data uncertainty (aleatoric): randomness that arises from the nature of data. Depends on what you decide to “not explain” with the model (as a noise). model uncertainty (epistemic): uncertainty that arises from the model complexity and the number of data. It will become more clear once we look at an example. Simple model We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation epistemic uncertainty is inperfection of the model, which may be alleviated by improving process representation. aleatoric uncertainty is inperfection of the data to which we apply our model, so even a model with (hypothetical) zero epistemic uncertainty might still yield uncertain predictions due to aleatoric input uncertainty. 5 Aleatory Variability and Epistemic Uncertainty Aleatory variability and epistemic uncertainty are terms used in seismic hazard analysis that are not commonly used in other fields, but the concepts are well known. 5.1 Example of the Unknown Die As a simple example, consider the problem of rolling a die. Assume that you have not An understanding of uncertainty can also improve the process of analyzing outside data. When looking at polling forecasts, for example, aleatoric uncertainty can speak to what probability ranges actually mean, e.g. understanding, on a gut level, that a 30% probability is meaningful. aleatoric epistemic Figure 1: Training data with non-Gaussian noise (blue dots), predicted median (solid line), 65% and 80% quantiles (dashed lines), aleatoric uncertainty or 95% prediction interval (gray shade, estimated by SQR Sec. 2), and epistemic uncertainty (pink shade, estimated by orthonormal certificates Sec. 3). For example, aleatoric uncertainty in images can be attributed to occlusions (because cameras can’t see through objects). Useful in : Large data situations; Real-time applications, because we can form aleatoric models as a deterministic function of the input data, without expensive Monte Carlo sampling. aleatoric and epistemic uncertainty (Hora, 1996). Roughly speaking, aleatoric (aka statistical) uncertainty refers to the notion of randomness, that is, the variability in the outcome of an experiment which is due to inherently random effects. The prototypical example of aleatoric uncertainty is coin flipping: The data-generating process in this type of experiment has a stochastic component that cannot be reduced by whatsoever additional source of information (except Laplace’s demon). For example, this uncertainty occurs when there are different models for the analyst to choose among, in order to analyze an event. Conflicting nature of pieces of information/data. This uncertainty occurs when some pieces of information give contradicting knowledge, and it cannot be reduced by increasing the amount of information. This variance in the house price is defined as aleatoric uncertainty. In our plot above, the aleatoric uncertainty is equal to the mean plus or minus 2 times the standard deviation. Epistemic uncertainty. Figure 2: Plot showing multiple linear fits (epistemic uncertainty), which all fit reasonably well. Epistemic uncertainty (or systematic uncertainty) is the uncertainty in the model. You can interpret this uncertainty as uncertainty due to a lack of knowledge.
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