Machine Learning + Pattern Recognition - Introduction - Polynomial Curve Fitting

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.
For linear-algebraic analysis of data, "fitting" usually means trying to find the curve that minimizes the vertical (y-axis) displacement of a point from the curve (e.g., ordinary least squares). However, for graphical and image applications, geometric fitting seeks to provide the best visual fit; which usually means trying to minimize the orthogonal distance to the curve (e.g., total least squares), or to otherwise include both axes of displacement of a point from the curve. Geometric fits are not popular because they usually require non-linear and/or iterative calculations, although they have the advantage of a more aesthetic and geometrically accurate result.

[@abhaypandey3921]

I have seen so many videos but your video is the perfect one among them.

[@JanNalivaika]

Thank you very much ❤️

[@supersnowva6717]

Hi Jan, are these tutorial series based on the book Pattern Recognition and Machine Learning by Chris Bishop? if so, you are saving my life! Please keep uploading the videos! This is super helpful! Thanks so much!

[@homeofdlsplayers2029]

Great video bro, am a financial markets trader and was looking for mathematical way to predict the next move, i think we can link up, we would make a good team

[@homeofdlsplayers2029]

Where can I reach u at bro?

[@akak8299]

i am not really a fan of videos like this without demonstrating from examples.

[@JanNalivaika]

Fair point! I’m working on a series right now with actual code examples!