Appliing Gradient Descent: Obliczenia etapowe for Machina Learning Przewodniczący Optimization

Gradient schodzi is an optimization algorithm used to minimize a function by y iteratively moving towards thee lowesto point. It i s widely used in machine learning to optimize models by addisting parameters to reduce error. This article explains the step-by- step calculations involved in appliing gradient extret for machine learning tasks.

Uzgodnienie to Gradient Descent Algorithm

Te cory idea of gradient descent is to update model parameters in thee direction of thee negative gradient of thee loss function. This process continues until the parameters converge te to a minimum point, ideally the global minimum.

Etap-by- Stopień procesu kalkulacyjnego

Suppose we have a simple linear regression model with a loss function, such as Mean Squared Error (MSE). The steps for applicying gradient descent are as follows:

• Initializaze parameters (np., weights andd bias) with small random values.
• Oblicz, że to przewidywał wyrzutnie using current parameters.
• Porównaj te losy funkcjonalne wartości bazowe przewidywania i aktualności data.
• Oblicz te gradient of thee loss function with respect to each parametr.
• Update each parameter by subtracting thee product of thee learning rate and thee corresponding gradient.

This process repeats for a set number of iteractions or until the change in loss becomes negligible.

Badanie Calculation

Consider a single data point input indi1; Xi1; FLT: 0 suppor3; Xi3; x = 2 suppor1; FLT: 1 supporte3; FLT: 1 supporte3; VI1; FLT: 2 supported 3; FLT: 3; YI3; YI1; FLT: 3 supported; YI3;. Initializaze weight 1; FLT: 4 supportee; FLT: 3; YIF: 5 supported; FLT: 3; YIF: 3d bias bepined 1; YAF: 6 supéref; YL: 1b = 0 supél; FLT: 1; FLT: 3D; FLT: 3D; FLT: 3D; FLT: 3D; FLT: 3D; FL; FL; FL: 3D; FL; FLT: 3D; FL; FL

Kalkulator prognozowany: 05x1x1FLT: 0 X3; X3; y Xix + b = 0,5 * 2 + 0 = 1 Xi1; FLT: 1 Xi3; Xi3x + b = 0,5 * 2 + 0 = 1 Xi1; FLT: 1 Xi3; Xi3; Xi3;

Komplute error: Xi1; Xi1; FLT: 0 Xi3; Xi3; error = y Xi- y = 1 - 4 = -3 Xi1; Xi1; FLT: 1 Xi3; Xi3; Xi3;

Gradienty kalkulatu:

Gradient w.r.t. waga: 1; 1; FLT: 0; 3; FLT: 2 * error * x = 2 * (-3) * 2 = -12; 1; FLT: 1; 3;

Gradient w.r.t. bia: Xi1; Xi1; FLT: 0 Xi3; Xi3; XiL / Xib = 2 * error = 2 * (-3) = -6 Xi1; Xi1; FLT: 1 Xi3; Xi3;

Update parameters:

Waga new: Xi1; Xi1; FLT: 0 Xi3; Xi3; w = 0,5 - 0,1 * (-12) = 0,5 + 1,2 = 1,7 Xi1; Xi1; FLT: 1 Xi3; Xi3;

New bias: Xi1; Xi1; FLT: 0 Xi3; Xi3; b = 0 - 0.1 * (-6) = 0 + 0.6 = 0,6 Xi1; Xi1; FLT: 1 Xi3; Xi3; Xi3;