Related papers: Rate Distortion Study for Time-Varying Autoregress…
We show that the mixed causal-noncausal Vector Autoregressive (VAR) processes satisfy the Markov property in both calendar and reverse time. Based on that property, we introduce closed-form formulas of forward and backward predictive…
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…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components…
In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One…
The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
We consider a multiterminal source coding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor which obtains a noisy…
We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data…
Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on…
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…
A causal rate distortion function is defined, its solution is described, and its relation to filtering theory is discussed. The relation to filtering is obtained via a causal constraint imposed on the reconstruction kernel to be realizable.
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
A disformal transformation is a very useful tool to analyze a general effective theory description of inflation. It can for example be used to set the tensor sound speed to unity, such that the tensor power spectrum only depends on 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…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
We revisit the Gray-Wyner lossy source coding problem and derive the first-order asymptotic optimal rate-distortion-perception region when additional perception constraints are imposed on reproduced source sequences. The optimal trade-off…