However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum likelihood learning of EBMs. PS-CD is derived from the maximization of a family of strictly proper homogeneous scoring rules, which avoids the computation of the intractable partition function and provides a generalized family of learning objectives that include contrastive divergence as a special case. Moreover, PS-CD allows us to flexibly choose various learning objectives to train EBMs without additional computational cost or variational minimax optimization. Theoretical analysis on the proposed method and extensive experiments on both synthetic data and commonly used image datasets demonstrate the effectiveness and modeling flexibility of PS-CD, as well as its robustness to data contamination, thus showing its superiority over maximum likelihood and f-EBMs.

Compared to existing techniques, our maps offer several advantages. The standard method for compressing point sets by random mappings relies on the Johnson-Lindenstrauss lemma and involves compressing point sets with a random linear map.

Dataset Distillation (DD) is designed to generate condensed representations of extensive image datasets, enhancing training efficiency. Despite recent advances, there remains considerable potential for improvement, particularly in addressing the notable redundancy within the color space of distilled images. In this paper, we propose AutoPalette, a framework that minimizes color redundancy at the individual image and overall dataset levels, respectively. At the image level, we employ a palette network, a specialized neural network, to dynamically allocate colors from a reduced color space to each pixel. The palette network identifies essential areas in synthetic images for model training and consequently assigns more unique colors to them. At the dataset level, we develop a color-guided initialization strategy to minimize redundancy among images. Representative images with the least replicated color patterns are selected based on the information gain. A comprehensive performance study involving various datasets and evaluation scenarios is conducted, demonstrating the superior performance of our proposed color-aware DD compared to existing DD methods.

We study bandit convex optimization methods that adapt to the norm of the comparator, a topic that has only been studied before for its full-information counterpart. Specifically, we develop convex bandit algorithms with regret bounds that are small whenever the norm of the comparator is small. We first use techniques from the full-information setting to develop comparator-adaptive algorithms for linear bandits. Then, we extend the ideas to convex bandits with Lipschitz or smooth loss functions, using a new variant of the standard single-point gradient estimator and carefully designed surrogate losses.

We provide theoretical analysis on the convergence of Flow and empirically demonstrate the superiority of Flow in improving clients' accuracy compared

In this section, we provide further experimental results and analysis, including ablative analysis, analysis on the selection of edge types and re-encoding gap, as well as additional qualitative results. The descriptions of each model setup are provided in Section 8.2. SG: We show the effectiveness of the distinction of agent node types. The reason is that different types of agents have distinct behavior patterns or feasibility constraints. For example, the trajectories of on-road vehicles are restricted by roadways, traffic rules and physical constraints, while the restrictions on pedestrian behaviors are much fewer.