Gradient dupented i an an optimization algorithm used d to minimize a function by iteratively moving towards the lowest point. It it i widely used in machine learningg to optimize models by configinig parameters to reduce error. This article exactainsepains the step- by- step calculations ind in appixyung gradient defent for machine splaskine sk.

Understanding the Gradient Descent Algorithm

The core idea of gradient dupent i s to update model parameters in te direction of te negative gradient of the loss function. Tiss process continues until the parameters converges to a minimum point, ideally the global minimum.

Step- by- Step- Calkulation processzek

Suppose we have a simplie linear regression model with a loss function, such as Mean Squared Error (MSE).

  • Initialize parameters (pl., súlyok and bias) with small random values.
  • Számítsa ki, hogy ez a előrejelzés túlmutat a paramétereken.
  • Számítsa ki, hogy milyen lehet a function értéke, és hogyan lehet előre jelezni a customát.
  • Számítsa ki, hogy milyen módon működik a dolog.
  • Update each parameter by subtracting the product of the learning rate and the competindig gradient.

A tiss proces ismétli a set numbers of iterations or until the change in los becomes negligible.

Example Calculation

A "Donyecki Népköztársaság" "miniszterelnöke".

Számítástechnikai prediktion: 1; 1; FLT: 0) 3; 3) y) = wx + b = 0, 5 * 2 + 0 = 1) 1; 1; FLT: 1) 3; 3;

Számítógép error: d.m.; 1; FLT: 0 d.m.m.m.m.;

Számológép gradients:

Gradient w.r.t. heavy: d.1; 1; FLT: 0 d.3; d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.@@

Gradient w.r.t. bias: d.1; 1; FLT: 0 d.3; d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d@@

Update parameters:

New heavy: d.1; 1; FLT: 0 d.3; d.3; w = 0.5 - 0.1 * (-12) = 0.5 + 1.2 = 1.7 d.1; 1d; FLT: 1 d.3; d.3d;

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