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Monotone and Partially Monotone Neural Networks
IEEE Transactions on Neural Networks, 2010In many classification and prediction problems it is known that the response variable depends on certain explanatory variables. Monotone neural networks can be used as powerful tools to build monotone models with better accuracy and lower variance compared to ordinary nonmonotone models.
Daniels, H., Velikova, Marina
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Chaos, Solitons & Fractals, 1996
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Kapitaniak, Tomasz, Thylwe, Karl-Erik
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Kapitaniak, Tomasz, Thylwe, Karl-Erik
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Combinatorica, 2000
This paper provides a valuable nontrivial contribution to the area of learning and to the study of the power of randomisation. The following task is considered. Given a Boolean function \(f\), one has to decide whether \(f\) is monotone or far from being monotone (it differs by more than on a \(c\) fraction of inputs from any monotone function).
Goldreich, Oded +4 more
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This paper provides a valuable nontrivial contribution to the area of learning and to the study of the power of randomisation. The following task is considered. Given a Boolean function \(f\), one has to decide whether \(f\) is monotone or far from being monotone (it differs by more than on a \(c\) fraction of inputs from any monotone function).
Goldreich, Oded +4 more
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Identifying monotonic and non-monotonic relationships
Economics Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yitzhaki, Shlomo, Schechtman, Edna
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Games and Economic Behavior, 2018
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Economic Theory, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Econometrica, 1994
Summary: We derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, we develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist ...
Milgrom, Paul, Shannon, Chris
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Summary: We derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, we develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist ...
Milgrom, Paul, Shannon, Chris
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On Monotone Automata and Monotone Languages
2002In this paper monotone string and monotone tree languages are studied. For the string case, the monotone languages are characterized by means of regular expressions and syntactic monoids. Tree languages recognized by monotone frontier-to-root and monotone root-to-frontier recognizers are also characterized by syntactic ...
Gécseg, Ferenc, Imreh, Balázs
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Some Absolutely Monotonic and Completely Monotonic Functions
SIAM Journal on Mathematical Analysis, 1974The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesaro summability for ultraspherical series, [7].
Askey, Richard, Pollard, Harry
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