AUTHOREA
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\begin{align} p(y_{i}=1\mid\mathbf{x_{i},w}) & =\sigma(\mathbf{w^{T}x_{i}}) \\ p(y_{i}=0\mid\mathbf{x_{i},w}) & =1-\sigma(\mathbf{w^{T}x_{i}}) \\ & =1-\frac{1}{1+\exp(-\mathbf{w^{T}x_{i}}}) \\ & =\frac{1}{1+\exp(\mathbf{w^{T}x_{i}})} \\ & =\sigma(\mathbf{-w^{T}x_{i}})\\ \end{align}