Related papers: Universal Densities Exist for Every Finite Referen…
In the article "Universal Densities Exist for Every Finite Reference Measure" (IEEE Trans. Inform. Theory, vol. 69, no. 8, pp. 5277--5288, 2023) we neglected to mention relevant contributions of Boris Ryabko. We cited a source by him that…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
The problem of joint universal source coding and modeling, treated in the context of lossless codes by Rissanen, was recently generalized to fixed-rate lossy coding of finitely parametrized continuous-alphabet i.i.d. sources. We extend…
Suppose that we have a method which estimates the conditional probabilities of some unknown stochastic source and we use it to guess which of the outcomes will happen. We want to make a correct guess as often as it is possible. What…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically_mismatched_ to the source distribution), followed by optimal…
We study universal decoding over unknown discrete additive channels determined by a finite-state (unifilar) random process. Aiming at low-complexity decoders, we study variants of noise-guessing decoders that use estimators for the…
The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…
A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's…
We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are…
We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems.…
Consider universal data compression: the length $l(x^n)$ of sequence $x^n\in A^n$ with finite alphabet $A$ and length $n$ satisfies Kraft's inequality over $A^n$, and $-\frac{1}{n}\log \frac{P^n(x^n)}{Q^n(x^n)}$ almost surely converges to…
Deep neural networks have shown incredible performance for inference tasks in a variety of domains. Unfortunately, most current deep networks are enormous cloud-based structures that require significant storage space, which limits scaling…
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
We prove the existence of codebooks for d-semifaithful lossy compression that are simultaneously universal with respect to both the class of finite-alphabet memoryless sources and the class of all bounded additive distortion measures. By…
The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuous-alphabet memoryless sources. We show that, for bounded distortion…