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Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's…
We demonstrate that embeddings derived from large language models, when processed with "Survey and Questionnaire Item Embeddings Differentials" (SQuID), can recover the structure of human values obtained from human rater judgments on the…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…
The Kemeny aggregation problem consists of computing the consensus rankings of an election with respect to the well-known Kemeny-Young voting method. These consensus rankings satisfy various fundamental properties and are the geometric…
The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods…
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
Despite variations in architecture and pretraining strategies, recent studies indicate that large-scale AI models often converge toward similar internal representations that also align with neural activity. We propose that scale-invariance,…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…