The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private version of the problem, however, is more challenging and in particular, the sample complexity must depend on the size $|X|$ of the domain. Progress on quantifying this dependence, via lower and upper bounds, was made in a line of works over the past decade. In this paper, we finally close the gap for approximate-DP and provide a nearly tight upper bound of $\tilde{O}(\log^* |X|)$, which matches a lower bound by Alon et al (that applies even with improper learning) and improves over a prior upper bound of $\tilde{O}((\log^* |X|)^{1.5})$ by Kaplan et al. We also provide matching upper and lower bounds of $\tilde{\Theta}(2^{\log^*|X|})$ for the additive error of private quasi-concave optimization (a related and more general problem). Our improvement is achieved via the novel Reorder-Slice-Compute paradigm for private data analysis which we believe will have further applications.

Countsketch和功能哈希（“ Hashhing Track”）是流行的随机降低降低方法，支持$ \ ell_2 $ -heavy hters的恢复（键$ i $ where $ v_i^2> \ epsilon \ epsilon \ | \ boldsymbol {v} \ | _2^2 $）和近似内部产品。当输入为{\ em不自适应}（不依赖于先前的输出）时，应用于尺寸$ o（\ ell/\ epsilon）$的经典估计器对于许多在$ \ \ \ \ \ \ \ \ \ hig的尺寸的草图（\ ell/\ epsilon）$都是准确的。 Ell $。但是，当输入是自适应的时，可以在$ o（\ ell）$ QUERIES具有经典估算器和最知名的稳健估计器后构建对抗输入，并且仅支持$ \ tilde {o}（\ ell^2）$ queries。在这项工作中，我们表明，这种二次依赖性在某种意义上是固有的：我们设计了$ O（\ ell^2）$ QUERIES之后的攻击，该攻击会产生一个对抗性输入向量，其草图是高度偏见的。我们的攻击使用“天然”非自适应输入（仅选择最终的对抗输入），并普遍适用任何正确的估计器，包括攻击者未知的估计器。在此，我们暴露了这种基本方法的固有脆弱性。

聚类是数据分析中的一个根本问题。在差别私有聚类中，目标是识别$ k $群集中心，而不披露各个数据点的信息。尽管研究进展显着，但问题抵制了实际解决方案。在这项工作中，我们的目的是提供简单的可实现的差异私有聚类算法，当数据“简单”时，提供实用程序，例如，当簇之间存在显着的分离时。我们提出了一个框架，允许我们将非私有聚类算法应用于简单的实例，并私下结合结果。在高斯混合的某些情况下，我们能够改善样本复杂性界限，并获得$ k $ -means。我们与合成数据的实证评估补充了我们的理论分析。

Differentially private algorithms for common metric aggregation tasks, such as clustering or averaging, often have limited practicality due to their complexity or to the large number of data points that is required for accurate results. We propose a simple and practical tool, $\mathsf{FriendlyCore}$, that takes a set of points ${\cal D}$ from an unrestricted (pseudo) metric space as input. When ${\cal D}$ has effective diameter $r$, $\mathsf{FriendlyCore}$ returns a "stable" subset ${\cal C} \subseteq {\cal D}$ that includes all points, except possibly few outliers, and is {\em certified} to have diameter $r$. $\mathsf{FriendlyCore}$ can be used to preprocess the input before privately aggregating it, potentially simplifying the aggregation or boosting its accuracy. Surprisingly, $\mathsf{FriendlyCore}$ is light-weight with no dependence on the dimension. We empirically demonstrate its advantages in boosting the accuracy of mean estimation and clustering tasks such as $k$-means and $k$-GMM, outperforming tailored methods.

经典流算法在（并非总是合理的）假设下运行的，即输入流已预先固定。最近，对于设计可靠的流算法，即使在执行过程中自适应地选择输入流也可以提供可证明的保证，越来越有兴趣。我们提出了一个新的框架，用于强大的流媒体，该框架结合了Hassidim等人最近建议的两个框架的技术。[神经2020]以及伍德拉夫和周[焦点2021]。这些最近建议的框架依赖于非常不同的想法，每个想法都具有自己的优势和劣势。我们将这两个框架组合到一个单一的混合框架中，该框架获得了``两全其美的''，从而解决了Woodruff和Zhou留下的问题。

Classical methods for acoustic scene mapping require the estimation of time difference of arrival (TDOA) between microphones. Unfortunately, TDOA estimation is very sensitive to reverberation and additive noise. We introduce an unsupervised data-driven approach that exploits the natural structure of the data. Our method builds upon local conformal autoencoders (LOCA) - an offline deep learning scheme for learning standardized data coordinates from measurements. Our experimental setup includes a microphone array that measures the transmitted sound source at multiple locations across the acoustic enclosure. We demonstrate that LOCA learns a representation that is isometric to the spatial locations of the microphones. The performance of our method is evaluated using a series of realistic simulations and compared with other dimensionality-reduction schemes. We further assess the influence of reverberation on the results of LOCA and show that it demonstrates considerable robustness.

