Aleatoric Uncertainty¶
Preface¶
In the context of machine learning, given predictor \(f\) and outcome \(y\):
\[
f(\mathbf{x}) - y = \underbrace{f(\mathbf{x}) - f_{\text{best}}(\mathbf{x})}_{\text{due to insufficient data}} + \underbrace{f_{\text{best}}(\mathbf{x}) - f^{*}(\mathbf{x})}_{\text{bias}} + \underbrace{f^{*}(\mathbf{x}) - y}_{\text{irreducible error}}
\]
Definition¶
Aleatoric Uncertainty refers to the inherent uncertainty in the data due to randomness or noise.
If we make a prediction, even if it is from the true function \(f^{*}(\mathbf{x})\), we will always have some uncertainty in our accuracy of the prediction due to the outcome being inherently stochastic.
It is the irreducible error in machine learning models, ie. the variance of \(y\): \(\sigma_{y}^2\).