- MCD: Marginal Contrastive Discrimination for conditional density estimation(arXiv)
Author : Benjamin Riu
Abstract : We take into consideration the problem of conditional density estimation, which is a big topic of curiosity throughout the fields of statistical and machine finding out. Our method, known as Marginal Contrastive Discrimination, MCD, reformulates the conditional density function into two elements, the marginal density function of the objective variable and a ratio of density capabilities which can be estimated by the use of binary classification. Like noise-contrastive methods, MCD can leverage state-of-the-art supervised finding out methods to hold out conditional density estimation, along with neural networks. Our benchmark reveals that our method significantly outperforms in observe present methods on most density fashions and regression datasets
2. Minimax Fees for Conditional Density Estimation by the use of Empirical Entropy(arXiv)
Author : Blair Bilodeau, Dylan J. Foster, Daniel M. Roy
Abstract : We take into consideration the responsibility of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental disadvantage with capabilities in every classification and uncertainty quantification for regression. For joint density estimation, minimax fees have been characterised for widespread density programs in terms of uniform (metric) entropy, a well-studied notion of statistical functionality. When making use of those outcomes to conditional density estimation, the utilization of uniform entropy — which is infinite when the covariate space is unbounded and suffers from the curse of dimensionality — may end up in suboptimal fees. Consequently, minimax fees for conditional density estimation can’t be characterised using these classical outcomes. We resolve this disadvantage for well-specified fashions, buying matching (inside logarithmic elements) increased and reduce bounds on the minimax Kullback — Leibler risk in terms of the empirical Hellinger entropy for the conditional density class. Utilizing empirical entropy permits us to attraction to focus arguments based totally on native Rademacher complexity, which — in distinction to uniform entropy — ends in matching fees for big, most likely nonparametric programs and captures the correct dependence on the complexity of the covariate space. Our outcomes require solely that the conditional densities are bounded above, and don’t require that they’re bounded beneath or in another case fulfill any tail conditions.
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