Related papers: Classification methods for Hilbert data based on s…

Heuristic optimisation algorithms explore the search space by sampling solutions, evaluating their fitness, and biasing the search in the direction of promising solutions. However, in many cases, this fitness function involves executing…

By taking the need for quantum reference frames into account, it is shown that Hilbert-space factorization is a dissipative process requiring on the order of kT to reduce by one bit an observer's uncertainty in the provenance of a…

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

Subsampling methods aim to select a subsample as a surrogate for the observed sample. As a powerful technique for large-scale data analysis, various subsampling methods are developed for more effective coefficient estimation and model…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling…

Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert…

In this paper, a novel semi-supervised dictionary learning and sparse representation (SS-DLSR) is proposed. The proposed method benefits from the supervisory information by learning the dictionary in a space where the dependency between the…

Many problems in computer vision have recently been tackled using models whose predictions cannot be easily interpreted, most commonly deep neural networks. Surrogate explainers are a popular post-hoc interpretability method to further…

Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these…

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…

We analyze a lightweight simulation-based inference method that infers simulator parameters using only a regression-based projection of the observed data. After fitting a surrogate linear regression once, the procedure simulates small…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

In many empirical settings, directly observing a treatment variable may be infeasible although an error-prone surrogate measurement of the latter will often be available. Causal inference based solely on the surrogate measurement is…

Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…

In this dissertation, we focus on several important problems in structured prediction. In structured prediction, the label has a rich intrinsic substructure, and the loss varies with respect to the predicted label and the true label pair.…

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…

Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…