TRMF_trend {TRMF}

Add Trend Model to a TRMF Object

Description

Creates a regularization scheme that favors trend-like solutions and adds it to a TRMF object. In matrix optimization form, it adds the following term to the TRMF cost function: R(x) = lambdaD^2||w(DX_s)||^2 + lambdaA^2||X_s||^2 where X_s is sub-set of the Xm matrix controlled by this model and D is a finite difference matrix.

Usage

TRMF_trend(obj,numTS = 1,order = 1,lambdaD=1,lambdaA=0.0001,weight=1)

Arguments

obj

A TRMF object

numTS

number of latent time series in this model

order

The order of derivative for finite difference constraint matrix. Fractionally and negative values allowed.

lambdaD

regularization parameter for temporal constraint matrix

lambdaA

regularization parameter to apply simple L2 regularization to this time series model

weight

optional vector of weights to weight constraints, i.e. R(x) = lambdaD^2*||w*(D%*%X)||^2

Details

An arbitrary number of time series models can be added. TRMF_trend(order = 1) fits a random walk. TRMF_trend(order = 2) fits a cubic smoothing spline. For a single time series, TRMF_trend(order = 2) is basically equivalent to the Hodge-Prescot filter. A fractional value for order minimizes a squared fractional derivative. A negative value minimizes a (possibly fractional order) squared integral of time-series. Using a fractional or negative order for TRMF_trend could drastically reduce the sparsity of constraint matrix and slow down training. Fractional or negative order has only been lightly tested, so use with care.

Value

Returns an updated object of class TRMF.

Note

Unlike TRMF_columns(), these lambdas are squared in the code.

Author(s)

Chad Hammerquist

References

Yu, Hsiang-Fu, Nikhil Rao, and Inderjit S. Dhillon. "High-dimensional time series prediction with missing values." arXiv preprint arXiv:1509.08333 (2015).

See Also

create_TRMF, TRMF_columns, TRMF_simple, TRMF_seasonal

Examples

# create test data
xm = poly(x = (-10:10)/10,degree=4)
fm = matrix(runif(40),4,10)
Am = xm%*%fm+rnorm(210,0,.1)

# create model
obj = create_TRMF(Am)
obj = TRMF_columns(obj,reg_type ="interval")
obj = TRMF_trend(obj,numTS=4,order=2,lambdaD=2)
out = train(obj)
plot(out)

# more complex model
require(magrittr) # for pipes

obj = create_TRMF(Am)%>%
    TRMF_columns(reg_type ="interval")%>%
    TRMF_trend(numTS=2,order=1,lambdaD=4)%>%
    TRMF_trend(numTS=2,order=2,lambdaD=4)%>%
    TRMF_trend(numTS=1,order=1.5)

out = train(obj)
plot(out)