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Register a new userOne estimator, many estimands: fine-grained quantification of uncertainty using conditional inference
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Added by
Ying Jin
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Statistical uncertainty has many components, such as measurement errors, temporal variation, or sampling. Not all of these sources are relevant when considering a specific application, since practitioners might view some attributes of observations as fixed. We study the statistical inference problem arising when data is drawn conditionally on some attributes. These attributes are assumed to be sampled from a super-population but viewed as fixed when conducting uncertainty quantification. The estimand is thus defined as the parameter of a conditional distribution. We propose methods to construct conditionally valid p-values and confidence intervals for these conditional estimands based on asymptotically linear estimators. In this setting, a given estimator is conditionally unbiased for potentially many conditional estimands, which can be seen as parameters of different populations. Testing different populations raises questions of multiple testing. We discuss simple procedures that control novel conditional error rates. In addition, we introduce a bias correction technique that enables transfer of estimators across conditional distributions arising from the same super-population. This can be used to infer parameters and estimators on future datasets based on some new data. The validity and applicability of the proposed methods are demonstrated on simulated and real-world data.
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Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on honest random forests, which add honesty to the original form of random forests and are proved to have better statistical properties. The main contribution is a new method that quantifies the uncertainties of the estimates and predictions produced by honest random forests. The proposed method is based on the generalized fiducial methodology, and provides a fiducial density function that measures how likely each single honest tree is the true model. With such a density function, estimates and predictions, as well as their confidence/prediction intervals, can be obtained. The promising empirical properties of the proposed method are demonstrated by numerical comparisons with several state-of-the-art methods, and by applications to a few real data sets. Lastly, the proposed method is theoretically backed up by a strong asymptotic guarantee.
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We propose an unsupervised multi-conditional image generation pipeline: cFineGAN, that can generate an image conditioned on two input images such that the generated image preserves the texture of one and the shape of the other input. To achieve this goal, we extend upon the recently proposed work of FineGAN citep{singh2018finegan} and make use of standard as well as shape-biased pre-trained ImageNet models. We demonstrate both qualitatively as well as quantitatively the benefit of using the shape-biased network. We present our image generation result across three benchmark datasets- CUB-200-2011, Stanford Dogs and UT Zappos50k.
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