However, in many scenarios, nodes also have attributes that are correlated with the clustering structure. Thus, network information (edges) and node information (attributes) can be jointly leveraged to design high-performance clustering algorithms. Under a general model for the network and node attributes, this work establishes an information-theoretic criterion for the exact recovery of community labels and characterizes a phase transition determined by the Chernoff-Hellinger divergence of the model.

Such feedback can be stochastic, e.g. the

Estimating the Riesz representer is central to debiased machine learning for causal and structural parameter estimation. We propose generalized Riesz regression, a unified framework that estimates the Riesz representer by fitting a representer model via Bregman divergence minimization. This framework includes the squared loss and the Kullback--Leibler (KL) divergence as special cases: the former recovers Riesz regression, while the latter recovers tailored loss minimization. Under suitable model specifications, the dual problems correspond to covariate balancing, which we call automatic covariate balancing. Moreover, under the same specifications, outcome averages weighted by the estimated Riesz representer satisfy Neyman orthogonality even without estimating the regression function, a property we call automatic Neyman orthogonalization. This property not only reduces the estimation error of Neyman orthogonal scores but also clarifies a key distinction between debiased machine learning and targeted maximum likelihood estimation. Our framework can also be viewed as a generalization of density ratio fitting under Bregman divergences to Riesz representer estimation, and it applies beyond density ratio estimation. We provide convergence analyses for both reproducing kernel Hilbert space (RKHS) and neural network model classes. A Python package for generalized Riesz regression is available at https://github.com/MasaKat0/grr.

We propose a novel and general method to learn Bregman divergences from raw high-dimensional data that measure similarity between images in pixel space. As a prototypical application, we learn divergences that consider real-world corruptions of images (e.g., blur) as close to the original and noisy perturbations as far, even if in $L^p$-distance the opposite holds. We also show that the learned Bregman divergence excels on datasets of human perceptual similarity judgment, suggesting its utility in a range of applications. We then define adversarial attacks by replacing the projected gradient descent (PGD) with the mirror descent associated with the learned Bregman divergence, and use them to improve the state-of-the-art in robustness through adversarial training for common image corruptions. In particular, for the contrast corruption that was found problematic in prior work we achieve an accuracy that exceeds the $L^p$- and the LPIPS-based adversarially trained neural networks by a margin of 27.16\% on the CIFAR-10-C corruption data set.