We investigate a low-rank model of quadratic classification inspired by previous work on factorization machines, polynomial networks, and capsule-based architectures for visual object recognition. The model is parameterized by a pair of affine transformations, and it classifies examples by comparing the magnitudes of vectors that these transformations produce. The model is also over-parameterized in the sense that different pairs of affine transformations can describe classifiers with the same decision boundary and confidence scores. We show that such pairs arise from discrete and continuous symmetries of the model's parameter space: in particular, the latter define symmetry groups of rotations and Lorentz transformations, and we use these group structures to devise appropriately invariant procedures for model alignment and averaging. We also leverage the form of the model's decision boundary to derive simple margin-based updates for online learning.

We investigate a low-rank model of quadratic classification inspired by previous work on factorization machines, polynomial networks, and capsule-based architectures for visual object recognition. The model is parameterized by a pair of affine transformations, and it classifies examples by comparing the magnitudes of vectors that these transformations produce. The model is also over-parameterized in the sense that different pairs of affine transformations can describe classifiers with the same decision boundary and confidence scores. We show that such pairs arise from discrete and continuous symmetries of the model's parameter space: in particular, the latter define symmetry groups of rotations and Lorentz transformations, and we use these group structures to devise appropriately invariant procedures for model alignment and averaging. We also leverage the form of the model's decision boundary to derive simple margin-based updates for online learning.

We present a unified view for online classification, regression, and uni- class problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also dis- cussed. The end result is new algorithms and accompanying loss bounds for the hinge-loss.

We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also discussed. The end result is new algorithms and accompanying loss bounds for the hinge-loss.

We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also discussed. The end result is new algorithms and accompanying loss bounds for the hinge-loss.

We present a unified view for online classification, regression, and uniclass problems.This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also discussed. Theend result is new algorithms and accompanying loss bounds for the hinge-loss.