STATSCALE SEMINARS
PREVIOUS SEMINAR - 22nd October 2021

Ichiro Takeuchi (Nagoya Institute of Technology)

Title: More powerful and general conditional selective inference by parametric programming and its application to multi-dimensional change-point detection

 


Abstract- A conditional selective inference (SI) framework was introduced as a statistical inference method for selected features by Lasso (Lee et al., 2016). This framework allows us to derive the exact conditional sampling distribution of the selected test statistic when the selection event is characterized by a polyhedron. In fact, this framework is not only useful for Lasso but also generally applicable to a certain class of data-driven hypotheses. A common limitation of existing conditional SI studies is that the hypothesis selection event must be characterized in a simple tractable form such as a set of linear or quadratic inequalities. This limitation causes the so-called over-conditioning problem, which leads to the loss of the power. Furthermore, this limitation makes the conditional SI framework applicable only to relatively simple problems. To overcome this limitation, we proposed a new computational method for conditional SI using parametric programming (PP), which we call PP-based SI. PP-based SI allows us to avoid the aforementioned over-conditioning problem and apply the conditional SI framework to more complex problems. In this talk, after briefly reviewing the conditional SI framework, we introduce the PP-based SI approach, and show that it is possible to improve the power of conditional SI for Lasso and other feature selection methods. Furthermore, as an example of how PP-based SI can extend the applicability of conditional SI, we present our recent work on the conditional SI for multi-dimensional change-point detection. 

# This is joint work with my ph.d student Vo Nguyen Le Duy.

References:
[1] Duy et al. (NeurIPS2020)
https://proceedings.neurips.cc/paper/2020/file/82b04cd5aa016d979fe048f3ddf0e8d3-Paper.pdf
[2] Duy et al. (AIStats2021)
http://proceedings.mlr.press/v130/nguyen-le-duy21a/nguyen-le-duy21a.pdf
[3] Sugiyama et al. (ICML2021)
http://proceedings.mlr.press/v139/sugiyama21a/sugiyama21a.pdf
[4] Duy et al. (arXiv)
https://arxiv.org/pdf/2010.01823.pdf

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