391 research outputs found
Ghost field realizations of the spinor strings based on the linear W(1,2,s) algebras
It has been shown that certain W algebras can be linearized by the inclusion
of a spin-1 current. This Provides a way of obtaining new realizations of the W
algebras. In this paper, we investigate the new ghost field realizations of the
W(2,s)(s=3,4) algebras, making use of the fact that these two algebras can be
linearized. We then construct the nilpotent BRST charges of the spinor
non-critical W(2,s) strings with these new realizations.Comment: 10 pages, no figure
Mutual Information Learned Regressor: an Information-theoretic Viewpoint of Training Regression Systems
As one of the central tasks in machine learning, regression finds lots of
applications in different fields. An existing common practice for solving
regression problems is the mean square error (MSE) minimization approach or its
regularized variants which require prior knowledge about the models. Recently,
Yi et al., proposed a mutual information based supervised learning framework
where they introduced a label entropy regularization which does not require any
prior knowledge. When applied to classification tasks and solved via a
stochastic gradient descent (SGD) optimization algorithm, their approach
achieved significant improvement over the commonly used cross entropy loss and
its variants. However, they did not provide a theoretical convergence analysis
of the SGD algorithm for the proposed formulation. Besides, applying the
framework to regression tasks is nontrivial due to the potentially infinite
support set of the label. In this paper, we investigate the regression under
the mutual information based supervised learning framework. We first argue that
the MSE minimization approach is equivalent to a conditional entropy learning
problem, and then propose a mutual information learning formulation for solving
regression problems by using a reparameterization technique. For the proposed
formulation, we give the convergence analysis of the SGD algorithm for solving
it in practice. Finally, we consider a multi-output regression data model where
we derive the generalization performance lower bound in terms of the mutual
information associated with the underlying data distribution. The result shows
that the high dimensionality can be a bless instead of a curse, which is
controlled by a threshold. We hope our work will serve as a good starting point
for further research on the mutual information based regression.Comment: 28 pages, 2 figures, presubmitted to AISTATS2023 for reviewin
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