๐จ๐ป๐ฑ๐ฒ๐ฟ๐๐๐ฎ๐ป๐ฑ๐ถ๐ป๐ด ๐๐ผ๐ด๐ถ๐๐๐ถ๐ฐ ๐ฅ๐ฒ๐ด๐ฟ๐ฒ๐๐๐ถ๐ผ๐ป ๐ง๐ต๐ฟ๐ผ๐๐ด๐ต ๐๐ป๐ถ๐บ๐ฎ๐๐ถ๐ผ๐ป
Visualizing complex concepts makes them easier to grasp, and logistic regression is no exception! This animation provides an intuitive way to understand how logistic regression learns through gradient descent.
๐น ๐๐ฒ๐ ๐ง๐ฎ๐ธ๐ฒ๐ฎ๐๐ฎ๐๐ ๐ณ๐ฟ๐ผ๐บ ๐๐ต๐ฒ ๐๐ป๐ถ๐บ๐ฎ๐๐ถ๐ผ๐ป:
๐ญ. ๐๐ฒ๐ฎ๐๐๐ฟ๐ฒ ๐ฆ๐ฝ๐ฎ๐ฐ๐ฒ & ๐๐ฒ๐ฐ๐ถ๐๐ถ๐ผ๐ป ๐๐ผ๐๐ป๐ฑ๐ฎ๐ฟ๐ (๐๐ฟ๐ฎ๐ฝ๐ต ๐ญ)
โ๏ธ The value of ๐ญ is determined by the ๐ฝ๐ฒ๐ฟ๐ฝ๐ฒ๐ป๐ฑ๐ถ๐ฐ๐๐น๐ฎ๐ฟ ๐ฑ๐ถ๐๐๐ฎ๐ป๐ฐ๐ฒ between a data point and the decision boundary.
โ๏ธ With each ๐ด๐ฟ๐ฎ๐ฑ๐ถ๐ฒ๐ป๐ ๐ฑ๐ฒ๐๐ฐ๐ฒ๐ป๐ ๐๐๐ฒ๐ฝ, the decision boundary shifts, and Z progressively increases.
๐ฎ. ๐ฃ๐ฟ๐ผ๐ฏ๐ฎ๐ฏ๐ถ๐น๐ถ๐๐ & ๐ฆ๐ถ๐ด๐บ๐ผ๐ถ๐ฑ ๐๐๐ป๐ฐ๐๐ถ๐ผ๐ป (๐๐ฟ๐ฎ๐ฝ๐ต ๐ฎ)
โ๏ธ Z is used to compute the ๐ฝ๐ฟ๐ฒ๐ฑ๐ถ๐ฐ๐๐ฒ๐ฑ ๐ฝ๐ฟ๐ผ๐ฏ๐ฎ๐ฏ๐ถ๐น๐ถ๐๐ via the ๐๐ถ๐ด๐บ๐ผ๐ถ๐ฑ ๐ณ๐๐ป๐ฐ๐๐ถ๐ผ๐ป.
โ๏ธ As Z increases, the model becomes more confident in its classifications, increasing the likelihood of correct predictions.
๐ฏ. ๐๐ฟ๐ฎ๐ฑ๐ถ๐ฒ๐ป๐ ๐๐ฒ๐๐ฐ๐ฒ๐ป๐ & ๐ช๐ฒ๐ถ๐ด๐ต๐ ๐จ๐ฝ๐ฑ๐ฎ๐๐ฒ๐ (๐๐ฟ๐ฎ๐ฝ๐ต ๐ฏ)
โ๏ธ Gradient descent ๐๐ฝ๐ฑ๐ฎ๐๐ฒ๐ ๐๐ต๐ฒ ๐๐ฒ๐ถ๐ด๐ต๐๐ iteratively to minimize the loss function.
โ๏ธ This process ๐๐ต๐ถ๐ณ๐๐ ๐๐ต๐ฒ ๐ฑ๐ฒ๐ฐ๐ถ๐๐ถ๐ผ๐ป ๐ฏ๐ผ๐๐ป๐ฑ๐ฎ๐ฟ๐ in the feature space, refining classification over time.
By animating these fundamental steps, we can clearly observe ๐ต๐ผ๐ ๐น๐ผ๐ด๐ถ๐๐๐ถ๐ฐ ๐ฟ๐ฒ๐ด๐ฟ๐ฒ๐๐๐ถ๐ผ๐ป ๐ผ๐ฝ๐๐ถ๐บ๐ถ๐๐ฒ๐ ๐ถ๐๐ ๐ฑ๐ฒ๐ฐ๐ถ๐๐ถ๐ผ๐ป ๐ฏ๐ผ๐๐ป๐ฑ๐ฎ๐ฟ๐.
For more AI and machine learning insights, check out ๐ฉ๐ถ๐๐๐ฟ๐ฎโ๐ ๐๐ ๐ก๐ฒ๐๐๐น๐ฒ๐๐๐ฒ๐ฟ: https://www.vizuaranewsletter.com?r=502twn.
For a detailed understanding, check out these videos:
1๏ธโฃ ๐๐ผ๐ด๐ถ๐๐๐ถ๐ฐ ๐ฅ๐ฒ๐ด๐ฟ๐ฒ๐๐๐ถ๐ผ๐ป ๐ฆ๐ถ๐บ๐ฝ๐น๐ถ๐ณ๐ถ๐ฒ๐ฑ: Your First Step into Classification | Intuitive Approach:
2๏ธโฃ ๐๐ผ๐๐ ๐๐๐ป๐ฐ๐๐ถ๐ผ๐ป ๐ณ๐ผ๐ฟ ๐๐ผ๐ด๐ถ๐๐๐ถ๐ฐ ๐ฅ๐ฒ๐ด๐ฟ๐ฒ๐๐๐ถ๐ผ๐ป | Negative Log Likelihood | Log(Odds) | Sigmoid: