Q.func

Auxiliary function for FISTA implementation

internal

Implementations of Thresholded Block Segmentation Scheme (TBSS) and Low-rank plus Sparse Two Step Procedure (LSTSP) algorithms for detecting multiple changes in structural VAR models. The package aims to address the problem of change point detection in piece-wise stationary VAR models, under different settings regarding the structure of their transition matrices (autoregressive dynamics); specifically, the following cases are included: (i) (weakly) sparse, (ii) structured sparse, and (iii) low rank plus sparse. It includes multiple algorithms and related extensions from Safikhani and Shojaie (2020) <doi:10.1080/01621459.2020.1770097> and Bai, Safikhani and Michailidis (2020) <doi:10.1109/TSP.2020.2993145>.

Yue Bai

VARDetect

Multiple Change Point Detection in Structural VAR Models

Peiliang Bai

Abolfazl Safikhani

George Michailidis

Q.func function

<dl><dt>x</dt>
<dd>Model parameter for previous update</dd>
<dt>y</dt>
<dd>Model parameter for updating</dd>
<dt>A</dt>
<dd>An n by p design matrix</dd>
<dt>b</dt>
<dd>A correspond vector, or matrix with size of n by 1 or n by p</dd>
<dt>L</dt>
<dd>Learning rate</dd>
<dt>AtA</dt>
<dd>Gram matrix for design matrix A</dd>
<dt>Atb</dt>
<dd>Inner product for design matrix A and correspond vector b</dd></dl>

Arguments

An auxiliary function in FISTA algorithm — Q.func

<dl>

<dt>x</dt>
<dd>Model parameter for previous update</dd>


<dt>y</dt>
<dd>Model parameter for updating</dd>


<dt>A</dt>
<dd>An n by p design matrix</dd>


<dt>b</dt>
<dd>A correspond vector, or matrix with size of n by 1 or n by p</dd>


<dt>L</dt>
<dd>Learning rate</dd>


<dt>AtA</dt>
<dd>Gram matrix for design matrix A</dd>


<dt>Atb</dt>
<dd>Inner product for design matrix A and correspond vector b</dd>

</dl>

Q.func: An auxiliary function in FISTA algorithm

Description

Usage

Value

Arguments