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While there is a general focus on prediction of values, real data often onlyallows to predict conditional probability distributions, with capabilitiesbounded by conditional entropy $H(Y|X)$. If additionally estimatinguncertainty, we can treat a predicted value as the center of Gaussian ofLaplace distribution - idealization which can be far from complex conditionaldistributions of real data. This article applies Hierarchical CorrelationReconstruction (HCR) approach to inexpensively predict quite complexconditional probability distributions (e.g. multimodal): by independent MSEestimation of multiple moment-like parameters, which allow to reconstruct theconditional distribution. Using linear regression for this purpose, we getinterpretable models: with coefficients describing contributions of features toconditional moments. This article extends on the original approach especiallyby using Canonical Correlation Analysis (CCA) for feature optimization and l1"lasso" regularization, focusing on practical problem of prediction of redshiftof Active Galactic Nuclei (AGN) based on Fourth Fermi-LAT Data Release 2 (4LAC)dataset.

Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction