Unverified50% confidenceFactExact time
Under the assumption of a Gaussian output distribution, minimizing negative log-likelihood (NLL) and minimizing mean squared error (MSE) are mathematically completely equivalent.
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9/11/2026
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UnverifiedThe mean squared error (MSE) cost function is defined as C(w,b) = 1/(2n) Σ ‖yᵢ − ŷᵢ‖², where each squared error term is always non-negative.76% similarUnverifiedAssuming the data follows a Gaussian distribution, maximizing the likelihood is equivalent to minimizing the mean squared error.72% similarUnverifiedThe load balancing loss uses the sum of squares of all expert selection frequencies L=ΣFi², and by the Cauchy–Schwarz inequality the loss is minimized when all Fi=1/N.68% similarUnverifiedWhen evaluating stock price predictions, directional accuracy and backtested returns are more meaningful than MSE or RMSE; a model with a very low RMSE but only 50% directional accuracy is ineffective or even loss-making in live trading.68% similarUnverifiedWhen the prediction error is assumed to follow a Gaussian distribution with zero mean and fixed variance, taking the negative logarithm of the likelihood function and expanding it yields a leading term that is exactly in the form of mean squared error.66% similar
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