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Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.

Anomaly detection among a large number of processes arises in many applications ranging from dynamic spectrum access to cybersecurity. In such problems one can often obtain noisy observations aggregated from a chosen subset of processes that conforms to a tree structure. The distribution of these observations, based on which the presence of anomalies is detected, may be only partially known. This gives rise to the need for a search strategy designed to account for both the sample complexity and the detection accuracy, as well as cope with statistical models that are known only up to some missing parameters. In this work we propose a sequential search strategy using two variations of the Generalized Local Likelihood Ratio statistic. Our proposed Hierarchical Dynamic Search (HDS) strategy is shown to be order-optimal with respect to the size of the search space and asymptotically optimal with respect to the detection accuracy. An explicit upper bound on the error probability of HDS is established for the finite sample regime. Extensive experiments are conducted, demonstrating the performance gains of HDS over existing methods.

Anomalies represent rare observations (e.g., data records or events) that deviate significantly from others. Over several decades, research on anomaly mining has received increasing interests due to the implications of these occurrences in a wide range of disciplines. Anomaly detection, which aims to identify rare observations, is among the most vital tasks in the world, and has shown its power in preventing detrimental events, such as financial fraud, network intrusion, and social spam. The detection task is typically solved by identifying outlying data points in the feature space and inherently overlooks the relational information in real-world data. Graphs have been prevalently used to represent the structural information, which raises the graph anomaly detection problem - identifying anomalous graph objects (i.e., nodes, edges and sub-graphs) in a single graph, or anomalous graphs in a database/set of graphs. However, conventional anomaly detection techniques cannot tackle this problem well because of the complexity of graph data. For the advent of deep learning, graph anomaly detection with deep learning has received a growing attention recently. In this survey, we aim to provide a systematic and comprehensive review of the contemporary deep learning techniques for graph anomaly detection. We compile open-sourced implementations, public datasets, and commonly-used evaluation metrics to provide affluent resources for future studies. More importantly, we highlight twelve extensive future research directions according to our survey results covering unsolved and emerging research problems and real-world applications. With this survey, our goal is to create a "one-stop-shop" that provides a unified understanding of the problem categories and existing approaches, publicly available hands-on resources, and high-impact open challenges for graph anomaly detection using deep learning.

Traditional object detection answers two questions; "what" (what the object is?) and "where" (where the object is?). "what" part of the object detection can be fine-grained further i.e. "what type", "what shape" and "what material" etc. This results in the shifting of the object detection tasks to the object description paradigm. Describing an object provides additional detail that enables us to understand the characteristics and attributes of the object ("plastic boat" not just boat, "glass bottle" not just bottle). This additional information can implicitly be used to gain insight into unseen objects (e.g. unknown object is "metallic", "has wheels"), which is not possible in traditional object detection. In this paper, we present a new approach to simultaneously detect objects and infer their attributes, we call it Detect and Describe (DaD) framework. DaD is a deep learning-based approach that extends object detection to object attribute prediction as well. We train our model on aPascal train set and evaluate our approach on aPascal test set. We achieve 97.0% in Area Under the Receiver Operating Characteristic Curve (AUC) for object attributes prediction on aPascal test set. We also show qualitative results for object attribute prediction on unseen objects, which demonstrate the effectiveness of our approach for describing unknown objects.

In this work we present point-level region contrast, a self-supervised pre-training approach for the task of object detection. This approach is motivated by the two key factors in detection: localization and recognition. While accurate localization favors models that operate at the pixel- or point-level, correct recognition typically relies on a more holistic, region-level view of objects. Incorporating this perspective in pre-training, our approach performs contrastive learning by directly sampling individual point pairs from different regions. Compared to an aggregated representation per region, our approach is more robust to the change in input region quality, and further enables us to implicitly improve initial region assignments via online knowledge distillation during training. Both advantages are important when dealing with imperfect regions encountered in the unsupervised setting. Experiments show point-level region contrast improves on state-of-the-art pre-training methods for object detection and segmentation across multiple tasks and datasets, and we provide extensive ablation studies and visualizations to aid understanding. Code will be made available.

