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\cite{rohe2016co} proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary directed graph data in network studies. However, ScBM completely ignores node weight, and is unable to explain the block structure of directed weighted network which appears in various areas, such as biology, sociology, physiology and computer science. Here, to model directed weighted network, we introduce a Directed Distribution-Free model by releasing ScBM's distribution restriction. We also build an extension of the proposed model by considering variation of node degree. Our models do not require a specific distribution on generating elements of adjacency matrix but only a block structure on the expected adjacency matrix. Spectral algorithms with theoretical guarantee on consistent estimation of node label are presented to identify communities. Our proposed methods are illustrated by simulated and empirical examples.

We give algorithms for approximating the partition function of the ferromagnetic Potts model on $d$-regular expanding graphs. We require much weaker expansion than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models, using extremal graph theory and applications of Karger's algorithm to counting cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We believe that these methods can shed more light on other important problems such as sub-exponential algorithms for approximate counting problems.

State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms. Existing frameworks such as moving horizon estimation (MHE) and the unscented Kalman filter (UKF) provide the flexibility to incorporate nonlinear dynamics and measurement models. However, this implies that the dynamics model within these algorithms has to be sufficiently accurate in order to warrant the accuracy of the state estimates. To enhance the dynamics models and improve the estimation accuracy, we utilize a deep learning framework known as knowledge-based neural ordinary differential equations (KNODEs). The KNODE framework embeds prior knowledge into the training procedure and synthesizes an accurate hybrid model by fusing a prior first-principles model with a neural ordinary differential equation (NODE) model. In our proposed LEARNEST framework, we integrate the data-driven model into two novel model-based state estimation algorithms, which are denoted as KNODE-MHE and KNODE-UKF. These two algorithms are compared against their conventional counterparts across a number of robotic applications; state estimation for a cartpole system using partial measurements, localization for a ground robot, as well as state estimation for a quadrotor. Through simulations and tests using real-world experimental data, we demonstrate the versatility and efficacy of the proposed learning-enhanced state estimation framework.

This work considers Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function (Stein, 1999, Section 6.7) with Fourier coefficients $\phi$($\alpha$^2 + j^2)^(--$\nu$--1/2). Convergence rates are studied for the joint maximum likelihood estimation of $\nu$ and $\phi$ when the data is sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a ''deterministic'' element of a continuous Sobolev space is also considered, suggesting that bounding assumptions on some parameters can lead to different estimates.

Community detection and orthogonal group synchronization are both fundamental problems with a variety of important applications in science and engineering. In this work, we consider the joint problem of community detection and orthogonal group synchronization which aims to recover the communities and perform synchronization simultaneously. To this end, we propose a simple algorithm that consists of a spectral decomposition step followed by a blockwise column pivoted QR factorization (CPQR). The proposed algorithm is efficient and scales linearly with the number of edges in the graph. We also leverage the recently developed `leave-one-out' technique to establish a near-optimal guarantee for exact recovery of the cluster memberships and stable recovery of the orthogonal transforms. Numerical experiments demonstrate the efficiency and efficacy of our algorithm and confirm our theoretical characterization of it.

While there have been numerous sequential algorithms developed to estimate community structure in networks, there is little available guidance and study of what significance level or stopping parameter to use in these sequential testing procedures. Most algorithms rely on prespecifiying the number of communities or use an arbitrary stopping rule. We provide a principled approach to selecting a nominal significance level for sequential community detection procedures by controlling the tolerance ratio, defined as the ratio of underfitting and overfitting probability of estimating the number of clusters in fitting a network. We introduce an algorithm for specifying this significance level from a user-specified tolerance ratio, and demonstrate its utility with a sequential modularity maximization approach in a stochastic block model framework. We evaluate the performance of the proposed algorithm through extensive simulations and demonstrate its utility in controlling the tolerance ratio in single-cell RNA sequencing clustering by cell type and by clustering a congressional voting network.

