Related papers: Adaptive Confidence Sets for the Optimal Approxima…

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…

We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…

We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with…

Traditional conformal prediction methods construct prediction sets such that the true label falls within the set with a user-specified coverage level. However, poorly chosen coverage levels can result in uninformative predictions, either…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating…

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…

Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground…

Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution…

We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. We use resampling methods to estimate the projection of $s$ onto finite dimensional linear spaces and a model selection procedure to choose an…

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…

In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…

Multi-fidelity Gaussian process is a common approach to address the extensive computationally demanding algorithms such as optimization, calibration and uncertainty quantification. Adaptive sampling for multi-fidelity Gaussian process is a…