Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk--not all mathematically rigorous and differing subtly in the details--have appeared in the literature. In this paper, we revisit these definitions, make them rigorous, and critically examine their similarities and differences. Our technical tools derive from optimal transport, robust statistics, functional analysis, and game theory. Our contributions include the following: generalizing Strassen's theorem to the unbalanced optimal transport setting with applications to adversarial classification with unequal priors; showing an equivalence between adversarial robustness and robust hypothesis testing with -Wasserstein uncertainty sets; proving the existence of a pure Nash equilibrium in the two-player game between the adversary and the algorithm; and characterizing adversarial risk by the minimum Bayes error between a pair of distributions belonging to the -Wasserstein uncertainty sets. Our results generalize and deepen recently discovered connections between optimal transport and adversarial robustness and reveal new connections to Choquet capacities and game theory.

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a much lower computational cost compared with the existing sorting-based methods proposed in the literature. We provide a theory for partial explanation and justification of the method. We demonstrate that the proposed algorithm can produce a solution of the projection problem with high precision on large scale datasets, and the algorithm is able to significantly outperform the state-of-the-art methods in terms of runtime (about 6-8 times faster than a commercial software with respect to CPU time for input vector with 1 million variables or more). We further illustrate the effectiveness of the proposed algorithm on solving sparse regression in a bioinformatics problem. Empirical results on the GWAS dataset (with 1,500,000 single-nucleotide polymorphisms) show that, when using the proposed method to accelerate the Projected Quasi-Newton (PQN) method, the accelerated PQN algorithm is able to handle huge-scale regression problem and it is more efficient (about 3-6 times faster) than the current state-of-the-art methods.

Here we describe the additional details of FlaMBé's curation including structured guidelines for each annotation task, corpus curation, and file assembly. All manual curation in FlaMBé was conducted by three annotators who have doctorate level expertise in computational biology. For named entity tagging annotations a set of structured guidelines were followed to ensure consistency. The guidelines given to reviewers are in the annotator guidelines section below. B.1 Tissue and cell type entities Generally, all terms, related synonyms, and text entities that can be mapped to an entry from the tissue, organ, body part, fluid, and cell type branches of the NCI thesaurus were labeled. Instead of a rigid vocabulary fixed on exact matches of NCIThesaurus (NCIT) terms and synonyms, annotators were encouraged to tag any word with the same meaning as an ontology term. For example, "Pancreatic ductal adenocarcinoma" describes cancer of the pancreas, which can be related back to the NCI Thesaurus, and thus was tagged as a "TISSUE". An initial set of rules was provided to each annotator. When one annotator encountered a corner case (e.g., "is neuron a tissue or cell type?") all annotators discussed, reached a consensus, then added the corner case to the set of annotation rules.

In this section, we demonstrate the effectiveness of low-rank matrix factorization in recovering the label relationship matrix. We first present four important facts: f1: the rank of the matrix is equivalent to the number of classes. Specifically, this also means that if ˆZi,k = 1, then ˆZj,k = 1. We consider a toy example (without self-loops), ˆZ = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A = 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 (14) In a standard LRMF problem, it is not possible to recover ˆZ from A since no entries are observed for the third and fourth rows. However, we can demonstrate how LRMF effectively performs in this situation. Recovery: We begin by assuming v1 is in class 1, resulting in U1,: = [1, 1, 1] and V1,: = [1,0,0]. By observing A1,4, we know that v4 is also in class 1, resulting in U4,: = [1, 1, 1]and V4,: = [1,0,0](f2). By analyzing A1,2 and A1,3, we determine that v2 and v3 do not belong to class 1.

We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by designating neighbors as "positives," non-neighbors as "negatives," and approximate membership queries as group tests.

OpenAI's Sam Altman apologizes for not reporting ChatGPT account of Tumbler Ridge suspect to police Altman penned a letter addressed to the community of Tumbler Ridge, two months following the mass shooting incident. Two months following the deadly shooting in Tumbler Ridge, British Columbia, OpenAI's Sam Altman has formally apologized for not informing police of the alarming ChatGPT conversations seen with the suspect's account. Before the incident, OpenAI banned the account belonging to the alleged shooter, Jesse Van Rootselaar, for violating its usage policy due to potential for real-world violence. I am deeply sorry that we did not alert law enforcement to the account that was banned in June, Altman wrote in the letter. While I know words can never be enough, I believe an apology is necessary to recognize the harm and irreversible loss your community has suffered.

This poison-coupling the modifies poison-coupling paper the presents training effect Lockdo ef protocol in fect. FL, wn, which Lockdo by an isolating isolated significantly wn follo subspace the ws de training three grades training ke the subspaces y procedures.

In this section, we present some preliminary results that will be useful in proving Theorem 3.2, Theorem 3.3 and Proposition 3.4. We draw upon existing theory on properties of random kernel matrices and extend these properties to cluster-correlated data. Specifically, we show the convergence of eigenvalues and eigenvectors of an empirical kernel matrix based on clustered data. Let (X,F,P) be a probability space and H be a Hilbert space over (X,F,P) with a symmetric kernel function k: X X R. Let H be a compact operator on H, defined by Hg(x) = Z Equivalently, Hn can be viewed as an n nreal matrix whose (i,j)-th entry is {Hn}i,j = 1 n k(Xi,Xj). This is the empirical kernel matrix scaled by a factor of 1/n. Here we restrict our discussion to a reproducing kernel Hilbert space (RKHS) H, where the kernel function k is positive semi-definite. We also assume that the operator H is Hilbert-Schmidt, with E[k2(X,X0)] < . Let λ(T) denote the spectrum of a compact, symmetric operator T. Then λ(H) and λ(Hn) are the sets of eigenvalues for H and Hn, respectively.