prox.nuclear.func

Proximal function with nuclear norm

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

prox.nuclear.func function

<dl><dt>w1</dt>
<dd>previously updated model parameter</dd>
<dt>y</dt>
<dd>updated model parameter</dd>
<dt>A</dt>
<dd>design matrix</dd>
<dt>b</dt>
<dd>correspond vector, or matrix</dd>
<dt>L</dt>
<dd>learning rate</dd>
<dt>lambda</dt>
<dd>tuning parameter for low-rank component</dd>
<dt>AtA</dt>
<dd>Gram matrix of design matrix A</dd>
<dt>Atb</dt>
<dd>inner product of design matrix A and correspond vector b</dd></dl>

Arguments

Proximal function with nuclear norm penalty updating — prox.nuclear.func

<dl>

<dt>w1</dt>
<dd>previously updated model parameter</dd>


<dt>y</dt>
<dd>updated model parameter</dd>


<dt>A</dt>
<dd>design matrix</dd>


<dt>b</dt>
<dd>correspond vector, or matrix</dd>


<dt>L</dt>
<dd>learning rate</dd>


<dt>lambda</dt>
<dd>tuning parameter for low-rank component</dd>


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


<dt>Atb</dt>
<dd>inner product of design matrix A and correspond vector b</dd>

</dl>

prox.nuclear.func: Proximal function with nuclear norm penalty updating

Description

Usage

Value

Arguments