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Unification of Information Maximization and Minimization

Neural Information Processing Systems

In the present paper, we propose a method to unify information maximization and minimization in hidden units. The information maximization and minimization are performed on two different levels: collective and individual level. Thus, two kinds of information: collective and individual information are defined. By maximizing collective information and by minimizing individual information, simple networks can be generated in terms of the number of connections and the number of hidden units. Obtained networks are expected to give better generalization and improved interpretation of internal representations.


Unification of Information Maximization and Minimization

Neural Information Processing Systems

In the present paper, we propose a method to unify information maximization and minimization in hidden units. The information maximization and minimization are performed on two different levels: collectiveand individual level. Thus, two kinds of information: collective and individual information are defined. By maximizing collective information and by minimizing individual information, simple networks can be generated in terms of the number of connections andthe number of hidden units. Obtained networks are expected to give better generalization and improved interpretation of internal representations.



Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications

arXiv.org Machine Learning

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a dierence between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the multiplicative inapproximability of minimizing the dierence between submodular functions. We show, however, that it is possible to give worst-case additive bounds by providing a polynomial time computable lower-bound on the minima. Finally we show how a number of machine learning problems can be modeled as minimizing the dierence between submodular functions. We experimentally show the validity of our algorithms by testing them on the problem of feature selection with submodular cost features.