Non-linear curve fitting


Many supervised learning tasks follow a fairly standardized workflow.

Step-1) Define the problem and assemble a dataset

Step-2) Define a model which can 'capture' the trends in the data.

Step-3) Divide your data-set into "training" and "validation" sets (to monitor over-fitting)

Step-4) Prepare your data: This is typically done by normalizing the data, which makes it easier to fit.

Step-5) Choose a measure of success to gauge the "quality" of a given parameterization of the model

For curve fitting the "success" often means finding a model with a low error metric such as mean square error (MSE)

Step-6) "Train" a model (numerical optimization)

For parametric models, training" means doing a "multi-variable" optimization problem to find the model parameters that "best fit" the data

This is done by finding the "best fit" model parameters which minimize some error metric, such as mean square error.

If your model is complex enough to over-fit the data, then you will need to regularize the model to prevent over fitting

This last bullet isn't applicable for simple models, however, they become vary important for more complex models such as neural networks.

Step-7) Use your trained model to make predictions for "new" unseen data points

This work-flow is often true for both classification and regression problems.

The reason we are showing you this is that the workflow maps perfectly onto training many more complicated models, such as neural networks.

If you understand the workflow below, then you are well on your way to learning how to "train" neural networks, ... more on this in other DSAN classes

In this lab we go through this workflow for a simple low dimensional non-linear curve fitting example.


You need to upload ONE document to Canvas when you are done

(1) A PDF (or HTML) of the completed form of this notebook

The final uploaded version should NOT have any code-errors present

All outputs must be visible in the uploaded version, including code-cell outputs, images, graphs, etc

Beceriler: Python, Veri İşleme, Data Analysis

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