Скачать или смотреть Understanding the Sensitivity of curve_fit to Initial Guess Parameters in Python

Learn why your `curve_fit` results may vary significantly and how to adjust initial guess parameters effectively when using Python's Scipy during curve fitting.
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Why is My Fitting with curve_fit So Sensitive to Initial Guess Parameters?

When working with curve fitting in Python using Scipy's curve_fit, it's not uncommon to encounter situations where your fit results vary markedly depending on your initial guess parameters. This sensitivity can lead to frustration, especially when you expect consistent results based on your data.

In this post, we'll dissect why this occurs and provide solutions to help you overcome the challenges associated with fitting curves, particularly when using periodic functions like cosine in your models.

Understanding the Problem

The core of the issue lies in how optimization algorithms operate. When using the curve_fit function, it starts from an initial guess and attempts to find the best fitting parameters by minimizing the differences between the observed data and the model predictions.

If the initial guess is too far from the optimal solution, the fitting process may converge to a local minimum instead of finding the global best fit. This is especially true for non-linear models, such as those using periodic functions, which can have multiple local minima leading to different fitting outcomes.

Common Symptoms of Sensitivity:

Fitting results vary significantly with minor changes to the initial guess.

The fit may not converge altogether, leading to errors or unpredictable outputs.

Adjustments in your model lead to qualitatively different fits without evident changes in the underlying data.

Strategies for Improving Fitting Reliability

1. Normalize Your Data

Before diving into fitting, it's often beneficial to normalize your data. This helps stabilize the fitting process by reducing the range of your variables.

Normalization can be executed by subtracting the mean and dividing by the standard deviation, ensuring that your data is centered around zero. Normalizing helps the optimization algorithm efficiently navigate the parameter space.

2. Tighter Boundaries

One key to reducing the sensitivity of curve_fit to initial guess parameters is to set appropriate boundaries. A large range for bounds can lead to erratic fitting behavior since the algorithm might explore regions far from the most plausible solutions.

How to Adjust the Bounds:

Instead of using overly broad limits, define bounds that are close to your initial guesses. For instance, you can expand the boundaries based on slightly adjusted initial guesses:

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3. Increase the Function Evaluations

Sometimes, simply providing the fitting algorithm with more opportunities to explore the parameter space can yield better results. You can do this by increasing the maxfev parameter, which dictates the maximum number of function evaluations:

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This adjustment allows the fitting algorithm to locate the global minimum more reliably, especially when the initial guess is not very close to the optimal parameters.

Summary

Curve fitting, especially with complex models, can be sensitive to initial conditions. By normalizing your data, setting tighter bounds based on refined initial guesses, and increasing the number of evaluations, you can facilitate a more stable fitting process.

By applying these strategies, you can significantly enhance the reliability of your fitting results using Scipy's curve_fit. Happy coding and may your curve fitting endeavors be less frustrating and more fruitful!