Total Variation Distance
Total variation distance is a measure in probability theory and statistics of the difference between two probability distributions, defined as the maximum difference in probability assigned to any event by the two distributions, with values from 0 to 1. In machine learning it is often used to assess the difference between a generated distribution and a target distribution.
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For the unconstrained hypothesis class, the relationship between the prediction error of MLIPs and sampling accuracy is exponentially ill-posed in terms of dimensionality: even if the prediction errors of energy and forces decay exponentially with dimensionality, the total variation distance between the learned distribution and the target distribution may still approach its maximum value.
Total variation distance is defined as the maximum difference in probability between two distributions on some event, with a range from 0 to 1; 0 means the distributions are completely identical, and 1 means they do not overlap at all.
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For the unconstrained hypothesis class, the relationship between the prediction error of MLIPs and sampling accuracy is exponentially ill-posed in terms of dimensionality: even if the prediction errors of energy and forces decay exponentially with dimensionality, the total variation distance between the learned distribution and the target distribution may still approach its maximum value.
50%UnverifiedTotal variation distance is defined as the maximum difference in probability between two distributions on some event, with a range from 0 to 1; 0 means the distributions are completely identical, and 1 means they do not overlap at all.
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