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Profunda LearningDeepLearning Multiple Linearibus Regressio Study Praecipua

2024-07-12

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Multidimensional features

Variabiles et Termini

Columna attributum x *jNumerus attributorum n x ⃗ vec{x}x************************** (ego)row vectorcertum valorem x ji vec{x}_j^ix************************** jegoSursum et deorsum
medium μstandardisationStandard declinatio σsigma(σ)

formula

w vec{w}w************** = [w1 w**2 w**3 …]
x ⃗ vec{x}x************************** = [x1 x**2 x**3 …]

fw ⃗ , b ( x ⃗ ) = w x + b = w 1 x 1 + w 2 x 2 + ... + wnxn + b f_{vec{w},b} (vec{x}) = vec{ w} * vec{x} + b = w_1x_1 + w_2x_2 + ... + w _nx_n + bf****w************** ,b(x************************** )=w************** x************************** +b=w**************1x**************************1+w**************2x**************************2++w**************nx**************************n+b

plures lineares procedere

import numpy
f = np.dot(w, x) + b
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Nota: est velocissimum, cum n magnum est (parallel processus)

normalis aequationis modus

  1. Plus quam 1000 inhabilis est
  2. Communicari non potest aliis algorithmis sicut regressio logistica, retiacula neurali vel aliis.
  3. nulla iteratio

wn = wn − α 1 m i = 1 mfw ⃗ , b ( x ⃗ ( i ) − y ( i ) ) xn ( i ) w_n = w_n - αdfrac{1}{m} sumlimits_{i=}^mf_ {vec{w},b}(vec{x}^{(i)}-y^{(i)})x_n^{(i)}w**************n=w**************nαm1ego=1mf****w************** ,b(x************************** (ego)y**(ego))x**************************n(ego)

b = b α 1 m i = 1 m ( fw , b ( x ⃗ ( i ) − y ( i ) ) b = b - α{dfrac{1}{m}} summae_{i=}^ m(f_{vec{w},b}(vec{x}^{(i)}-y^{(i)})b=bαm1ego=1m(f****w************** ,b(x************************** (ego)y**(ego))

Pondera variabilibus independentibus respondentia in ampliori ambitu minora esse tendunt, et pondera independens variabilium correspondentia in minore ambitu maiora tendunt.

Medium ordinationem

Divide per maximum valorem range ut pondus versus [0, 1] variabilis independens

Abscissa: x 1 = x 1 − μ 1 2000 − 300 x_1 = dfrac{x_1-μ_1}{2000-300}x**************************1=2000300x**************************1μ1 Y-axis: x 2 = x 2 − μ 2 5 − 0 x_2 = dfrac{x_2 - μ_2}{5-0}x**************************2=50x**************************2μ2

0.18 ≤ x 1 ≤ 0.82 -0.18le x_1le0.820.18x**************************10.82 0.46 ≤ x 2 ≤ 0.54 -0.46le x_2le0.540.46x**************************20.54

Z-score ordinationem

300 ≤ x 1 ≤ 2000 300le x_1le2000300x**************************12000 0 ≤ x 2 ≤ 5 0le x_2le50x**************************25

x 1 = x 1 − μ 1 σ 1 x1 = dfrac{x_1-μ_1}{σ_1}x**************************1=σ1x**************************1μ1 0.67 ≤ x 1 ≤ 3.1 -0.67le x_1le3.10.67x**************************13.1

Conare valores omnium lineamentorum in simili ambitu per scalas conservare, ut ictum earum mutationum in valores praedictorum prope sit (-3,3).

Si sumptus munus J magnum fit, significat gradum magnitudinis (learning rate) ineptum esse vel codicem esse perperam.

Insert imaginem descriptionis hic

Nota: numerus iterations variat ab machina ad machinam

Praeter curvas hauriendas ut iterationis punctum determinare, concursus latae sententiae etiam adhiberi potest
Sit ε aequalis 1 0 − 3 10^{-3} 103si decre- mentum J minor est quam hoc paucitas, confluendum putatur.

Oportet rate de doctrina constitue

  1. Cum temptas, potes perquam minimi momenti videre, si J decrescat.
  2. Discens rate in iteratione nimis magna vel nimis parva esse non debet.
  3. Singulis diebus *3 in probatione, eruditionem rate quam maximas elige, vel paulo minorem quam valor rationabilis

Feature engineering

Aedificare pluma engineering per mutationem vel compositionem ad plura optiones

fw ⃗ , b ( x ) = w 1 x 1 + w 2 x 2 + w 3 x 3 + b f_{vec{w},b}(vec{x}) = w_1x_1+w_2x_2+w_3x_3+bf****w************** ,b(x************************** )=w**************1x**************************1+w**************2x**************************2+w**************3x**************************3+b

Nota: regressio polynomialis adhiberi potest pro congruentibus linearibus et nonlinearibus