The Lasso for High-Dimensional Regression with a Possible Change-Point

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the $\ell_1$ estimation loss for regression coefficients. Since the Lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a nearly $n^{-1}$ factor even when the number of regressors can be much larger than the sample size ($n$). We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data

Attention-Propagation Network for Egocentric Heatmap to 3D Pose Lifting

We present EgoTAP, a heatmap-to-3D pose lifting method for highly accurate stereo egocentric 3D pose estimation. Severe self-occlusion and out-of-view limbs in egocentric camera views make accurate pose estimation a challenging problem. To address the challenge, prior methods employ joint heatmaps-probabilistic 2D representations of the body pose, but heatmap-to-3D pose conversion still remains an inaccurate process. We propose a novel heatmap-to-3D lifting method composed of the Grid ViT Encoder and the Propagation Network. The Grid ViT Encoder summarizes joint heatmaps into effective feature embedding using self-attention. Then, the Propagation Network estimates the 3D pose by utilizing skeletal information to better estimate the position of obscure joints. Our method significantly outperforms the previous state-of-the-art qualitatively and quantitatively demonstrated by a 23.9\% reduction of error in an MPJPE metric. Our source code is available in GitHub.Comment: 16 pages, 9 figures, to be published as CVPR 2024 pape

Testing for threshold effects in regression models

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online.

Factor-Driven Two-Regime Regression

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies

Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy distribution. For both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically'' generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {\it beyond the truncation cutoff}, which leads to a crossover between a L\'{e}vy stable power law and the present ``dynamically-generated'' power law. We show that the process can explain the crossover behavior recently observed in the S&P500 stock index.Comment: 7 pages, five figures. To appear in Europhysics Letters (2000