We present a low-rank multi-linear model for the task of solving prepositional phrase attachment ambiguity (PP task). Our model exploits tensor products of word embeddings, capturing all possible conjunctions of latent embeddings. Our results on a wide range of datasets and task settings show that tensor products are the best compositional operation and that a relatively simple multi-linear mod...

DISTINCT POPULATIONS THAT REPLACE EACH OTHER GEOGRAPHICALLY were recognized either as full species or as lower-level ‘‘varieties’’ or ‘‘forms’’ under the original Linnaean taxonomy. In zoology, a practical resolution of this ambiguity took place largely between about 1880 and 1920, with the recognition of a single additional taxonomic rank, the geographic subspecies (while in botany, many infra...

Nonadditive expected utility models were developed for explaining preferences in settings where probabilities cannot be assigned to events. In the absence of probabilities, difficulties arise in the interpretation of likelihoods of events. In this paper we introduce a notion of revealed likelihood that is defined entirely in terms of preferences and that does not require the existence of (subje...

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion

supplier selection is a multi-criteria problem. this study proposes a hybrid model for supporting the suppliers’ selection and ranking. this research is a two-stage model designed to fully rank the suppliers where each supplier has multiple inputs and outputs. first, the supplier evaluation problem is formulated by data envelopment analysis (dea), since the regarded decision deals with uncertai...

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a constraint, it avoids the inherent ambiguity of basis number selection conventional base-shape or base-trajectory methods. Despite efficiency deformable shape reconstruction, remains unclear how to assess uncertainty recovered SDP process. In this paper, we present ...

Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on factorization are provably solved by simple gradient descent algorithms with strong computational statistical guarantees. However, when the low-rank matrices asymmetric, existing approaches rely adding regularization term to balance scale of two facto...