Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret

We investigate a generalized framework for estimating latent low-rank tensors in an online setting, encompassing both linear and generalized linear models. This framework offers a flexible approach for handling continuous or categorical variables. Additionally, we investigate two specific applications: online tensor completion and online binary tensor learning. To address these challenges, we propose the online Riemannian gradient descent algorithm, which demonstrates linear convergence and the ability to recover the low-rank component under appropriate conditions in all applications. Furthermore, we establish a precise entry-wise error bound for online tensor completion. Notably, our work represents the first attempt to incorporate noise in the online low-rank tensor recovery task. Intriguingly, we observe a surprising trade-off between computational and statistical aspects in the presence of noise. Increasing the step size accelerates convergence but leads to higher statistical error, whereas a smaller step size yields a statistically optimal estimator at the expense of slower convergence. Moreover, we conduct regret analysis for online tensor regression. Under the fixed step size regime, a fascinating trilemma concerning the convergence rate, statistical error rate, and regret is observed. With an optimal choice of step size we achieve an optimal regret of $O(\sqrt{T})$. Furthermore, we extend our analysis to the adaptive setting where the horizon T is unknown. In this case, we demonstrate that by employing different step sizes, we can attain a statistically optimal error rate along with a regret of $O(\log T)$. To validate our theoretical claims, we provide numerical results that corroborate our findings and support our assertions

Semiparametric Tensor Factor Analysis by Iteratively Projected SVD

This paper introduces a general framework of Semiparametric TEnsor FActor analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. STEFA models extend tensor factor models by incorporating instrumental covariates in the loading matrices. We propose an algorithm of Iteratively Projected SVD (IP-SVD) for the semiparametric estimations. It iteratively projects tensor data onto the linear space spanned by covariates and applies SVD on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. Compared with the Tucker decomposition, IP-SVD yields more accurate estimates with a faster convergence rate. Besides estimation, we show several prediction methods with newly observed covariates based on the STEFA model. On both real and synthetic tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.Comment: 23 pages, 6 figures, submitte

End-to-End Adversarial Shape Learning for Abdomen Organ Deep Segmentation

Automatic segmentation of abdomen organs using medical imaging has many potential applications in clinical workflows. Recently, the state-of-the-art performance for organ segmentation has been achieved by deep learning models, i.e., convolutional neural network (CNN). However, it is challenging to train the conventional CNN-based segmentation models that aware of the shape and topology of organs. In this work, we tackle this problem by introducing a novel end-to-end shape learning architecture -- organ point-network. It takes deep learning features as inputs and generates organ shape representations as points that located on organ surface. We later present a novel adversarial shape learning objective function to optimize the point-network to capture shape information better. We train the point-network together with a CNN-based segmentation model in a multi-task fashion so that the shared network parameters can benefit from both shape learning and segmentation tasks. We demonstrate our method with three challenging abdomen organs including liver, spleen, and pancreas. The point-network generates surface points with fine-grained details and it is found critical for improving organ segmentation. Consequently, the deep segmentation model is improved by the introduced shape learning as significantly better Dice scores are observed for spleen and pancreas segmentation.Comment: Accepted to International Workshop on Machine Learning in Medical Imaging (MLMI2019

3-Carboxy­pyrazino[2,3-f][1,10]phenanthrolin-9-ium-2-carboxyl­ate

In the title zwitterionic compound, C16H8N4O4, the dihedral angle between the carboxyl and carboxyl­ate groups is 72.14 (2)°. In the crystal, mol­ecules are linked by strong inter­molecular O—H⋯O− and N+—H⋯O− hydrogen bonds into double chains extended along [001]. These chains are additionally stabilized by π–π stacking inter­actions between the pyridine and benzene rings [centroid–centroid distance = 3.5542 (8) Å]

Clinical efficacy and safety of Kanglaite injection, adjuvant cemcitabine and cisplatin chemotherapy for advanced non-small-cell lung cancer: A systematic review and meta-analysis

Purpose: To investigate the effectiveness and safety of the combination of Kanglaite injection (KLTi) and gemcitabine and cisplatin (GP) chemotherapy in the treatment of advanced non-small cell lung cancer (NSCLC).Methods: PubMed, Web of Science, Embase, Cochrane Library, CNKI, Wan-Fang, CBM, and CQVIP were comprehensively searched from January 2010 till November 2020. Randomized controlled trials (RCTs) of KLTi plus GP in the treatment of NSCLC were selected and assessed for inclusion. Review Manager 5.3 software was used for meta-analysis.Results: Twenty-five RCTs on advanced NSCLC examined the inclusion criteria. The meta-analysis showed that compared with GP chemotherapy alone, KLTi plus GP chemotherapy significantly improved objective response rate (ORR) (RR = 1.36, 95% CI 1.23-1.51, p < 0.00001), disease control rate (DCR) (RR = 1.17, 95% CI 1.11 - 1.23, p < 0.00001), and reduced adverse drug reactions(ADRs) such as hair loss (RR = 0.60, 95% CI 0.47 - 0.76, p < 0.0001), gastrointestinal reaction (RR = 0.68, 95% CI 0.62 - 0.75, p < 0.00001), impairment of liver and kidney function (RR = 0.65, 95% CI 0.53 - 0.80, p < 0.001), nervous system damage (RR = 0.42, 95% CI 0.26 - 0.69, p = 0.0005), myelosuppression (I-II phase) (RR = 0.79, 95 % CI 0.66 - 0.95, p = 0.01), myelosuppression (III-IV phase) (RR = 0.44, 95 % CI0.27 - 0.72, p = 0.001), anemia (RR = 0.74, 95 % CI 0.60 - 0.91, p = 0.006), leukopenia (RR = 0.78, 95% CI 0.69, 0.87, p < 0.0001), thrombocytopenia (RR = 0.59, 95 % CI 0.49, 0.72, p < 0.00001), hypochromia (RR = 0.74, 95% CI 0.59, 0.92, p = 0.008).Conclusion: KLTi adjuvant GP chemotherapy reduces adverse effects in patients with advanced NSCLC. Thus, KLTi might be an effective and safe intervention for NSCLC&nbsp

Comparison of preprocessing methods and storage times for touch DNA samples

Aim To select appropriate preprocessing methods for different substrates by comparing the effects of four different preprocessing methods on touch DNA samples and to determine the effect of various storage times on the results of touch DNA sample analysis. Method Hand touch DNA samples were used to investigate the detection and inspection results of DNA on different substrates. Four preprocessing methods, including the direct cutting method, stubbing procedure, double swab technique, and vacuum cleaner method, were used in this study. DNA was extracted from mock samples with four different preprocessing methods. The best preprocess protocol determined from the study was further used to compare performance after various storage times. DNA extracted from all samples was quantified and amplified using standard procedures. Results The amounts of DNA and the number of alleles detected on the porous substrates were greater than those on the non-porous substrates. The performances of the four preprocessing methods varied with different substrates. The direct cutting method displayed advantages for porous substrates, and the vacuum cleaner method was advantageous for non-porous substrates. No significant degradation trend was observed as the storage times increased. Conclusion Different substrates require the use of different preprocessing method in order to obtain the highest DNA amount and allele number from touch DNA samples. This study provides a theoretical basis for explorations of touch DNA samples and may be used as a reference when dealing with touch DNA samples in case work