We study differentially private (DP) stochastic optimization (SO) with data containing outliers and loss functions that are not Lipschitz continuous. To date, the vast majority of work on DP SO assumes that the loss is Lipschitz (i.e. stochastic gradients are uniformly bounded), and their error bounds scale with the Lipschitz parameter of the loss. While this assumption is convenient, it is often unrealistic: in many practical problems where privacy is required, data may contain outliers or be unbounded, causing some stochastic gradients to have large norm. In such cases, the Lipschitz parameter may be prohibitively large, leading to vacuous excess risk bounds. Thus, building on a recent line of work [WXDX20, KLZ22], we make the weaker assumption that stochastic gradients have bounded $k$-th moments for some $k \geq 2$. Compared with works on DP Lipschitz SO, our excess risk scales with the $k$-th moment bound instead of the Lipschitz parameter of the loss, allowing for significantly faster rates in the presence of outliers. For convex and strongly convex loss functions, we provide the first asymptotically optimal excess risk bounds (up to a logarithmic factor). Moreover, in contrast to the prior works [WXDX20, KLZ22], our bounds do not require the loss function to be differentiable/smooth. We also devise an accelerated algorithm that runs in linear time and yields improved (compared to prior works) and nearly optimal excess risk for smooth losses. Additionally, our work is the first to address non-convex non-Lipschitz loss functions satisfying the Proximal-PL inequality; this covers some classes of neural nets, among other practical models. Our Proximal-PL algorithm has nearly optimal excess risk that almost matches the strongly convex lower bound. Lastly, we provide shuffle DP variations of our algorithms, which do not require a trusted curator (e.g. for distributed learning).

Multiple-objective optimization (MOO) aims to simultaneously optimize multiple conflicting objectives and has found important applications in machine learning, such as minimizing classification loss and discrepancy in treating different populations for fairness. At optimality, further optimizing one objective will necessarily harm at least another objective, and decision-makers need to comprehensively explore multiple optima (called Pareto front) to pinpoint one final solution. We address the efficiency of finding the Pareto front. First, finding the front from scratch using stochastic multi-gradient descent (SMGD) is expensive with large neural networks and datasets. We propose to explore the Pareto front as a manifold from a few initial optima, based on a predictor-corrector method. Second, for each exploration step, the predictor solves a large-scale linear system that scales quadratically in the number of model parameters and requires one backpropagation to evaluate a second-order Hessian-vector product per iteration of the solver. We propose a Gauss-Newton approximation that only scales linearly, and that requires only first-order inner-product per iteration. This also allows for a choice between the MINRES and conjugate gradient methods when approximately solving the linear system. The innovations make predictor-corrector possible for large networks. Experiments on multi-objective (fairness and accuracy) misinformation detection tasks show that 1) the predictor-corrector method can find Pareto fronts better than or similar to SMGD with less time; and 2) the proposed first-order method does not harm the quality of the Pareto front identified by the second-order method, while further reduce running time.

Automatic License Plate Recognition (ALPR) has been a frequent topic of research due to many practical applications. However, many of the current solutions are still not robust in real-world situations, commonly depending on many constraints. This paper presents a robust and efficient ALPR system based on the state-of-the-art YOLO object detection. The Convolutional Neural Networks (CNNs) are trained and fine-tuned for each ALPR stage so that they are robust under different conditions (e.g., variations in camera, lighting, and background). Specially for character segmentation and recognition, we design a two-stage approach employing simple data augmentation tricks such as inverted License Plates (LPs) and flipped characters. The resulting ALPR approach achieved impressive results in two datasets. First, in the SSIG dataset, composed of 2,000 frames from 101 vehicle videos, our system achieved a recognition rate of 93.53% and 47 Frames Per Second (FPS), performing better than both Sighthound and OpenALPR commercial systems (89.80% and 93.03%, respectively) and considerably outperforming previous results (81.80%). Second, targeting a more realistic scenario, we introduce a larger public dataset, called UFPR-ALPR dataset, designed to ALPR. This dataset contains 150 videos and 4,500 frames captured when both camera and vehicles are moving and also contains different types of vehicles (cars, motorcycles, buses and trucks). In our proposed dataset, the trial versions of commercial systems achieved recognition rates below 70%. On the other hand, our system performed better, with recognition rate of 78.33% and 35 FPS.

Object detection is an important and challenging problem in computer vision. Although the past decade has witnessed major advances in object detection in natural scenes, such successes have been slow to aerial imagery, not only because of the huge variation in the scale, orientation and shape of the object instances on the earth's surface, but also due to the scarcity of well-annotated datasets of objects in aerial scenes. To advance object detection research in Earth Vision, also known as Earth Observation and Remote Sensing, we introduce a large-scale Dataset for Object deTection in Aerial images (DOTA). To this end, we collect $2806$ aerial images from different sensors and platforms. Each image is of the size about 4000-by-4000 pixels and contains objects exhibiting a wide variety of scales, orientations, and shapes. These DOTA images are then annotated by experts in aerial image interpretation using $15$ common object categories. The fully annotated DOTA images contains $188,282$ instances, each of which is labeled by an arbitrary (8 d.o.f.) quadrilateral To build a baseline for object detection in Earth Vision, we evaluate state-of-the-art object detection algorithms on DOTA. Experiments demonstrate that DOTA well represents real Earth Vision applications and are quite challenging.