We propose a novel method for estimating heterogeneous treatment effects based on the fused lasso. By first ordering samples based on the propensity or prognostic score, we match units from the treatment and control groups. We then run the fused lasso to obtain piecewise constant treatment effects with respect to the ordering defined by the score. Similar to the existing methods based on discretizing the score, our methods yield interpretable subgroup effects. However, existing methods fixed the subgroup a priori, but our causal fused lasso forms data-adaptive subgroups. We show that the estimator consistently estimates the treatment effects conditional on the score under very general conditions on the covariates and treatment. We demonstrate the performance of our procedure using extensive experiments that show that it can be interpretable and competitive with state-of-the-art methods.

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.

This paper addresses the problem of localizing and inferring multiple change points, in non-parametric multivariate time series settings. Specifically, we consider a multivariate time series with potentially short-range dependence, whose underlying distributions have Hölder smooth densities and can change over time in a piecewise-constant manner. The change points, which correspond to the times when the distribution changes, are unknown. We present the limiting distributions of the change point estimators under the scenarios where the minimal jump size vanishes or remains constant. Such results have not been revealed in the literature in non-parametric change point settings. As byproducts, we develop a sharp estimator that can accurately localize the change points in multivariate non-parametric time series, and a consistent block-type long-run variance estimator. Numerical studies are provided to complement our theoretical findings.

We study the problem of change-point detection and localisation for functional data sequentially observed on a general $d$-dimensional space, where we allow the functional curves to be either sparsely or densely sampled. Data of this form naturally arise in a wide range of applications such as biology, neuroscience, climatology and finance. To achieve such a task, we propose a kernel-based algorithm named functional seeded binary segmentation (FSBS). FSBS is computationally efficient, can handle discretely observed functional data, and is theoretically sound for heavy-tailed and temporally-dependent observations. Moreover, FSBS works for a general $d$-dimensional domain, which is the first in the literature of change-point estimation for functional data. We show the consistency of FSBS for multiple change-point estimation and further provide a sharp localisation error rate, which reveals an interesting phase transition phenomenon depending on the number of functional curves observed and the sampling frequency for each curve. Extensive numerical experiments illustrate the effectiveness of FSBS and its advantage over existing methods in the literature under various settings. A real data application is further conducted, where FSBS localises change-points of sea surface temperature patterns in the south Pacific attributed to El Ni\~{n}o.