Related papers: The Sample Complexity of Lossless Data Compression
The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis…
This thesis deals with the problem of communicating and storing non-sequential data. We investigate this problem through the lens of lossless source coding, also sometimes referred to as lossless compression, from both an algorithmic 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…
Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…
Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…
We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm…
This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
In this monograph, we review recent advances in second-order asymptotics for lossy source coding, which provides approximations to the finite blocklength performance of optimal codes. The monograph is divided into three parts. In part I, we…
Data compression algorithms are generally perceived as being of interest for data communication and storage purposes only. However, their use in the field of data classification and analysis is also of equal importance. Automatic data…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…
We present the first efficient averaging sampler that achieves asymptotically optimal randomness complexity and near-optimal sample complexity. For any $\delta < \varepsilon$ and any constant $\alpha > 0$, our sampler uses $m + O(\log (1 /…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary…