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All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…
We model time-varying network data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time…
The rate-distortion (RD) theory is one of the key concepts in information theory, providing theoretical limits for compression performance and guiding the source coding design, with both theoretical and practical significance. The…
This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based…
In this paper, we propose Image Downscaling Assessment by Rate-Distortion (IDA-RD), a novel measure to quantitatively evaluate image downscaling algorithms. In contrast to image-based methods that measure the quality of downscaled images,…
3D Gaussian Splatting (3DGS) has become an emerging technique with remarkable potential in 3D representation and image rendering. However, the substantial storage overhead of 3DGS significantly impedes its practical applications. In this…
A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success…
We consider the dynamics of gradient descent (GD) in overparameterized single hidden layer neural networks with a squared loss function. Recently, it has been shown that, under some conditions, the parameter values obtained using GD achieve…
Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data…
Providing accurate uncertainty estimations is essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold…
This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multiple-input…
The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps, and provides a good approximation to the Newton method for large-scale optimization problems. GGN has been found particularly…
One of the challenges of computer vision is that it needs to adapt to color deviations in changeable environments. Therefore, minimizing the adverse effects of color deviation on the prediction is one of the main goals of vision task.…
CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
Sparse representation leads to an efficient way to approximately recover a signal by the linear composition of a few bases from a learnt dictionary, based on which various successful applications have been achieved. However, in the scenario…
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…
Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To…
The total variation distance is a metric of central importance in statistics and probability theory. However, somewhat surprisingly, questions about computing it algorithmically appear not to have been systematically studied until very…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…