Related papers: Discovering Active Subspaces for High-Dimensional …

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…

Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…

We present a novel method that integrates subspace modeling with an adaptive generative image prior for high-dimensional MR image reconstruction. The subspace model imposes an explicit low-dimensional representation of the high-dimensional…

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

Recently, there has been a growing interest in mixed-categorical metamodels based on Gaussian Process (GP) for Bayesian optimization. In this context, different approaches can be used to build the mixed-categorical GP. Many of these…

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…

We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…

Bayesian optimization (BO) is a powerful paradigm for efficient optimization of black-box objective functions. High-dimensional BO presents a particular challenge, in part because the curse of dimensionality makes it difficult to define --…

Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…

We investigate the ability to reconstruct and derive spatial structure from sparsely sampled 3D piezoresponse force microcopy data, captured using the band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for weakly…

Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian process (GP) models are commonly employed for emulation, they face limitations…

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…

Many real-world situations allow for the acquisition of additional relevant information when making an assessment with limited or uncertain data. However, traditional ML approaches either require all features to be acquired beforehand or…

Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…

In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain…