Adaptive Recursive Partitioning Research Articles

Efficient in-situ image and video compression through probabilistic image representation

Fast and effective image compression for multi-dimensional images has become increasingly important for efficient storage and transfer of massive amounts of high-resolution images and videos. In this paper, we present an efficient in-situ method for multi-dimensional image and video compression called Compression via Adaptive Recursive Partitioning (CARP). CARP uses an optimal permutation of the image pixels inferred from a Bayesian probabilistic model on recursive partitions of the image to reduce its effective dimensionality, achieving a parsimonious representation that preserves information. Furthermore, it adopts a multi-layer Bayesian hierarchical model to achieve in-situ compression along with self-tuning and regularization, with just one single parameter to be specified by the user to achieve the desired compression rate. The properties of our proposed method include high reconstruction quality at a wide range of compression rates while preserving key local details, applicability to a variety of different image/video types and of different dimensions, computational scalability, progressive transmission and ease of tuning. Extensive numerical experiments using a variety of datasets including 2D still images, real-life YouTube videos, and surveillance videos show that CARP compares favorably to—and often uniformly outperforms—a wide range of popular image/video compression approaches, including JPEG, JPEG2000, AVI, BPG, MPEG4, HEVC, AV1, and three neural network-based methods.

Wage Determinants Analysis by Quantile Regression Tree

Quantile regression proposed by Koenker and Bassett (1978) is a statistical technique that estimates conditional quantiles. The advantage of using quantile regression is the robustness in response to large outliers compared to ordinary least squares(OLS) regression. A regression tree approach has been applied to OLS problems to fit flexible models. Loh (2002) proposed the GUIDE algorithm that has a negligible selection bias and relatively low computational cost. Quantile regression can be regarded as an analogue of OLS, therefore it can also be applied to GUIDE regression tree method. Chaudhuri and Loh (2002) proposed a nonparametric quantile regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning. Lee and Lee (2006) investigated wage determinants in the Korean labor market using the Korean Labor and Income Panel Study(KLIPS). Following Lee and Lee, we fit three kinds of quantile regression tree models to KLIPS data with respect to the quantiles, 0.05, 0.2, 0.5, 0.8, and 0.95. Among the three models, multiple linear piecewise quantile regression model forms the shortest tree structure, while the piecewise constant quantile regression model has a deeper tree structure with more terminal nodes in general. Age, gender, marriage status, and education seem to be the determinants of the wage level throughout the quantiles; in addition, education experience appears as the important determinant of the wage level in the highly paid group.

Asymptotic consistency of median regression trees

Estimation of a function parameter by adaptive recursive partitioning of the covariate space is a well known and effective non-parametric statistical technique. Piecewise constant nonparametric estimate of a conditional median function based on least absolute deviations regression tree has been proposed and discussed by Breiman et al. (Classification and Regression Trees. Wadsworth, Belmont, 1984). In this article, we derive and discuss some general regularity conditions that can ensure asymptotic consistency of such an estimate. We also discuss a weighted average technique following Chaudhuri et al. (Statist. Sinica 4 (1994) 143) based on smooth weight functions that can nicely glue the discontinuous constant pieces of such an estimate to yield a smooth and consistent estimate.