1,729 research outputs found
On the Volume of Isolated Singularities
We give an equivalent definition of the local volume of an isolated
singularity Vol_{BdFF}(X,0) given in [BdFF12] in the Q-Gorenstein case and we
generalize it to the non-Q-Gorenstein case. We prove that there is a positive
lower bound depending only on the dimension for the non-zero local volume of an
isolated singularity if X is Gorenstein. We also give a non-Q-Gorenstein
example with Vol_{BdFF}(X,0)=0, which does not allow a boundary \Delta such
that the pair (X,\Delta) is log canonical.Comment: 12 pages. Final version. To appear in Compos. Mat
Stochastic Primal-Dual Coordinate Method for Regularized Empirical Risk Minimization
We consider a generic convex optimization problem associated with regularized
empirical risk minimization of linear predictors. The problem structure allows
us to reformulate it as a convex-concave saddle point problem. We propose a
stochastic primal-dual coordinate (SPDC) method, which alternates between
maximizing over a randomly chosen dual variable and minimizing over the primal
variable. An extrapolation step on the primal variable is performed to obtain
accelerated convergence rate. We also develop a mini-batch version of the SPDC
method which facilitates parallel computing, and an extension with weighted
sampling probabilities on the dual variables, which has a better complexity
than uniform sampling on unnormalized data. Both theoretically and empirically,
we show that the SPDC method has comparable or better performance than several
state-of-the-art optimization methods
Macro Grammars and Holistic Triggering for Efficient Semantic Parsing
To learn a semantic parser from denotations, a learning algorithm must search
over a combinatorially large space of logical forms for ones consistent with
the annotated denotations. We propose a new online learning algorithm that
searches faster as training progresses. The two key ideas are using macro
grammars to cache the abstract patterns of useful logical forms found thus far,
and holistic triggering to efficiently retrieve the most relevant patterns
based on sentence similarity. On the WikiTableQuestions dataset, we first
expand the search space of an existing model to improve the state-of-the-art
accuracy from 38.7% to 42.7%, and then use macro grammars and holistic
triggering to achieve an 11x speedup and an accuracy of 43.7%.Comment: EMNLP 201
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