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Variational Imbalanced Regression: Fair Uncertainty Quantification via Probabilistic Smoothing
Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's vari-ational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation.
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8 Supplementary Material 8.1 Details and Proofs for the Proposed EOC 8.1.1 Calculation of T Given data D
Fourier transform of a power of a Euclidean distance, i.e., According to Jensen's inequality and Lipschitzness assumption, we have X According to the law of total probability and Theorem 4.1, we have P { Y A feasible solution to Equation (1) can be quickly found. Pseudocode for Algorithm 2 The pseudocode for the constrained optimization is detailed in Algorithm 2. 18 Algorithm 2 Robust Optimization Method with EOC Constraint Input: Initiate Array A of shape 2 A M that stores the max possible step. Our proposed algorithm is highly computationally efficient.
Appendix A Broader Impact
Overconfidence in deep neural networks could easily lead to deployments where predictions are made that should have been withheld. For validation set, on the other hand, we care about the confidence of the "top predicted class". Independent binning: when training samples and validation samples are grouped independently into their respective training-bins and validation-bins (Figure 1). The binning is adaptive with 15 equal-mass bins. Figure 10: Common binning: training samples are grouped using the bin boundaries of the validation-bins.