2,005 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
Weakly Supervised Audio Source Separation via Spectrum Energy Preserved Wasserstein Learning
Separating audio mixtures into individual instrument tracks has been a long
standing challenging task. We introduce a novel weakly supervised audio source
separation approach based on deep adversarial learning. Specifically, our loss
function adopts the Wasserstein distance which directly measures the
distribution distance between the separated sources and the real sources for
each individual source. Moreover, a global regularization term is added to
fulfill the spectrum energy preservation property regardless separation. Unlike
state-of-the-art weakly supervised models which often involve deliberately
devised constraints or careful model selection, our approach need little prior
model specification on the data, and can be straightforwardly learned in an
end-to-end fashion. We show that the proposed method performs competitively on
public benchmark against state-of-the-art weakly supervised methods
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