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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 present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum eigenvalue of the expected design matrix grows as $\Omega(\sqrt{n})$ whenever the expected cumulative regret of the algorithm is $O(\sqrt{n})$, where $n$ is the learning horizon, and the action-space has a constant Hessian around the optimal arm. This shows that such action-spaces force a polynomial lower bound rather than a logarithmic lower bound, as shown by \cite{lattimore2017end}, in discrete (i.e., well-separated) action spaces. Furthermore, while the previous result is shown to hold only in the asymptotic regime (as $n \to \infty$), our result for these ``locally rich" action spaces is any-time. Additionally, under a mild technical assumption, we obtain a similar lower bound on the minimum eigen value holding with high probability. We apply our result to two practical scenarios -- \emph{model selection} and \emph{clustering} in linear bandits. For model selection, we show that an epoch-based linear bandit algorithm adapts to the true model complexity at a rate exponential in the number of epochs, by virtue of our novel spectral bound. For clustering, we consider a multi agent framework where we show, by leveraging the spectral result, that no forced exploration is necessary -- the agents can run a linear bandit algorithm and estimate their underlying parameters at once, and hence incur a low regret.

This paper investigates the best arm identification (BAI) problem in stochastic multi-armed bandits in the fixed confidence setting. The general class of the exponential family of bandits is considered. The state-of-the-art algorithms for the exponential family of bandits face computational challenges. To mitigate these challenges, a novel framework is proposed, which views the BAI problem as sequential hypothesis testing, and is amenable to tractable analysis for the exponential family of bandits. Based on this framework, a BAI algorithm is designed that leverages the canonical sequential probability ratio tests. This algorithm has three features for both settings: (1) its sample complexity is asymptotically optimal, (2) it is guaranteed to be $\delta-$PAC, and (3) it addresses the computational challenge of the state-of-the-art approaches. Specifically, these approaches, which are focused only on the Gaussian setting, require Thompson sampling from the arm that is deemed the best and a challenger arm. This paper analytically shows that identifying the challenger is computationally expensive and that the proposed algorithm circumvents it. Finally, numerical experiments are provided to support the analysis.

We introduce bloomRF as a unified method for approximate membership testing that supports both point- and range-queries. As a first core idea, bloomRF introduces novel prefix hashing to efficiently encode range information in the hash-code of the key itself. As a second key concept, bloomRF proposes novel piecewise-monotone hash-functions that preserve local order and support fast range-lookups with fewer memory accesses. bloomRF has near-optimal space complexity and constant query complexity. Although, bloomRF is designed for integer domains, it supports floating-points, and can serve as a multi-attribute filter. The evaluation in RocksDB and in a standalone library shows that it is more efficient and outperforms existing point-range-filters by up to 4x across a range of settings and distributions, while keeping the false-positive rate low.

Optimizing noisy functions online, when evaluating the objective requires experiments on a deployed system, is a crucial task arising in manufacturing, robotics and many others. Often, constraints on safe inputs are unknown ahead of time, and we only obtain noisy information, indicating how close we are to violating the constraints. Yet, safety must be guaranteed at all times, not only for the final output of the algorithm. We introduce a general approach for seeking a stationary point in high dimensional non-linear stochastic optimization problems in which maintaining safety during learning is crucial. Our approach called LB-SGD is based on applying stochastic gradient descent (SGD) with a carefully chosen adaptive step size to a logarithmic barrier approximation of the original problem. We provide a complete convergence analysis of non-convex, convex, and strongly-convex smooth constrained problems, with first-order and zeroth-order feedback. Our approach yields efficient updates and scales better with dimensionality compared to existing approaches. We empirically compare the sample complexity and the computational cost of our method with existing safe learning approaches. Beyond synthetic benchmarks, we demonstrate the effectiveness of our approach on minimizing constraint violation in policy search tasks in safe reinforcement learning (RL).

This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to have information rate at most $1/2$ (achieved by the trivial 2-fold repetition code). Previously, it was (erroneously) reported that more generally no non-trivial linear codes correcting $k$ deletions exist, i.e., that the $(k+1)$-fold repetition codes and its rate of $1/(k+1)$ are basically optimal for any $k$. We disprove this and show the existence of binary linear codes of length $n$ and rate just below $1/2$ capable of correcting $\Omega(n)$ insertions and deletions. This identifies rate $1/2$ as a sharp threshold for recovery from deletions for linear codes, and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically-good linear code for Hamming errors into an asymptotically-good linear code for insdel errors. Lastly, we show that the $\frac{1}{2}$-rate limitation does not hold for affine codes by giving an explicit affine code of rate $1-\epsilon$ which can efficiently correct a constant fraction of insdel errors.

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.

Deep Learning algorithms have achieved the state-of-the-art performance for Image Classification and have been used even in security-critical applications, such as biometric recognition systems and self-driving cars. However, recent works have shown those algorithms, which can even surpass the human capabilities, are vulnerable to adversarial examples. In Computer Vision, adversarial examples are images containing subtle perturbations generated by malicious optimization algorithms in order to fool classifiers. As an attempt to mitigate these vulnerabilities, numerous countermeasures have been constantly proposed in literature. Nevertheless, devising an efficient defense mechanism has proven to be a difficult task, since many approaches have already shown to be ineffective to adaptive attackers. Thus, this self-containing paper aims to provide all readerships with a review of the latest research progress on Adversarial Machine Learning in Image Classification, however with a defender's perspective. Here, novel taxonomies for categorizing adversarial attacks and defenses are introduced and discussions about the existence of adversarial examples are provided. Further, in contrast to exisiting surveys, it is also given relevant guidance that should be taken into consideration by researchers when devising and evaluating defenses. Finally, based on the reviewed literature, it is discussed some promising paths for future research.

Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to increase the receptive field, we propose a novel deep Hierarchical Graph Convolutional Network (H-GCN) for semi-supervised node classification. H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and then refines the coarsened graph to the original to restore the representation for each node. Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned. Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods. Notably, our model gains substantial improvements when only a few labeled samples are provided.

Deep Learning has enabled remarkable progress over the last years on a variety of tasks, such as image recognition, speech recognition, and machine translation. One crucial aspect for this progress are novel neural architectures. Currently employed architectures have mostly been developed manually by human experts, which is a time-consuming and error-prone process. Because of this, there is growing interest in automated neural architecture search methods. We provide an overview of existing work in this field of research and categorize them according to three dimensions: search space, search strategy, and performance estimation strategy.