✍️
mathematics_basic_for_ML
  • README
  • README
    • Summary
    • Geometry
      • EulerAngle
      • Gimbal lock
      • Quaternion
      • RiemannianManifolds
      • RotationMatrix
      • SphericalHarmonics
    • Information
      • Divergence
      • 信息熵 entropy
    • LinearAlgebra
      • 2D仿射变换(2D Affine Transformation)
      • 2DTransformation
      • 3D变换(3D Transformation)
      • ComplexTransformation
      • Conjugate
      • Hessian
      • IllConditioning
      • 逆变换(Inverse transform)
      • SVD
      • det
      • eigendecomposition
      • 矩阵
      • norm
      • orthogonal
      • special_matrix
      • trace
      • vector
    • Mathematics
      • Complex
      • ExponentialDecay
      • average
      • calculus
      • convex
      • derivative
      • 距离
      • function
      • space
      • Formula
        • euler
        • jensen
        • taylor
        • trigonometric
    • Numbers
      • 几何级数
      • SpecialNumbers
    • NumericalComputation
      • ConstrainedOptimization
      • GradientDescent
      • Newton
      • Nominal
      • ODE_SDE
      • Preprocessing
    • Probability
      • bayes
      • distribution
      • expectation_variance
      • 贝叶斯公式
      • functions
      • likelihood
      • mixture_distribution
      • 一些术语
      • probability_distribution
Powered by GitBook
On this page

Was this helpful?

  1. README
  2. Mathematics

average

PreviousExponentialDecayNextcalculus

Last updated 2 years ago

Was this helpful?

算术平均:

average=14(a+b+c+d)average = \frac{1}{4}(a+b+c+d)average=41​(a+b+c+d)

:

average=(4abcd)average = \sqrt[4](abcd)average=4(​abcd)

调和平均:更重视较小值

average=2aba+b1average=12(1a+1b)\begin{aligned} average = \frac{2ab}{a+b} \\ \frac{1}{average} = \frac{1}{2}(\frac{1}{a} + \frac{1}{b}) \end{aligned}average=a+b2ab​average1​=21​(a1​+b1​)​

加权调和平均:

averageβ=(1+β2)×a×b(β2×a)+b1averageβ=11+β2(1a+β2b)\begin{aligned} average_\beta = \frac{(1+\beta^2)\times a \times b}{(\beta^2 \times a) + b} \\ \frac{1}{average_\beta} = \frac{1}{1+\beta^2}(\frac{1}{a} + \frac{\beta^2}{b}) \end{aligned}averageβ​=(β2×a)+b(1+β2)×a×b​averageβ​1​=1+β21​(a1​+bβ2​)​

$\beta < 1$:更注重a $\beta = 1$:相当于调和平均 $\beta > 1$:更注重b

几何平均