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There are different types of cost functions like Cross-entropy, absolute error, mean squared error.

When can we expect the cost function to be non-convex? Does this depend upon the type of cost function we choose? Or does this depend upon the Model we choose like when we have higher order polynomial Model?

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    $\begingroup$ I think it is not convex in truest sense but we try to make it so and also make sure not to get trapped in a local minima $\endgroup$ – DuttaA Jun 26 '18 at 12:21
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    $\begingroup$ It all depends on your final function which is going to be optimised. $\endgroup$ – Media Aug 25 '18 at 17:29
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The cost function is convex if its Second Order Derivative is positive semidefinite (i.e. $\geq0$ ).

But this definition depends on the function with respect to which you take the derivative. This convexity changes when we are talking about Neural Networks, as in that case, our derivatives are taken with respect to the weights.

Refer: Why Cross Entropy is convex, but not necessarily in neural nets and Why RMSE is convex but not necessarily in neural nets

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