Abstract
This article leans on some previous results already presented in [10], based on the Fréchet’s works, Wilson’s entropy and Minimal Trade models in connection with the MKP transportation problem (MKP, stands for Monge-Kantorovich Problem). Using the duality between “independance” and “indetermination” structures, shown in this former paper, we are in a position to derive a novel approach to design a copula, suitable and efficient for anomaly detection in IT systems analysis.
Keywords
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- 1.
This explains the term: “Minimal Trade Model”.
- 2.
There exist some constraints to satisfy for garanteeing the positivity of the optimal values \(\pi _{uv}\) (see [9]).
- 3.
\(C(u,v)- C(u,v')- C(u',v)+ C(u',v')\ge 0\) \(\forall 0\le u \le u' \le 1\) \(\forall 0\le v \le v' \le 1\) is known as the 2-increasing property. It is nothing but the so called Monge’s condition which was coined by Alan Hoffmann in 1963 (see [6]), this is an additional link between optimal transport and copula theory.
- 4.
In the last paragraph we suppose X to be at least bivariate.
- 5.
Where \(\{\hat{Y}=0\} = \{P(X\le x)\le s\}\).
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Huyot, B., Mabiala, Y., Marcotorchino, J.F. (2015). Optimal Transport, Independance Versus Indetermination Duality, Impact on a New Copula Design. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_8
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