{"ID":2869999,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.14229","arxiv_id":"2509.14229","title":"Spacing Test for Fused Lasso","abstract":"Detecting changepoints in a one-dimensional signal is a classical yet fundamental problem. The fused lasso provides an elegant convex formulation that produces a stepwise estimate of the mean, but quantifying the uncertainty of the detected changepoints remains difficult. Post-selection inference (PSI) offers a principled way to compute valid $p$-values after a data-driven selection, but its application to the fused lasso has been considered computationally cumbersome, requiring the tracking of many ``hit'' and ``leave'' events along the regularization path. In this paper, we show that the one-dimensional fused lasso has a surprisingly simple geometry: each changepoint enters in a strictly one-sided fashion, and there are no leave events. This structure implies that the so-called \\emph{conservative spacing test} of Tibshirani et al.\\ (2016), previously regarded as an approximation, is in fact \\emph{exact}. The truncation region in the selective law reduces to a single lower bound given by the next knot on the LARS path. As a result, the exact selective $p$-value takes a closed form identical to the simple spacing statistic used in the LARS/lasso setting, with no additional computation. This finding establishes one of the rare cases in which an exact PSI procedure for the generalized lasso admits a closed-form pivot. We further validate the result by simulations and real data, confirming both exact calibration and high power. Keywords: fused lasso; changepoint detection; post-selection inference; spacing test; monotone LASSO","short_abstract":"Detecting changepoints in a one-dimensional signal is a classical yet fundamental problem. The fused lasso provides an elegant convex formulation that produces a stepwise estimate of the mean, but quantifying the uncertainty of the detected changepoints remains difficult. Post-selection inference (PSI) offers a princip...","url_abs":"https://arxiv.org/abs/2509.14229","url_pdf":"https://arxiv.org/pdf/2509.14229v3","authors":"[\"Rieko Tasaka\",\"Tatsuya Kimura\",\"Joe Suzuki\"]","published":"2025-09-17T17:58:28Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.LG\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}