\frac{x^3}{3}+4x+\frac{16}{3})}{4\alpha + 2\beta(1-e^{\frac{-2}{\beta}}) + \frac{32\gamma}{3}} & -2 \leq x \leq 0\\ \displaystyle \frac{\alpha(2x-\frac{x^2}{2}-2) + \beta(e^{\frac{-2}{\beta}}-e^{\frac{x}{\beta}}) + \gamma(4x-\frac{x^3}{3}-\frac{16}{3})}{4\alpha + 2\beta(1-e^{\frac{-2}{\beta}}) + \frac{32\gamma}{3}} & 0 < x \leq 2\\ 1 & x > 2 \end{array}\right.

Value

dnorm gives the density, pnorm gives the distribution function.

The length of the result is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters are recycled to the length of the result.

Author(s)

Ed Curry e.curry@imperial.ac.uk

ML Estimation of Laplace Beta

Description

Estimates initial value of parameter Beta from the PTL distribution used in LCA analysis.

Usage

estimateB(x)

Arguments

Details

Calculates maximum-likelihood estimate for Beta in the Laplace distribution fit to distribution of x.

Value

Numeric value for initial estimate of PTL distribution parameter Beta

Author(s)

Ed Curry e.curry@imperial.ac.uk

Evaluate Statistical Significance of an Observed Difference Between Two Objects

Description

Use PTL model to estimate the significance of a difference between the values of some feature of interest in two selected objects from a dataset.

Usage

evaluateDiffSignificance(d,diff,PTLmodel)

Arguments

Details

Evaluates statistical significance of observing as great a difference as that observed between the values of a selected feature of interest in the selected objects, given the global dissimilarity between those objects and the PTL models fitted to characterise these distributions across the whole dataset.

Value

Numeric value giving p-value representing significance estimate of the observed difference, given the fitted models.

Author(s)

Ed Curry e.curry@imperial.ac.uk

Calibrate Polynomial-Tail Laplace (PTL) model prdictions for LCA analysis

Description

Fits PTL models to randomly sampled pairs of the dataset, to enable prediction of PTL model parameter values based on hyperparameter d.

Usage

fitPTLmodel(x,nPairs=10000)

Arguments

Details

Evaluates parameters for PTL model fits to the distributions of feature-wise differences between each of a specified (large) number of pairs of objects represented in dataset x. Obtains subsequent model fits explaining the individual PTL parameters alpha,beta,gamma in terms of the global (Euclidean) distances between the corresponding pairs of objects.

Value

List with the following components:

Author(s)

Ed Curry e.curry@imperial.ac.uk

Predict Distribution of Feature-Wise Differences

Description

Predicts the expected number of features with a difference between two objects of a given global dissimilarity lying within a set of specified ranges.

Usage

getPTLExpectedCounts(alpha,beta,gamma,bin_limits,ntrials)

Arguments

Details

Uses a PTL model with the specified parameters to estimate the expected number of features with differences between specified ranges. Used in calibration of PTL model parameter prediction to the dataset.

Value

Numeric vector giving expected counts for numbers of features with a difference lying within the given set of specified ranges.

Author(s)

Ed Curry e.curry@imperial.ac.uk

Find best values of PTL parameters

Description

Finds parameters alpha, beta and gamma in PTL model to fit an observed distribution of differences in each feature's values between two given objects from a dataset.

Usage

getPTLparams(x1,x2)

Arguments

Details

Uses iterative NLS fitting to determine parameters of PTL model to represent the distribution of the differences observed between two objects selected from the dataset being analysed with LCA.

Value

List with the following elements:

Author(s)

Ed Curry e.curry@imperial.ac.uk

Predict Values for PTL Model

Description

Generates parameter values for PTL model, based on a specified value of the hyperparameter

Usage

predictPTLparams(d,PTLmodel)

Arguments

Details

Uses hyperparameter-based prediction linear models, calibrated to the dataset being analysed using the fitPTLmodel function, to estimate PTL model parameters for a pair of objects in the dataset with a global dissimilarity d.

Value

List with elements:

Author(s)

Ed Curry e.curry@imperial.ac.uk