https://github.com/raphsenn/logistic-regression-model-py

Simple logistic regression model using raw python and numpy.
https://github.com/raphsenn/logistic-regression-model-py

Last synced: 11 months ago
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Simple logistic regression model using raw python and numpy.

• Host: GitHub
• URL: https://github.com/raphsenn/logistic-regression-model-py
• Owner: raphsenn
• License: mit
• Created: 2024-06-11T09:33:45.000Z (about 2 years ago)
• Default Branch: main
• Last Pushed: 2024-09-27T07:30:49.000Z (over 1 year ago)
• Last Synced: 2025-01-21T13:09:53.258Z (over 1 year ago)
• Language: Python
• Size: 184 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# logistic-regression-model-py

Simple logistic regression model using raw python and numpy.

## Logistic Regression in a nutshell.

![image](./res/logisticregressio.jpg)

### Forward propagation

For one training example $x = (x_1, ..., x_n)$ of dimension n, the forward propgation is:

$z = dot(w, x) + b$

$a = sigmoid(z)$

$L = -(ylog(a) + (1-y)log(1-a))$

### Backpropagation

Training the model means updating the weights and biases, W and b, using the gradient of the

loss with respect to these parameters.

At each step, we need to calcualate: 

####  $\frac{dL}{dw} $, $ \frac{dL}{db}$

We can use the cain rule:

#### Chain rule

Let $u(x)$ and $v(x)$ be two function.

We want the derivative of the product of u and v:

$\frac{dvu}{dx} $ = $\frac{dv}{dx} u + \frac{du}{dx} $ v

in another notation:

$(v(x)*u(x))'$ = $v'(x) * u(x) + v(x) * u'(x)$