Related papers: On the Rate-Distortion-Perception Function for Gau…
The error exponent of fixed-length lossy source coding was established by Marton. Ahlswede showed that this exponent can be discontinuous at a rate $R$, depending on the probability distribution $P$ of the given information source and the…
The multivariate Gaussian rate-distortion (RD) function is crucial in various applications, such as digital communications, data storage, or neural networks. However, the complex form of the multivariate Gaussian RD function prevents its…
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…
Rate distortion theory is concerned with optimally encoding a given signal class $\mathcal{S}$ using a budget of $R$ bits, as $R\to\infty$. We say that $\mathcal{S}$ can be compressed at rate $s$ if we can achieve an error of…
We apply statistical mechanics to an inverse problem of linear mapping to investigate the physics of the irreversible compression. We use the replica symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's result.…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
In this paper, we present an extension to the recursive Gaussian Process (RGP) regression that enables the satisfaction of inequality constraints and is well suited for a real-time execution in control applications. The soft inequality…
The distortion-perception (DP) tradeoff reveals a fundamental conflict between distortion metrics (e.g., MSE and PSNR) and perceptual quality. Recent research has increasingly concentrated on evaluating denoising algorithms within the DP…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Preprocessing is a well-established technique for optimizing compression, yet existing methods are predominantly Rate-Distortion (R-D) optimized and constrained by pixel-level fidelity. This work pioneers a shift towards Rate-Perception…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…
Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…
For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational…
We derive the optimal second-order coding region and moderate deviations constant for successive refinement source coding with a joint excess-distortion probability constraint. We consider two scenarios: (i) a discrete memoryless source…
Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence.…
Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…