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Arg max information


As an example, both unnormalised and normalised sinc functions above have of {0} because both attain their global maximum value of 1 at x = 0.

The unnormalised sinc function (red) has arg min of {−4.49, 4.49}, approximately, because it has 2 global minimum values of approximately −0.217 at x = ±4.49. However, the normalised sinc function (blue) has arg min of {−1.43, 1.43}, approximately, because their global minima occur at x = ±1.43, even though the minimum value is the same.[1]

In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points at which a function output value is maximized and minimized, respectively.[note 1] While the arguments are defined over the domain of a function, the output is part of its codomain.

  1. ^ "The Unnormalized Sinc Function Archived 2017-02-15 at the Wayback Machine", University of Sydney


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Arg max

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the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points at which...

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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...

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Generative adversarial network

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arg ⁡ min μ G max μ D L ( μ G , μ D ) , μ ^ D ∈ argmax μ D L ( μ ^ G , μ D ) , {\displaystyle {\hat {\mu }}_{G}\in \arg \min _{\mu _{G}}\max _{\mu...

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Principal component analysis

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1 ) = argmax ‖ w ‖ = 1 { ∑ i ( t 1 ) ( i ) 2 } = argmax ‖ w ‖ = 1 { ∑ i ( x ( i ) ⋅ w ) 2 } {\displaystyle \mathbf {w} _{(1)}=\arg \max _{\Vert...

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Gumbel distribution

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then by routine integration, P r ( j = argmax i ( g i + log ⁡ π i ) ) = π j ∑ i π i {\displaystyle Pr(j=\arg \max _{i}(g_{i}+\log \pi _{i}))={\frac {\pi...

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Likelihood function

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\theta } is the actual parameter. In maximum likelihood estimation, the arg max (over the parameter θ {\displaystyle \theta } ) of the likelihood function...

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Prompt engineering

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use gradient descent to search for argmax Z ~ ∑ i log ⁡ P r [ Y i | Z ~ ∗ E ( X i ) ] {\displaystyle \arg \max _{\tilde {Z}}\sum _{i}\log Pr[Y^{i}|{\tilde...

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Orthogonal Procrustes problem

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B ⟩ F = argmax Ω ⟨ Ω A , B ⟩ F = argmax Ω ⟨ Ω , B A T ⟩ F = argmax Ω ⟨ Ω , U Σ V T ⟩ F = argmax Ω ⟨ U T Ω V , Σ ⟩ F = argmax Ω ⟨ S , Σ...

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Hierarchical clustering

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largest diameter: C ∗ = argmax C ∈ C max i 1 , i 2 ∈ C δ ( i 1 , i 2 ) {\displaystyle C_{*}=\arg \max _{C\in {\mathcal {C}}}\max _{i_{1},i_{2}\in C}\delta...

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Supervised learning

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that gives the highest score: g ( x ) = argmax y f ( x , y ) {\displaystyle g(x)={\underset {y}{\arg \max }}\;f(x,y)} . Let F {\displaystyle F} denote...

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Maximum likelihood estimation

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

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Guarded Command Language

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is omitted and error is False, the result is abort. if a ≥ b → max := a □ b ≥ a → max := b fi If a = b, either a or b is chosen as the new value for the...

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Evidence lower bound

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{\displaystyle p} and moving towards the maximum likelihood argmax z ln ⁡ p θ ( x | z ) {\displaystyle \arg \max _{z}\ln p_{\theta }(x|z)} . H ( q ϕ ( ⋅ | x ) )...

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Maximum a posteriori estimation

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

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Monotone comparative statics

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correspondence argmax x ∈ X f ( x ; s ) {\displaystyle \arg \max _{x\in X}f(x;s)} is said to be increasing if argmax x ∈ X f ( x ; s ′ ) ≥ S S O argmax x...

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Diffusion model

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estimate argmax x p ( x | y ) {\displaystyle \arg \max _{x}p(x|y)} . If we want to force the model to move towards the maximum likelihood estimate arg ⁡ max...

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Neural machine translation

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( i ) ) {\displaystyle \theta ^{*}={\underset {\theta }{\operatorname {arg\,max} }}\sum _{i}^{T}P_{\theta }(\mathbf {y} ^{(i)}|\mathbf {x} ^{(i)})} Expanding...

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Statistical machine translation

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~ = a r g max e ∈ e ∗ p ( e | f ) = a r g max e ∈ e ∗ p ( f | e ) p ( e ) {\displaystyle {\tilde {e}}=arg\max _{e\in e^{*}}p(e|f)=arg\max _{e\in e^{*}}p(f|e)p(e)}...

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Generalized logistic distribution

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maximum-likelihood parameter estimate is: α ^ , β ^ = argmax α , β 1 n ∑ i = 1 n log ⁡ f ( x i ; α , β ) = argmax α , β α ( 1 n ∑ i log ⁡ σ ( x i ) ) + β (...

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Mathematical optimization

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and {−5, (2k + 1)π}, where k ranges over all integers. Operators arg min and arg max are sometimes also written as argmin and argmax, and stand for argument...

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Common spatial pattern

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maximized between the two windows: w = argmax w ‖ w X 1 ‖ 2 ‖ w X 2 ‖ 2 {\displaystyle \mathbf {w} ={\arg \max }_{\mathbf {w} }{\frac {\left\|\mathbf...

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Forward algorithm

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argmax x t p ( x t | y 1 : t ) = argmax x t α ( x t ) , {\displaystyle {\widehat {x}}_{t}^{MAP}=\arg \max _{x_{t}}\;p(x_{t}|y_{1:t})=\arg \max _{x_{t}}\;\alpha...

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Sigmoid function

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function in data analysis Softmax function – Smooth approximation of one-hot arg max Swish function – Mathematical activation function in data analysis Weibull...

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Flux

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\mathbf {I} (A,\mathbf {p} )={\underset {\mathbf {\hat {n}} }{\operatorname {arg\,max} }}\mathbf {\hat {n}} _{\mathbf {p} }{\frac {\mathrm {d} q}{\mathrm {d}...

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Belief propagation

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setting), and it can be defined using the arg max: * ⁡ argmax x g ( x ) . {\displaystyle \operatorname {*} {\arg \max }_{\mathbf {x} }g(\mathbf {x} ).} An...

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Discriminative model

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decision function is defined as: f ( x ; w ) = argmax y w T ϕ ( x , y ) {\displaystyle f(x;w)=\arg \max _{y}w^{T}\phi (x,y)} According to Memisevic's...

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