Related papers: Realizable Rate Distortion Function and Bayesian F…
Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work we transformed DFT…
In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual In-formation (MMI) distributions and ME distributions are expressed by Bayes-like formulas, in-cluding Negative Exponential Functions (NEFs) and partition…
Rate distortion theory was developed for optimizing lossy compression of data, but it also has a lot of applications in statistics. In this paper we will see how rate distortion theory can be used to analyze a complicated data set involving…
We study large deviations of a ratio observable in discrete-time reset processes. The ratio takes the form of a current divided by the number of reset steps and as such it is not extensive in time. A large deviation rate function can be…
Berger's paper `The Source Coding Game', IEEE Trans. Inform. Theory, 1971, considers the problem of finding the rate-distortion function for an adversarial source comprised of multiple known IID sources. The adversary, called the…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
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…
The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for Partial Frequency Redistribution (PFR) between absorbed and reemitted radiation.…
We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error correction, through the lens of distributional robustness. We assume that the distribution of the source or of the additive…
Fairness in machine learning has attracted increasing attention in recent years. The fairness methods improving algorithmic fairness for in-distribution data may not perform well under distribution shifts. In this paper, we first…
Since artificial intelligence has seen tremendous recent successes in many areas, it has sparked great interest in its potential for trustworthy and interpretable risk prediction. However, most models lack causal reasoning and struggle with…
Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to…
In this paper, distributed (or multiterminal) source coding with one distortion criterion and correlated messages is considered. This problem can be also called ``Berger-Yeung problem with correlated messages''. It corresponds to the source…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence…
Deep neural networks can obtain impressive performance on various tasks under the assumption that their training domain is identical to their target domain. Performance can drop dramatically when this assumption does not hold. One…
While standard computational protocols for density functional theory (DFT) have universal applicability, differences exist in code implementations. Specific applications require manual parameter optimization, whereas high-throughput…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…