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We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC‐Bayes risk certification paradigm. Classifiers are realized as linearly parametrized deep assignment flows with random initial conditions. Building on the recent PAC‐Bayes literature and data‐dependent priors, this approach enables (i) to use risk bounds as training objectives for learning posterior...
Assignment flows are smooth dynamical systems for data labeling on graphs. Although they exhibit structural similarities with the well‐studied class of replicator dynamics, it is nontrivial to apply existing tools to their analysis. We propose an embedding of the underlying assignment manifold into the interior of a single probability simplex. Under this embedding, a large class of assignment flows...
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self‐assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low‐rank matrix that is parametrized by the variables of the assignment flow, which entails an assignment of the data to themselves...
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