Multinomial Logistic Regression

$$$$C_pred == h_W * Y == diag * 1/(exp(Y * W) e_n_c) * exp(Y * W)

Multinomial Logistic Regression

$$$$Phi(C, Y * W) == - tr(C__star**top * log(C_pred))

== - tr(C__star**top * log((diag * 1/(exp(Y * W) * e_n_c) *

exp(Y * W))))

== - e_n_e**top(C odot(Y * W)) e_n_c + e_n_e**top * log((exp(Y

* W) e_n_c))

== - sum(sum(c_(i, j) (y_i**top * w_j) + sum(log((sum(exp(y_i**top

* w_j)))))))

Multinomial Logistic Regression

$$$$min_W * F * W == Phi(C, Y * W) + alpha * R(W)

Multinomial Logistic Regression

$$$$C_pred == h_W * Y == diag * 1/(exp(Y * W) e_n_c) * exp(Y * W)

Multinomial Logistic Regression

$$$$Phi(C, Y * W) == - tr(C__star**top * log(C_pred))

== - tr(C__star**top * log((diag * 1/(exp(Y * W) * e_n_c) *

exp(Y * W))))

== - e_n_e**top(C odot(Y * W)) e_n_c + e_n_e**top * log((exp(Y

* W) e_n_c))

== - sum(sum(c_(i, j) (y_i**top * w_j) + sum(log((sum(exp(y_i**top

* w_j)))))))

Multinomial Logistic Regression

$$$$min_W * F * W == Phi(C, Y * W) + alpha * R(W)

Multinomial Logistic Regression

$$$$C_pred == h_W * Y == diag * 1/(exp(Y * W) e_n_c) * exp(Y * W)

Multinomial Logistic Regression

$$$$Phi(C, Y * W) == - tr(C__star**top * log(C_pred))

== - tr(C__star**top * log((diag * 1/(exp(Y * W) * e_n_c) *

exp(Y * W))))

== - e_n_e**top(C odot(Y * W)) e_n_c + e_n_e**top * log((exp(Y

* W) e_n_c))

== - sum(sum(c_(i, j) (y_i**top * w_j) + sum(log((sum(exp(y_i**top

* w_j)))))))

Multinomial Logistic Regression

$$$$min_W * F * W == Phi(C, Y * W) + alpha * R(W)