Arg max

In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function

In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function

Softmax function

considering the arg max as a function with categorical output 1 , … , n {\displaystyle 1,\dots ,n} (corresponding to the index), consider the arg max function

considering the arg max as a function with categorical output 1 , … , n {\displaystyle 1,\dots ,n} (corresponding to the index), consider the arg max function

Orthogonal Procrustes problem

B ‖ F 2 − 2 ⟨ Ω A , B ⟩ = arg max Ω ⟨ Ω , B A T ⟩ = arg max Ω ⟨ Ω , U Σ V T ⟩ = arg max Ω ⟨ U T Ω V , Σ ⟩ = arg max Ω ⟨ S , Σ ⟩ where S = U T

B ‖ F 2 − 2 ⟨ Ω A , B ⟩ = arg max Ω ⟨ Ω , B A T ⟩ = arg max Ω ⟨ Ω , U Σ V T ⟩ = arg max Ω ⟨ U T Ω V , Σ ⟩ = arg max Ω ⟨ S , Σ ⟩ where S = U T

Viterbi algorithm

B_{iy_{j}})}} T 2 [ i , j ] ← arg max k ( T 1 [ k , j − 1 ] ⋅ A k i ⋅ B i y j ) {\displaystyle T_{2}[i,j]\gets \arg \max _{k}{(T_{1}[k,j-1]\cdot A_{ki}\cdot

B_{iy_{j}})}} T 2 [ i , j ] ← arg max k ( T 1 [ k , j − 1 ] ⋅ A k i ⋅ B i y j ) {\displaystyle T_{2}[i,j]\gets \arg \max _{k}{(T_{1}[k,j-1]\cdot A_{ki}\cdot

Maximum likelihood estimation

{\displaystyle {\hat {\theta }}={\underset {\theta \in \Theta }{\operatorname {arg\;max} }}\ {\widehat {L}}_{n}(\theta \,;\mathbf {y} )} Intuitively, this selects

{\displaystyle {\hat {\theta }}={\underset {\theta \in \Theta }{\operatorname {arg\;max} }}\ {\widehat {L}}_{n}(\theta \,;\mathbf {y} )} Intuitively, this selects

Restricted Boltzmann machine

treated as a visible vector v {\displaystyle v} ), arg max W ∏ v ∈ V P ( v ) {\displaystyle \arg \max _{W}\prod _{v\in V}P(v)} or equivalently, to maximize

treated as a visible vector v {\displaystyle v} ), arg max W ∏ v ∈ V P ( v ) {\displaystyle \arg \max _{W}\prod _{v\in V}P(v)} or equivalently, to maximize

Maximum a posteriori estimation

}(x)={\underset {\theta }{\operatorname {arg\,max} }}\ f(\theta \mid x)={\underset {\theta }{\operatorname {arg\,max} }}\ {\frac {f(x\mid \theta )\,g(\theta

}(x)={\underset {\theta }{\operatorname {arg\,max} }}\ f(\theta \mid x)={\underset {\theta }{\operatorname {arg\,max} }}\ {\frac {f(x\mid \theta )\,g(\theta

Multiclass classification

confidence score: y ^ = arg max k ∈ { 1 … K } f k ( x ) {\displaystyle {\hat {y}}={\underset {k\in \{1\ldots K\}}{\arg \!\max }}\;f_{k}(x)} Although this

confidence score: y ^ = arg max k ∈ { 1 … K } f k ( x ) {\displaystyle {\hat {y}}={\underset {k\in \{1\ldots K\}}{\arg \!\max }}\;f_{k}(x)} Although this

Principal component analysis

=1}{\operatorname {\arg \,max} }}\,\left\{\sum _{i}\left(t_{1}\right)_{(i)}^{2}\right\}={\underset {\Vert \mathbf {w} \Vert =1}{\operatorname {\arg \,max} }}\,\left\{\sum

=1}{\operatorname {\arg \,max} }}\,\left\{\sum _{i}\left(t_{1}\right)_{(i)}^{2}\right\}={\underset {\Vert \mathbf {w} \Vert =1}{\operatorname {\arg \,max} }}\,\left\{\sum

Alternate reality game

An alternate reality game (ARG) is an interactive networked narrative that uses the real world as a platform and employs transmedia storytelling to deliver

An alternate reality game (ARG) is an interactive networked narrative that uses the real world as a platform and employs transmedia storytelling to deliver