Remote-sensing (RS) Change Detection (CD) aims to detect "changes of interest" from co-registered bi-temporal images. The performance of existing deep supervised CD methods is attributed to the large amounts of annotated data used to train the networks. However, annotating large amounts of remote sensing images is labor-intensive and expensive, particularly with bi-temporal images, as it requires pixel-wise comparisons by a human expert. On the other hand, we often have access to unlimited unlabeled multi-temporal RS imagery thanks to ever-increasing earth observation programs. In this paper, we propose a simple yet effective way to leverage the information from unlabeled bi-temporal images to improve the performance of CD approaches. More specifically, we propose a semi-supervised CD model in which we formulate an unsupervised CD loss in addition to the supervised Cross-Entropy (CE) loss by constraining the output change probability map of a given unlabeled bi-temporal image pair to be consistent under the small random perturbations applied on the deep feature difference map that is obtained by subtracting their latent feature representations. Experiments conducted on two publicly available CD datasets show that the proposed semi-supervised CD method can reach closer to the performance of supervised CD even with access to as little as 10% of the annotated training data. Code available at //github.com/wgcban/SemiCD.

In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we propose a transfer learning algorithm on GLM, and derive its $\ell_1/\ell_2$-estimation error bounds as well as a bound for a prediction error measure. The theoretical analysis shows that when the target and source are sufficiently close to each other, these bounds could be improved over those of the classical penalized estimator using only target data under mild conditions. When we don't know which sources to transfer, an algorithm-free transferable source detection approach is introduced to detect informative sources. The detection consistency is proved under the high-dimensional GLM transfer learning setting. We also propose an algorithm to construct confidence intervals of each coefficient component, and the corresponding theories are provided. Extensive simulations and a real-data experiment verify the effectiveness of our algorithms. We implement the proposed GLM transfer learning algorithms in a new R package glmtrans, which is available on CRAN.

A novel topological-data-analytical (TDA) method is proposed to distinguish, from noise, small holes surrounded by high-density regions of a probability density function whose mass is concentrated near a manifold (or more generally, a CW complex) embedded in a high-dimensional Euclidean space. The proposed method is robust against additive noise and outliers. In particular, sample points are allowed to be perturbed away from the manifold. Traditional TDA tools, like those based on the distance filtration, often struggle to distinguish small features from noise, because of their short persistence. An alternative filtration, called Robust Density-Aware Distance (RDAD) filtration, is proposed to prolong the persistence of small holes surrounded by high-density regions. This is achieved by weighting the distance function by the density in the sense of Bell et al. Distance-to-measure is incorporated to enhance stability and mitigate noise due to the density estimation. The utility of the proposed filtration in identifying small holes, as well as its robustness against noise, are illustrated through an analytical example and extensive numerical experiments. Basic mathematical properties of the proposed filtration are proven.

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.

Semi-supervised object detection (SSOD) aims to facilitate the training and deployment of object detectors with the help of a large amount of unlabeled data. Though various self-training based and consistency-regularization based SSOD methods have been proposed, most of them are anchor-based detectors, ignoring the fact that in many real-world applications anchor-free detectors are more demanded. In this paper, we intend to bridge this gap and propose a DenSe Learning (DSL) based anchor-free SSOD algorithm. Specifically, we achieve this goal by introducing several novel techniques, including an Adaptive Filtering strategy for assigning multi-level and accurate dense pixel-wise pseudo-labels, an Aggregated Teacher for producing stable and precise pseudo-labels, and an uncertainty-consistency-regularization term among scales and shuffled patches for improving the generalization capability of the detector. Extensive experiments are conducted on MS-COCO and PASCAL-VOC, and the results show that our proposed DSL method records new state-of-the-art SSOD performance, surpassing existing methods by a large margin. Codes can be found at \textcolor{blue}{//github.com/chenbinghui1/DSL}.