Uncertainty-Aware Attention for Reliable Interpretation and Prediction

Department of Computer Science and EngineeringAttention mechanism is effective in both focusing the deep learning models on relevant features and interpreting them. However, attentions may be unreliable since the networks that generate them are often trained in a weakly-supervised manner. To overcome this limitation, we introduce the notion of input-dependent uncertainty to the attention mechanism, such that it generates attention for each feature with varying degrees of noise based on the given input, to learn larger variance on instances it is uncertain about. We learn this Uncertainty-aware Attention (UA) mechanism using variational inference, and validate it on various risk prediction tasks from electronic health records on which our model significantly outperforms existing attention models. The analysis of the learned attentions shows that our model generates attentions that comply with clinicians' interpretation, and provide richer interpretation via learned variance. Further evaluation of both the accuracy of the uncertainty calibration and the prediction performance with "I don't know'' decision show that UA yields networks with high reliability as well.ope

Varieties with maximum likelihood degree one

We show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under monomial maps with finite fibers. The maximum likelihood estimator corresponding to such a variety is Kapranov's Horn uniformization. This extends Kapranov's characterization of A-discriminantal hypersurfaces to varieties of arbitrary codimension.Comment: 14 pages, changed title, minor revisio

Correspondences between projective planes

We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.Comment: Improved readability, 14 page

Cubic symmetroids and vector bundles on a quadric surface

We investigate the jumping conics of stable vector bundles \Ee of rank 2 on a smooth quadric surface $Q$ with the Chern classes c_1=\Oo_Q(-1,-1) and $c_2=4$ with respect to the ample line bundle \Oo_Q(1,1). We describe the set of jumping conics of \Ee, a cubic symmetroid in \PP_3, in terms of the cohomological properties of \Ee. As a consequence, we prove that the set of jumping conics, S(\Ee), uniquely determines \Ee. Moreover we prove that the moduli space of such vector bundles is rational.Comment: 6 pages; Comments welcom