mean squared error

The average of the squared differences between predicted and true values. It is the standard loss for regressionregression, n.: Predicting a number rather than a category — a house's price, tomorrow's temperature, a patient's blood pressure — by learning from past examples where the answer is known. and the quantity minimized by ordinary least squaresordinary least squares, n.: The standard way to fit a line through data: choose the line that makes the total of the squared vertical distances from the points to the line as small as possible.; minimizing it yields predictions of the conditional mean, and it corresponds to maximum likelihoodmaximum likelihood estimation, n.: Tuning a model's settings until the real data it learns from looks as likely, and so as unsurprising, to the model as possible. Most AI training, including the pretraining of chatbots, is a version of this. under Gaussian noise. Squaring makes the loss smooth and differentiable, which suits gradient descentgradient descent, n.: A method for training models by repeatedly nudging every setting a small step in whichever direction most reduces the error, like a hiker who cannot see the valley but keeps stepping wherever the ground tilts down., but also makes it sensitive to outliers, since one large error outweighs many small ones. Its square root, the root mean squared error (RMSE), is in the target's units and is the more commonly reported metric; the coefficient of determinationcoefficient of determination, n.: A score for numerical predictions showing how much of the variation in the true values a model accounts for, compared with always guessing the average: 1 is perfect, 0 is no better than the average. rescales MSE relative to the variance of the target. For an estimator, MSE decomposes into squared bias plus variance, the basis of the bias–variance tradeoffbias–variance tradeoff, n.: The balancing act between models too simple to capture a pattern and models so flexible that they also learn the noise. The best predictions usually come from somewhere in between.. Beyond regression, MSE is the reconstruction loss of many autoencodersautoencoder, n.: A neural network trained to squeeze its input into a compact code and then rebuild the original from that code. Learning to compress this way forces it to capture what matters in the data., the denoising objective of diffusion modelsdiffusion model, n.: An AI that learns to create images, sound or video by practicing noise removal: shown pictures buried under static, it learns to clean them up, then builds new ones starting from pure static. and the value-fitting loss in reinforcement learningreinforcement learning, n.: A way of teaching a computer program by trial and error: it tries actions, earns points for good results and penalties for bad ones, and gradually learns which choices pay off over time.. When outliers or heavy tails matter, mean absolute errormean absolute error, n.: A way of scoring numerical predictions: average how far off each prediction is, ignoring direction, so the score reads as 'typically off by this much'. Lower is better. or the Huber loss is preferred.

RMSE on next-day demand fell from 41 to 33 units after we added weather features.