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We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
In 1976, Lai constructed a nontrivial confidence sequence for the mean $\mu$ of a Gaussian distribution with unknown variance $\sigma^2$. Curiously, he employed both an improper (right Haar) mixture over $\sigma$ and an improper (flat)…
The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…
We study distribution-free nonparametric regression following a notion of average smoothness initiated by Ashlagi et al. (2021), which measures the "effective" smoothness of a function with respect to an arbitrary unknown underlying…
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends…
We investigate the frequentist coverage properties of Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining…
We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include…
In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real-life problems, especially in complex and high-dimensional scientific applications.…
In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem…
In the nonparametric Gaussian sequence space model an $\ell^2$-confidence ball $C_n$ is constructed that adapts to unknown smoothness and Sobolev-norm of the infinite-dimensional parameter to be estimated. The confidence ball has exact and…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…