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This article mainly introduces the example analysis of the basic principles of Python deep learning neural network, which has a certain reference value, and interested friends can refer to it. I hope you will gain a lot after reading this article.

Neural network

Gradient descent method

Before we take a closer look at the gradient descent algorithm, let's take a look at some related concepts.

1. Step size (Learning rate): the step size determines the length of each step along the negative direction of the gradient during the iterative process of gradient descent. Using the example of going downhill above, the step length is the length of the step along the steepest and easiest position to go downhill at the current step.

two。 Feature: refers to the input part of a sample, such as two single-feature samples (x (0), y (0), (x (1), y (1)) (x (0), y (0)), (x (1), y (1)), then the first sample feature is x (0) x (0), and the first sample output is y (0) y (0).

3. Hypothetical function (hypothesis function): in supervised learning, the hypothetical function used to fit the input sample is written as h θ (x) h θ (x). For example, for m samples of a single feature (x (I), y (I)) (iatro1 1xh 2) (m) (x (I), y (I)) (iLim), the fitting function can be used as follows: h θ (x) = θ 0 + θ θ (x) = θ 0 + θ 1x.

4. Loss function (loss function): in order to evaluate the quality of model fitting, loss function is usually used to measure the degree of fitting. The minimization of the loss function means that the fitting degree is the best, and the corresponding model parameters are the optimal parameters. In linear regression, the loss function is usually the square of the difference between the sample output and the hypothesis function. For example, for m samples (xi,yi) (iMagel 2m) (xi,yi), linear regression is used, and the loss function is:

J (θ 0, θ 1) = ∑ ionization 1m (h θ (xi) − yi) 2J (θ 0, θ 1) = ∑ ionization 1m (h θ (xi) − yi) 2

Where xixi represents the I th sample feature, yiyi represents the corresponding output of the I th sample, and h θ (xi) h θ (xi) is a hypothetical function.

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