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6 months ago in Multimodal AI Systems By Pradeep Kumar

How can you prove the Mean Squared Error (MSE) surface is multimodal for a nonlinear system parameter estimation?

Why does the error surface in nonlinear parameter estimation often have many hills and valleys (i.e., is multimodal)?

MeanSquaredError(MSE)

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By Jasmin Answered 8 months ago

To demonstrate that the Mean Squared Error (MSE) surface is multimodal for a nonlinear-in-parameters model, which is inherently non-convex, you can employ both analytical and empirical methods. Analytically, prove the existence of multiple stationary points where the gradient vanishes, including distinct local minima. Empirically, run the estimation algorithm (like gradient descent) from numerous random starting points; convergence to different parameter sets with comparable low MSE values strongly indicates multiple local minima, a result often corroborated by visualizing the cost surface for low-dimensional parameter subsets.

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