More Like this

1. Heavy-Tailed Density Estimation

   https://doi.org/10.1080/01621459.2022.2104727  

   Tokdar, Surya T.; Jiang, Sheng; Cunningham, Erika L. (September 2022, Journal of the American Statistical Association)

   A novel statistical method is proposed and investigated for estimating a heavy tailed density under mildsmoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem ofsparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk.The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularizationthrough a carefully specified semiparametric prior distribution, and is able to consistently estimate boththe density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood drivenestimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tailindex parameter and offer more accurate and reliable estimates of the high tail quantiles compared tothresholding methods. Supplementary materials for this article are available online. 

   more » « less
2. Semiparametric Counterfactual Density Estimation

   https://doi.org/10.1093/biomet/asad017  

   Kennedy, Edward; Balakrishnan, Sivaraman; Wasserman, Larry (January 2023, Biometrika)

   Causal effects are often characterized with averages, which can give an incomplete picture of the underlying counterfactual distributions. Here we consider estimating the entire counterfactual density and generic functionals thereof. We focus on two kinds of target parameters. The first is a density approximation, defined by a projection onto a finite-dimensional model using a generalized distance metric, which includes f-divergences as well as Lp norms. The second is the distance between counterfactual densities, which can be used as a more nuanced effect measure than the mean difference, and as a tool for model selection. We study nonparametric efficiency bounds for these targets, giving results for smooth but otherwise generic models and distances. Importantly, we show how these bounds connect to means of particular non-trivial functions of counterfactuals, linking the problems of density and mean estimation. We go on to propose doubly robust-style estimators for the density approximations and distances, and study their rates of convergence, showing they can be optimally efficient in large nonparametric models. We also give analogous methods for model selection and aggregation, when many models may be available and of interest. Our results all hold for generic models and distances, but throughout we highlight what happens for particular choices, such as L2 projections on linear models, and KL projections on exponential families. Finally we illustrate by estimating the density of CD4 count among patients with HIV, had all been treated with combination therapy versus zidovudine alone, as well as a density effect. Our results suggest combination therapy may have increased CD4 count most for high-risk patients. Our methods are implemented in the freely available R package npcausal on GitHub. 

   more » « less
3. Sublinear time spectral density estimation

   https://doi.org/10.1145/3519935.3520009  

   Braverman, Vladimir; Krishnan, Aditya; Musco, Christopher (June 2022, Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing)
4. Analysis of KNN Density Estimation

   https://doi.org/10.1109/TIT.2022.3195870  

   Zhao, Puning; Lai, Lifeng (December 2022, IEEE Transactions on Information Theory)
5. Data Structures for Density Estimation

   Aamand, Anders; Andoni, Alexandr; Chen, Justin Y.; Indyk, Piotr; Narayanan, Shyam; Silwal, Sandeep (January 2023, International Conference on Machine Learning, {ICML} 2023)