Software Defect Prediction aims at predicting which software modules are the most probable to contain defects. The idea behind this approach is to save time during the development process by helping find bugs early. Defect Prediction models are based on historical data. Specifically, one can use data collected from past software distributions, or Versions, of the same target application under analysis. Defect Prediction based on past versions is called Cross Version Defect Prediction (CVDP). Traditionally, Static Code Metrics are used to predict defects. In this work, we use the Class Dependency Network (CDN) as another predictor for defects, combined with static code metrics. CDN data contains structural information about the target application being analyzed. Usually, CDN data is analyzed using different handcrafted network measures, like Social Network metrics. Our approach uses network embedding techniques to leverage CDN information without having to build the metrics manually. In order to use the embeddings between versions, we incorporate different embedding alignment techniques. To evaluate our approach, we performed experiments on 24 software release pairs and compared it against several benchmark methods. In these experiments, we analyzed the performance of two different graph embedding techniques, three anchor selection approaches, and two alignment techniques. We also built a meta-model based on two different embeddings and achieved a statistically significant improvement in AUC of 4.7% (p < 0.002) over the baseline method.

Autonomous underwater vehicles (AUVs) are regularly used for deep ocean applications. Commonly, the autonomous navigation task is carried out by a fusion between two sensors: the inertial navigation system and the Doppler velocity log (DVL). The DVL operates by transmitting four acoustic beams to the sea floor, and once reflected back, the AUV velocity vector can be estimated. However, in real-life scenarios, such as an uneven seabed, sea creatures blocking the DVL's view and, roll/pitch maneuvers, the acoustic beams' reflection is resulting in a scenario known as DVL outage. Consequently, a velocity update is not available to bind the inertial solution drift. To cope with such situations, in this paper, we leverage our BeamsNet framework and propose a Set-Transformer-based BeamsNet (ST-BeamsNet) that utilizes inertial data readings and previous DVL velocity measurements to regress the current AUV velocity in case of a complete DVL outage. The proposed approach was evaluated using data from experiments held in the Mediterranean Sea with the Snapir AUV and was compared to a moving average (MA) estimator. Our ST-BeamsNet estimated the AUV velocity vector with an 8.547% speed error, which is 26% better than the MA approach.

We consider a long-term average profit maximizing admission control problem in an M/M/1 queuing system with a known arrival rate but an unknown service rate. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue-length of the system. \cite[Econometrica]{Naor} showed that if all the parameters of the model are known, then it is optimal to use a static threshold policy - admit if the queue-length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full information model of \cite{Naor}. We show that the algorithm achieves an $O(1)$ regret when all optimal thresholds with full information are non-zero, and achieves an $O(\ln^{3+\epsilon}(N))$ regret in the case that an optimal threshold with full information is $0$ (i.e., an optimal policy is to reject all arrivals), where $N$ is the number of arrivals and $\epsilon>0$.

Contrastive learning has been successfully used for retrieval of semantically aligned sentences, but it often requires large batch sizes or careful engineering to work well. In this paper, we instead propose a generative model for learning multilingual text embeddings which can be used to retrieve or score sentence pairs. Our model operates on parallel data in $N$ languages and, through an approximation we introduce, efficiently encourages source separation in this multilingual setting, separating semantic information that is shared between translations from stylistic or language-specific variation. We show careful large-scale comparisons between contrastive and generation-based approaches for learning multilingual text embeddings, a comparison that has not been done to the best of our knowledge despite the popularity of these approaches. We evaluate this method on a suite of tasks including semantic similarity, bitext mining, and cross-lingual question retrieval -- the last of which we introduce in this paper. Overall, our Variational Multilingual Source-Separation Transformer (VMSST) model outperforms both a strong contrastive and generative baseline on these tasks.