High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limits their ability to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose \emph{Hyperbolic Secant-squared Gibbs-Sampling (HiSS)}, a novel family of sampling algorithms that integrates a \emph{Metropolis-within-Gibbs} framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design allows the auxiliary variable to encapsulate the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization.

Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables.

But spectral clustering remains a frequently used baseline, and a serious contender to state-of-the-art graphembeddingmethods,e.g.[20,11,28,22].

Figure 5: Comparison of GenStat architecture to selected graph generative models. This proof uses two properties of LDP: composability and immunity to post-processing [2]. Figure 6 illustrates the PGM of Randomized algorithms. The GGM parameters are a function of the perturbed graph statistics as learning input. The implementation can be easily extended to directed graphs. A statistics-based GGM that takes the degree sequence as sufficient statistics [5].

In this paper, we present a comprehensive study of the performance of average-link in metric spaces, regarding several natural criteria that capture separability and cohesion, and aremore interpretable than Dasgupta'scost function and itsvariants.

To address this gap, we first formulate the DRO problem from causality and individual fairness perspectives.