Search

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness parameter which was previously used in parametric models. Compared to other robust methods such as median regression, the distinction is that the proposed method aims to estimate the conditional mean robustly, instead of estimating the conditional median. We only require $(1+\kappa)$-th moment assumption ($\kappa>0$) on the noise distribution, and the established error bounds match the optimal rate in the least-squares case as soon as $\kappa\ge 1$. We establish convergence rate in probability when the functional predictor has a finite 4-th moment, and finite-sample bound with exponential tail when the functional predictor is Gaussian, in terms of both prediction error and $L^2$ error. The results also extend to the case of functional estimation in a reproducing kernel Hilbert space (RKHS).

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested, which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quaternion matrices. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy.

Due to the non-linear ionizing and heating processes, the 21-cm signals from epoch of reionization (EoR) are expected to have strong non-Gaussian fluctuations. In this paper, we use the semi-numerical simulations to study the non-Gaussian statistics i.e. skew spectrum and smoothed skewness of the 21-cm signals from EoR. We find the 21-cm skew spectrum and smoothed skewness have similar evolution features with the 21-cm bispectrum. All of them are sensitive to the EoR models, while not too much to the cosmic volume applied. With the SKA1-low telescope as reference, we find both the skew spectrum and smoothed skewness have much higher S/N ratios than the 21-cm bispectrum., Comment: 7 pages, 5 figures, mnras accepted

Accurate organ at risk (OAR) segmentation is critical to reduce the radiotherapy post-treatment complications. Consensus guidelines recommend a set of more than 40 OARs in the head and neck (H&N) region, however, due to the predictable prohibitive labor-cost of this task, most institutions choose a substantially simplified protocol by delineating a smaller subset of OARs and neglecting the dose distributions associated with other OARs. In this work we propose a novel, automated and highly effective stratified OAR segmentation (SOARS) system using deep learning to precisely delineate a comprehensive set of 42 H&N OARs. SOARS stratifies 42 OARs into anchor, mid-level, and small & hard subcategories, with specifically derived neural network architectures for each category by neural architecture search (NAS) principles. We built SOARS models using 176 training patients in an internal institution and independently evaluated on 1327 external patients across six different institutions. It consistently outperformed other state-of-the-art methods by at least 3-5% in Dice score for each institutional evaluation (up to 36% relative error reduction in other metrics). More importantly, extensive multi-user studies evidently demonstrated that 98% of the SOARS predictions need only very minor or no revisions for direct clinical acceptance (saving 90% radiation oncologists workload), and their segmentation and dosimetric accuracy are within or smaller than the inter-user variation. These findings confirmed the strong clinical applicability of SOARS for the OAR delineation process in H&N cancer radiotherapy workflows, with improved efficiency, comprehensiveness, and quality.

Background: The current clinical workflow for esophageal gross tumor volume (GTV) contouring relies on manual delineation of high labor-costs and interuser variability. Purpose: To validate the clinical applicability of a deep learning (DL) multi-modality esophageal GTV contouring model, developed at 1 institution whereas tested at multiple ones. Methods and Materials: We collected 606 esophageal cancer patients from four institutions. 252 institution-1 patients had a treatment planning-CT (pCT) and a pair of diagnostic FDG-PETCT; 354 patients from other 3 institutions had only pCT. A two-streamed DL model for GTV segmentation was developed using pCT and PETCT scans of a 148 patient institution-1 subset. This built model had the flexibility of segmenting GTVs via only pCT or pCT+PETCT combined. For independent evaluation, the rest 104 institution-1 patients behaved as unseen internal testing, and 354 institutions 2-4 patients were used for external testing. We evaluated manual revision degrees by human experts to assess the contour-editing effort. The performance of the deep model was compared against 4 radiation oncologists in a multiuser study with 20 random external patients. Contouring accuracy and time were recorded for the pre-and post-DL assisted delineation process. Results: Our model achieved high segmentation accuracy in internal testing (mean Dice score: 0.81 using pCT and 0.83 using pCT+PET) and generalized well to external evaluation (mean DSC: 0.80). Expert assessment showed that the predicted contours of 88% patients need only minor or no revision. In multi-user evaluation, with the assistance of a deep model, inter-observer variation and required contouring time were reduced by 37.6% and 48.0%, respectively. Conclusions: Deep learning predicted GTV contours were in close agreement with the ground truth and could be adopted clinically with mostly minor or no changes., Comment: 36 pages, 10 figures

Lymph node station (LNS) delineation from computed tomography (CT) scans is an indispensable step in radiation oncology workflow. High inter-user variabilities across oncologists and prohibitive laboring costs motivated the automated approach. Previous works exploit anatomical priors to infer LNS based on predefined ad-hoc margins. However, without voxel-level supervision, the performance is severely limited. LNS is highly context-dependent - LNS boundaries are constrained by anatomical organs - we formulate it as a deep spatial and contextual parsing problem via encoded anatomical organs. This permits the deep network to better learn from both CT appearance and organ context. We develop a stratified referencing organ segmentation protocol that divides the organs into anchor and non-anchor categories and uses the former's predictions to guide the later segmentation. We further develop an auto-search module to identify the key organs that opt for the optimal LNS parsing performance. Extensive four-fold cross-validation experiments on a dataset of 98 esophageal cancer patients (with the most comprehensive set of 12 LNSs + 22 organs in thoracic region to date) are conducted. Our LNS parsing model produces significant performance improvements, with an average Dice score of 81.1% +/- 6.1%, which is 5.0% and 19.2% higher over the pure CT-based deep model and the previous representative approach, respectively.