Second, we show the first core-set w.r.t. the sum-of-nearest-neighbor distances. Finally, we run several experiments showing the effectiveness of our core-set approach. In particular, we apply constrained diversity maximization to summarize a set of timed messages that takes into account the messages' recency.

It is well known that this is unlearnable, but we sketch a proof here.

For the convenience of the reader, we summarize a list of notations blow. 1. null G In Appendix B.1, we present a general statement of Theorem 3.1 (a) along with its proof. Theorem 3.1 (a) states the order recovery guarantee for a specified parameter We summarize the bounds for (I) and (II) in Lemma B.1 and Lemma B.2, which can be found in Collecting the results in Lemma B.1 and Lemma B.2 and reorganizing the terms in the inequalities, we have the following conclusion. We now state the proof of this Lemma. Then we bound the first term using the concentration bound on Chi-squared random variables. For the non-identifiable models, we can use Lemma H.1 in a similar way to obtain that with probability We now state the proof of this Lemma.

Unsupervised 3D object detection methods have emerged to leverage vast amounts of data without requiring manual labels for training. Recent approaches rely on dynamic objects for learning to detect mobile objects but penalize the detections of static instances during training. Multiple rounds of (self) training are used to add detected static instances to the set of training targets; this procedure to improve performance is computationally expensive. To address this, we propose the method UNION. We use spatial clustering and self-supervised scene flow to obtain a set of static and dynamic object proposals from LiDAR.

We provide a complete theory of optimal universal rates for binary classification in the agnostic setting. This extends the realizable-case theory of Bousquet, Hanneke, Moran, van Handel, and Yehudayoff (2021) by removing the realizability assumption on the distribution. We identify a fundamental tetrachotomy of optimal rates: for every concept class, the optimal universal rate of convergence of the excess error rate is one of $e^{-n}$, $e^{-o(n)}$, $o(n^{-1/2})$, or arbitrarily slow. We further identify simple combinatorial structures which determine which of these categories any given concept class falls into.

We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The permutation is a key component of the data-generating process, yet its statistical investigation remains challenging due to its discrete nature. We develop a general statistical inference framework on the permutation and regression coefficients. First, we introduce a localization step that reduces the permutation space to a small candidate set building on recent advances in the repro samples method, whose miscoverage decays polynomially with the number of Monte Carlo samples. Then, based on this localized set, we provide statistical inference procedures: a conditional Monte Carlo test of permutation structures with valid finite-sample Type-I error control. We also develop coefficient inference that remains valid under alignment uncertainty of permutations. For computational purposes, we develop a linear assignment problem computable in polynomial time and demonstrate that, with high probability, the solution is equivalent to that of the conventional least squares with large computational cost. Extensions to partially permuted designs and ridge regularization are further discussed. Extensive simulations and an application to air-quality data corroborate finite-sample validity, strong power to detect mismatches, and practical scalability.

Israeli forces killed at least 11 people in the Gaza Strip on Wednesday, Gaza health officials said, including three Palestinian journalists who the Israeli military said were flying a drone. The Palestinian Journalists Syndicate, a labor union, said the three men were documenting the "suffering of civilians in displacement camps." The Israeli military said they were operating a drone that was "affiliated with Hamas" and that its forces believed it posed a threat. The Israeli military said the details of the incident were under examination. The three journalists were identified as Abdel Raouf Shaath, Mohammad Salah Qishta and Anas Ghneim by the journalists' union.

Activists are demanding a way to hold the memory-chip maker accountable to its promises to protect the environment and embrace communities of color in central New York. Days after Micron broke ground on a $100 billion chip factory in New York state, a coalition of environmentalists, labor unions, and civil rights groups are urging the US tech giant to sign a deal that would make a series of promises to be a good neighbor legally enforceable. Micron's megafab to make memory chips is on track to become the biggest commercial development in state history and the largest chipmaking complex in the country . Officials held a groundbreaking ceremony in the city of Clay, near Syracuse, last Friday. The first chips could arrive in five years, though the entire site won't be finished for 20 years.

The overwhelming vulnerability of deep neural networks to carefully crafted perturbations known as adversarial attacks has led to the development of various training techniques to produce robust models. While the primary focus of existing approaches has been directed toward addressing the worst-case performance achieved under a single-threat model, it is imperative that safety-critical systems are robust with respect to multiple threat models simultaneously. Existing approaches that address worst-case performance under the union of such threat models ($\ell_{\infty}, \ell_2, \ell_1$) either utilize adversarial training methods that require multi-step attacks which are computationally expensive in practice, or rely upon fine-tuning of pre-trained models that are robust with respect to a single-threat model. In this work, we show that by carefully choosing the objective function used for robust training, it is possible to achieve similar, or improved worst-case performance over a union of threat models while utilizing only single-step attacks, thereby achieving a significant reduction in computational resources necessary for training. Furthermore, prior work showed that adversarial training specific to the $\ell_1$ threat model is relatively difficult, to the extent that even multi-step adversarially trained models were shown to be prone to gradient-masking. However, the proposed method--when applied on the $\ell_1$ threat model specifically--enables us to obtain the first $\ell_1$ robust model trained solely with single-step adversaries. Finally, to demonstrate the merits of our approach, we utilize a modern set of attack evaluations to better estimate the worst-case performance under the considered union of threat models.

Logical reasoning over Knowledge Graphs (KGs) is a fundamental technique that can provide an efficient querying mechanism over large and incomplete databases. Current approaches employ spatial geometries such as boxes to learn query representations that encompass the answer entities and model the logical operations of projection and intersection. However, their geometry is restrictive and leads to non-smooth strict boundaries, which further results in ambiguous answer entities. Furthermore, previous works propose transformation tricks to handle unions which results in non-closure and, thus, cannot be chained in a stream. In this paper, we propose a Probabilistic Entity Representation Model (PERM) to encode entities as a Multivariate Gaussian density with mean and covariance parameters to capture its semantic position and smooth decision boundary, respectively. Additionally, we also define the closed logical operations of projection, intersection, and union that can be aggregated using an end-to-end objective function. On the logical query reasoning problem, we demonstrate that the proposed PERM significantly outperforms the state-of-the-art methods on various public benchmark KG datasets on standard evaluation metrics. We also evaluate PERM's competence on a COVID-19 drug-repurposing case study and show that our proposed work is able to recommend drugs with substantially better F1 than current methods. Finally, we demonstrate the working of our PERM's query answering process through a low-dimensional visualization of the Gaussian representations.