Efficient Estimation for Longitudinal Network via Adaptive Merging

Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.Comment: 26 pages and 2 figures; appendix including technical proof will be uploaded late

Self-Supervised Pre-training for 3D Point Clouds via View-Specific Point-to-Image Translation

The past few years have witnessed the great success and prevalence of self-supervised representation learning within the language and 2D vision communities. However, such advancements have not been fully migrated to the field of 3D point cloud learning. Different from existing pre-training paradigms designed for deep point cloud feature extractors that fall into the scope of generative modeling or contrastive learning, this paper proposes a translative pre-training framework, namely PointVST, driven by a novel self-supervised pretext task of cross-modal translation from 3D point clouds to their corresponding diverse forms of 2D rendered images. More specifically, we begin with deducing view-conditioned point-wise embeddings through the insertion of the viewpoint indicator, and then adaptively aggregate a view-specific global codeword, which can be further fed into subsequent 2D convolutional translation heads for image generation. Extensive experimental evaluations on various downstream task scenarios demonstrate that our PointVST shows consistent and prominent performance superiority over current state-of-the-art approaches as well as satisfactory domain transfer capability. Our code will be publicly available at https://github.com/keeganhk/PointVST

Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomalies

Signed networks are frequently observed in real life with additional sign information associated with each edge, yet such information has been largely ignored in existing network models. This paper develops a unified embedding model for signed networks to disentangle the intertwined balance structure and anomaly effect, which can greatly facilitate the downstream analysis, including community detection, anomaly detection, and network inference. The proposed model captures both balance structure and anomaly effect through a low rank plus sparse matrix decomposition, which are jointly estimated via a regularized formulation. Its theoretical guarantees are established in terms of asymptotic consistency and finite-sample probability bounds for network embedding, community detection and anomaly detection. The advantage of the proposed embedding model is also demonstrated through extensive numerical experiments on both synthetic networks and an international relation network.Comment: 24 pages, 4 figures. The appendix containing technical proof is not included, but will be uploaded in the futur

Efficient estimation and inference for the signed β\beta-model in directed signed networks

This paper proposes a novel signed $\beta$-model for directed signed network, which is frequently encountered in application domains but largely neglected in literature. The proposed signed $\beta$-model decomposes a directed signed network as the difference of two unsigned networks and embeds each node with two latent factors for in-status and out-status. The presence of negative edges leads to a non-concave log-likelihood, and a one-step estimation algorithm is developed to facilitate parameter estimation, which is efficient both theoretically and computationally. We also develop an inferential procedure for pairwise and multiple node comparisons under the signed $\beta$-model, which fills the void of lacking uncertainty quantification for node ranking. Theoretical results are established for the coverage probability of confidence interval, as well as the false discovery rate (FDR) control for multiple node comparison. The finite sample performance of the signed $\beta$-model is also examined through extensive numerical experiments on both synthetic and real-life networks

Multi-color optical monitoring of the quasar 3C 273 from 2005 to 2016

We have monitored the quasar 3C 273 in optical $V$, $R$ and $I$ bands from 2005 to 2016. Intraday variability (IDV) is detected on seven nights. The variability amplitudes for most of nights are less than 10\% and four nights more than 20\%. When considering the nights with time spans $>4$ hours, the value of duty cycle (DC) is 14.17 per cent. Over the twelve years, the overall magnitude and color index variabilities are $\bigtriangleup I=0^{\rm m}.67$, $\bigtriangleup R=0^{\rm m}.72$, $\bigtriangleup V=0^{\rm m}.68$, and $\bigtriangleup (V-R)=0^{\rm m}.25$ respectively. The largest clear IDV has an amplitude of 42% over just 5.8 minutes and the weakest detected IDV is 5.4% over 175 minutes. The BWB (bluer when brighter) chromatic trend is dominant for 3C 273 and appears at different flux levels on intraday timescales. The BWB trend exists for short-term timescales and intermediate-term timescales but different timescales have different correlations. There is no BWB trend for our whole time-series data sets. A significant anti-correlation between BWB trend and length of timescales is found. Combining with $V$-band data from previous works, we find a possible quasi-periodicity of $P=3918\pm1112$ days. The possible explanations for the observed variability, BWB chromatic trend and periodicity are discussed.Comment: 63 pages, 11 figures, 6 tables. Accepted for publication in ApJ

A statistical normalization method and differential expression analysis for RNA-seq data between different species

Background: High-throughput techniques bring novel tools but also statistical challenges to genomic research. Identifying genes with differential expression between different species is an effective way to discover evolutionarily conserved transcriptional responses. To remove systematic variation between different species for a fair comparison, the normalization procedure serves as a crucial pre-processing step that adjusts for the varying sample sequencing depths and other confounding technical effects. Results: In this paper, we propose a scale based normalization (SCBN) method by taking into account the available knowledge of conserved orthologous genes and hypothesis testing framework. Considering the different gene lengths and unmapped genes between different species, we formulate the problem from the perspective of hypothesis testing and search for the optimal scaling factor that minimizes the deviation between the empirical and nominal type I errors. Conclusions: Simulation studies show that the proposed method performs significantly better than the existing competitor in a wide range of settings. An RNA-seq dataset of different species is also analyzed and it coincides with the conclusion that the proposed method outperforms the existing method. For practical applications, we have also developed an R package named "SCBN" and the software is available at http://www.bioconductor.org/packages/devel/bioc/html/SCBN.html

PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal Distillation for 3D Shape Recognition

As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era, remarkable progress in processing such two data modalities has been achieved through respectively customizing compatible 3D and 2D network architectures. However, unlike multi-view image-based 2D visual modeling paradigms, which have shown leading performance in several common 3D shape recognition benchmarks, point cloud-based 3D geometric modeling paradigms are still highly limited by insufficient learning capacity, due to the difficulty of extracting discriminative features from irregular geometric signals. In this paper, we explore the possibility of boosting deep 3D point cloud encoders by transferring visual knowledge extracted from deep 2D image encoders under a standard teacher-student distillation workflow. Generally, we propose PointMCD, a unified multi-view cross-modal distillation architecture, including a pretrained deep image encoder as the teacher and a deep point encoder as the student. To perform heterogeneous feature alignment between 2D visual and 3D geometric domains, we further investigate visibility-aware feature projection (VAFP), by which point-wise embeddings are reasonably aggregated into view-specific geometric descriptors. By pair-wisely aligning multi-view visual and geometric descriptors, we can obtain more powerful deep point encoders without exhausting and complicated network modification. Experiments on 3D shape classification, part segmentation, and unsupervised learning strongly validate the effectiveness of our method. The code and data will be publicly available at https://github.com/keeganhk/PointMCD