Utilisateur:Reyman/BacSable

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$g(x_k,w) \,$

$g(x)=4+2x+4x^2\,$

$g(x)=2 sigmoide( \sum_{j=1}^{n} w_{i,j} * x_j )+ 3 sigmoide( \sum_{j+1=1}^{n} w_{i+1,j} * x_{j+1} ) \,$

$w_0 \,$ $w_1 \,$ $w_2 \,$ $w_3 \,$

$\left ( \frac {\partial J^k} {\partial w_{ij}} \right )_k = \left ( \frac {\partial J^k} {\partial v_i} \right )_k \left ( \frac {\partial v_i} {\partial w_{ij}} \right )_k = \delta^k_i x^k_j\,$

$\left ( \frac {\partial J^k} {\partial w_{ij}} \right )_k \,$

$\left ( \frac {\partial J^k} {\partial v_i} \right )_k \,$

$\left ( \frac {\partial v_i} {\partial w_{ij}} \right )_k \,$

$x^k_j \,$

$\delta^k_i = \left ( \frac {\partial J^k} {\partial v_i} \right )_k = \left ( \frac {\partial}{\partial v_i} \left[ (y^k_p - g(x,w))^2 \right ]_k \right ) = -2 g(x^k,w) \left ( \frac {\partial g(x,w)}{\partial vi} \right )_k$

$\delta^k_i = -2g(x^k,w)f'(v^k_i) \,$

$\delta^k_i = -2g(x^k,w) \,$

$f'(v^k_i) \,$

$\delta^k_i \equiv \left ( \frac {\partial J^k} {\partial v_i} \right )_k = \sum_{m}{} \left ( \frac {\partial J^k} {\partial v_m} \right )_k \left ( \frac {\partial v_m} {\partial v_i} \right )_k = \sum_{m}{} \delta^k_m \left ( \frac {\partial v_m} {\partial v_i} \right )_k$

$v^k_m = \sum_{i}{}w_{mi}x^k_i = \sum_{i}{}w_mif(v^k_i)\,$ d'ou

$\left ( \frac { \partial v_m}{\partial v_i} \right )_k = w_{mi}f'(v^k_i) \,$

$\delta^k_i = \sum_{m}{} \delta^k_m w_{mi} f'(v^k_i) = f'(v^k_i) \sum_{m}{} \delta^k_m w_{mi} \,$

$y(x_i,w_i) = logis ( w_0 + v ) \,$

$y(x_i,w_i) = logis \left (w_0 + \sum_{i=1}^{n-1} w_i x_i \right)$

$P(A|B) = \frac{P(B | A) P(A)}{P(B)}$

$J(w) = \sum_{k=1}^{N} \left( y_p^k-g(x^k,w))^2 \right) = \sum_{k=1}^{N} J^k(w)$

$\alpha \beta \gamma \delta \epsilon \varepsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \varpi \rho \sigma \varsigma \tau \upsilon \phi \varphi \chi \psi \omega \,$