uopt_presi/prep/07Problem_Statement/q

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2022-06-27 15:13:50 +02:00
Given $N$ Anomaly detection methods $M_i = TrainModel(X_{train})$, find $f(M_i)$ so that Score $S_i = f(M_i)$ can be used to find an above average AD method $M_{argmax(S)}$.
Let $TrainMany(X_{train},C)=TrainModel(X_{train})_{argmax(f(M_0...M_C))}$. We assume the distribution of $TrainMany$ to be gaussian and describe it through $\mu_C$ and $\sigma_C$. We consider a function $f(M)$ to be helpful, if $\Delta = \frac{sqrt(N) \cdot (\mu_C-\mu_1)}{sqrt(\sigma_C^2+\sigma_1^2)} > 3$ for some number of models tested $N$.