A kinetic-based regularization method for data science applications
This provides a more efficient regularization method for data science applications dealing with noisy or high-dimensional data.
The paper tackles the problem of function learning in data science by proposing a physics-based regularization technique that minimizes discrepancy between discrete and continuum data representations, resulting in improved accuracy for interpolation and regression tasks without requiring empirical parameter tuning.
We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.