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Face clustering is a promising way to scale up face recognition systems using large-scale unlabeled face images. It remains challenging to identify small or sparse face image clusters that we call hard clusters, which is caused by the heterogeneity, \ie, high variations in size and sparsity, of the clusters. Consequently, the conventional way of using a uniform threshold (to identify clusters) often leads to a terrible misclassification for the samples that should belong to hard clusters. We tackle this problem by leveraging the neighborhood information of samples and inferring the cluster memberships (of samples) in a probabilistic way. We introduce two novel modules, Neighborhood-Diffusion-based Density (NDDe) and Transition-Probability-based Distance (TPDi), based on which we can simply apply the standard Density Peak Clustering algorithm with a uniform threshold. Our experiments on multiple benchmarks show that each module contributes to the final performance of our method, and by incorporating them into other advanced face clustering methods, these two modules can boost the performance of these methods to a new state-of-the-art. Code is available at: //github.com/echoanran/On-Mitigating-Hard-Clusters.

We study \textit{rescaled gradient dynamical systems} in a Hilbert space $\mathcal{H}$, where implicit discretization in a finite-dimensional Euclidean space leads to high-order methods for solving monotone equations (MEs). Our framework can be interpreted as a natural generalization of celebrated dual extrapolation method~\citep{Nesterov-2007-Dual} from first order to high order via appeal to the regularization toolbox of optimization theory~\citep{Nesterov-2021-Implementable, Nesterov-2021-Inexact}. More specifically, we establish the existence and uniqueness of a global solution and analyze the convergence properties of solution trajectories. We also present discrete-time counterparts of our high-order continuous-time methods, and we show that the $p^{th}$-order method achieves an ergodic rate of $O(k^{-(p+1)/2})$ in terms of a restricted merit function and a pointwise rate of $O(k^{-p/2})$ in terms of a residue function. Under regularity conditions, the restarted version of $p^{th}$-order methods achieves local convergence with the order $p \geq 2$. Notably, our methods are \textit{optimal} since they have matched the lower bound established for solving the monotone equation problems under a standard linear span assumption~\citep{Lin-2022-Perseus}.

We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or 'missing at random' assumption. We consider two alternative strategies for identification; the first is closely related to the difference-in-differences methodology in the causal inference literature. The second enables correction for violations of the parallel trend assumption, so long as one has access to a valid 'bespoke instrumental variable'. These are compared with existing approaches, first conceptually and then in an analysis of data from the Framingham Heart Study.

In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic L\'evy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of mass, heavy-tailed equilibrium and (hypo)coercivity properties. We perform a thorough analysis of the numerical scheme and show exponential stability and convergence of the scheme. Along the way, we introduce new tools of discrete functional analysis, such as discrete nonlocal Poincar\'e and interpolation inequalities adapted to fractional diffusion. Our theoretical findings are illustrated and complemented with numerical simulations.

We develop a new approach to drifting games, a class of two-person games with many applications to boosting and online learning settings, including Prediction with Expert Advice and the Hedge game. Our approach involves (a) guessing an asymptotically optimal potential by solving an associated partial differential equation (PDE); then (b) justifying the guess, by proving upper and lower bounds on the final-time loss whose difference scales like a negative power of the number of time steps. The proofs of our potential-based upper bounds are elementary, using little more than Taylor expansion. The proofs of our potential-based lower bounds are also rather elementary, combining Taylor expansion with probabilistic or combinatorial arguments. Most previous work on asymptotically optimal strategies has used potentials obtained by solving a discrete dynamic programming principle; the arguments are complicated by their discrete nature. Our approach is facilitated by the fact that the potentials we use are explicit solutions of PDEs; the arguments are based on basic calculus. Not only is our approach more elementary, but we give new potentials and derive corresponding upper and lower bounds that match each other in the asymptotic regime.

This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrite the problem into a system with a second-order spatial derivative, then apply the energy-based discontinuous Galerkin method to the system. The proposed scheme, on the one hand, is more computationally efficient compared with the local discontinuous Galerkin method because of fewer auxiliary variables. On the other hand, it is unconditionally stable without adding any penalty terms, and admits optimal convergence in the $L^2$ norm for both solution and auxiliary variables. In addition, the energy-dissipating or energy-conserving property of the scheme follows from simple, mesh-independent choices of the interelement fluxes. We also present a stability and convergence analysis along with numerical experiments to demonstrate optimal convergence for certain choices of the interelement fluxes.

Modern convolutional neural networks (CNNs)-based face detectors have achieved tremendous strides due to large annotated datasets. However, misaligned results with high detection confidence but low localization accuracy restrict the further improvement of detection performance. In this paper, the authors first predict high confidence detection results on the training set itself. Surprisingly, a considerable part of them exist in the same misalignment problem. Then, the authors carefully examine these cases and point out that annotation misalignment is the main reason. Later, a comprehensive discussion is given for the replacement rationality between predicted and annotated bounding-boxes. Finally, the authors propose a novel Bounding-Box Deep Calibration (BDC) method to reasonably replace misaligned annotations with model predicted bounding-boxes and offer calibrated annotations for the training set. Extensive experiments on multiple detectors and two popular benchmark datasets show the effectiveness of BDC on improving models' precision and recall rate, without adding extra inference time and memory consumption. Our simple and effective method provides a general strategy for improving face detection, especially for light-weight detectors in real-time situations.

We present a flow-based control strategy that enables resource-constrained marine robots to patrol gyre-like flow environments on an orbital trajectory with a periodicity in a given range. The controller does not require a detailed model of the flow field and relies only on the robot's location relative to the center of the gyre. Instead of precisely tracking a pre-defined trajectory, the robots are tasked to stay in between two bounding trajectories with known periodicity. Furthermore, the proposed strategy leverages the surrounding flow field to minimize control effort. We prove that the proposed strategy enables robots to cycle in the flow satisfying the desired periodicity requirements. Our method is tested and validated both in simulation and in experiments using a low-cost, underactuated, surface swimming robot, i.e. the Modboat.

We identify a new class of vulnerabilities in implementations of differential privacy. Specifically, they arise when computing basic statistics such as sums, thanks to discrepancies between the implemented arithmetic using finite data types (namely, ints or floats) and idealized arithmetic over the reals or integers. These discrepancies cause the sensitivity of the implemented statistics (i.e., how much one individual's data can affect the result) to be much higher than the sensitivity we expect. Consequently, essentially all differential privacy libraries fail to introduce enough noise to hide individual-level information as required by differential privacy, and we show that this may be exploited in realistic attacks on differentially private query systems. In addition to presenting these vulnerabilities, we also provide a number of solutions, which modify or constrain the way in which the sum is implemented in order to recover the idealized or near-idealized bounds on sensitivity.

Link prediction on knowledge graphs (KGs) is a key research topic. Previous work mainly focused on binary relations, paying less attention to higher-arity relations although they are ubiquitous in real-world KGs. This paper considers link prediction upon n-ary relational facts and proposes a graph-based approach to this task. The key to our approach is to represent the n-ary structure of a fact as a small heterogeneous graph, and model this graph with edge-biased fully-connected attention. The fully-connected attention captures universal inter-vertex interactions, while with edge-aware attentive biases to particularly encode the graph structure and its heterogeneity. In this fashion, our approach fully models global and local dependencies in each n-ary fact, and hence can more effectively capture associations therein. Extensive evaluation verifies the effectiveness and superiority of our approach. It performs substantially and consistently better than current state-of-the-art across a variety of n-ary relational benchmarks. Our code is publicly available.