We perform a non-asymptotic analysis of the contrastive divergence (CD) algorithm, a training method for unnormalized models. While prior work has established that (for exponential family distributions) the CD iterates asymptotically converge at an O(n 1/3) rate to the true parameter of the data distribution, we show, under some regularity assumptions, that CD can achieve the parametric rate O(n 1/2). Our analysis provides results for various data batching schemes, including the fully online and minibatch ones. We additionally show that CD can be near-optimal, in the sense that its asymptotic variance is close to the Cramér-Rao lower bound.

The families of victims of a school shooting in a remote Canadian Rockies town are suing artificial intelligence company OpenAI in a United States federal court, alleging that the ChatGPT maker failed to alert police to the shooter's alarming interactions with the chatbot. A lawsuit filed on Wednesday on behalf of 12-year-old Maya Gebala, who was critically injured in the February shooting, is among the first of more than two dozen cases from families in Tumbler Ridge, British Columbia, in what their lawyers say represents "an entire community stepping forward to hold OpenAI accountable". The cases represent the families of the five slain children targeted in the school shooting. Those include Zoey Benoit, Abel Mwansa Jr, Ticaria "Tiki" Lampert, Kylie Smith, all 12, and Ezekiel Schofield, 13, as well as education assistant Shannda Aviugana-Durand. Jesse Van Rootselaar, whose interactions with ChatGPT are at the centre of the lawsuits, shot her mother and stepbrother at home before killing an educational assistant and five students aged 12 to 13 at her former school on February 10, according to police.

HCCV datasets constructed through nonconsensual web scraping lack crucial metadata for comprehensive fairness and robustness evaluations. Current remedies are post hoc, lack persuasive justification for adoption, or fail to provide proper contextualization for appropriate application. Our research focuses on proactive, domain-specific recommendations, covering purpose, privacy and consent, and diversity, for curating HCCV evaluation datasets, addressing privacy and bias concerns. We adopt an ante hoc reflective perspective, drawing from current practices, guidelines, dataset withdrawals, and audits, to inform our considerations and recommendations.

We consider adversarial multi-armed bandit problems where the learner is allowed to observe losses of a number of arms beside the arm that it actually chose. We study the case where all non-chosen arms reveal their loss with a fixed but unknown probability $r$, independently of each other and the action of the learner. We propose two algorithms that work for different ranges of $r$. We show that after $T$ rounds in a bandit problem with $N$ arms, the expected regret of our first algorithm is $O(\sqrt{(T /r) \log N })$ whenever $r\ge(\log T)/(2N)$, while our second algorithm achieves a regret of $O(\sqrt{(T/r) \log (N+T)})$ for smaller values of $r$. We also give a quick estimation procedure that decides the range of~$r$. All our bounds are within logarithmic factors of the best achievable performance of any algorithm that is even allowed to know~$r$.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this work, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node of an undirected graph and its expected rating is similar to the one of its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose three algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of node evaluations.

In this supplementary material, we provide the proofs of convergence analysis in Section 1, 1-vs-1 transformation employed in the classification and semantic segmentation tasks in Section 2, the coordinate-wise and the preprocessing method of the LSTM teacher in Section 3, the loss functions of YOLO-v3 in Section 4, more experiments of image classification in Section 5, and the inferences of semantic segmentation in Section 6. A differentiable function e()is L-smooth with gradient Lipschitz constant C (uniformly Lipschitz continuous), if e(x) e(y) C x y, x,y. The function is called block-wise smooth with gradient Lipschitz Ci, if i e(x i,xi) ie(x i,x i) Ci xi x i, x,x (1) or with gradient Lipschitz constants { Ci}, if i e(x i,xi) ie(x i,xi) Ci x i x i, x,x (2) Further, Let Gmax max{Ci, Ci, k} C. Definition 2. For a differentiable function e(), if e(x) = 0, then x is a first-order stationary solution (SS1). For a differentiable function e(), if x is a SS1, and there exists ϵ > 0 so that for any y in the ϵ-neighborhood of x, we have e(x) e(y), then xis a local minimum. A saddle point xis an SS1 that is not a local minimum. If λmin( 2e(x)) < 0, x is a strict (non-degenerate) saddle point.