This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by character, outputting each character's self-delimiting codeword before reading the next one. We show how to encode and decode each character in constant worst-case time while producing an encoding whose length is worst-case optimal. In another chapter we consider one-pass compression with memory bounded in terms of the alphabet size and context length, and prove a nearly tight tradeoff between the amount of memory we can use and the quality of the compression we can achieve. In a third chapter we consider compression in the read/write streams model, which allows us passes and memory both polylogarithmic in the size of the input. We first show how to achieve universal compression using only one pass over one stream. We then show that one stream is not sufficient for achieving good grammar-based compression. Finally, we show that two streams are necessary and sufficient for achieving entropy-only bounds.
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over a zero-rate noiseless link. The decision center sends a single bit of feedback to the sensor to request for more samples for compression/testing or to stop the transmission. We have characterized the optimal exponent of type-II error probability under the constraint that type-I error probability does not exceed a given threshold $ε\in (0,1)$ and also when t…
Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded within a limited interval. Sequential probability assignment algorithms are essential in many applications that require fast and accurate estimation of the maximizing sequence probability. These applications include learning, regression, channel estimation and decoding, prediction, and universal compression. On the other hand, constrained distributions introdu…
Exploration-Exploitation Tradeoff in Universal Lossy Compression
Viterbi Faculty of Electrical and Computer Engineering, Technion – Israel Institute of Technology（维特比电气工程与计算机科学学院，技术学院–以色列理工学院）；Department of Electrical Engineering-Systems, Tel Aviv University（电气工程-系统系，特拉维夫大学）
Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic, sequential-based compression methods on these graph-based data. Therefore, it is necessary to develop new methods for graph compression. In this paper, we present universal source coding methods for the lossless compression of unweighted, undirected, unlabelled graphs. We encode in two steps: 1) transforming graph into a rooted binary tree, 2) the encoding root…
Universal compression algorithms have been studied in the past for sequential change detection, where they have been used to estimate the post-change distribution in the modified version of the Cumulative Sum (CUSUM) Test. In this paper, we introduce a modified CUSUM test where the pre-change distribution is also unknown and an empirical version of the pre-change distribution is used to implement the algorithm. We present a study of various characteristics of this modified CUSUM Test and then prove its asymptotic optimality.
The problem of online prediction with sequential side information under logarithmic loss is studied, and general upper and lower bounds on the minimax regret incurred by the predictor is established. The upper bounds on the minimax regret are obtained by providing and analyzing a probability assignment inspired by mixture probability assignments in universal compression, and the lower bounds are obtained by way of a redundancy-capacity theorem. The tight characterization of the regret is provided in some special settings.
This paper considers an uplink massive machine-type communication (mMTC) scenario, where a large number of user devices are connected to a base station (BS). A novel grant-free massive random access (MRA) strategy is proposed, considering both the sporadic user traffic and short packet features. Specifically, the notions of active detection time (ADT) and active detection period (ADP) are introduced so that active user detection can be performed multiple times within one coherence time. By taking sporadic user traffic and short packet features into consideration, we model the joint active user…
Indian Institute of Technology Delhi（德里印度理工学院）；Samsung R&D Institute India - Delhi（三星印度德里研发中心）
In the last few years, compression of deep neural networks has become an important strand of machine learning and computer vision research. Deep models require sizeable computational complexity and storage, when used for instance for Human Action Recognition (HAR) from videos, making them unsuitable to be deployed on edge devices. In this paper, we address this issue and propose a method to effectively compress Recurrent Neural Networks (RNNs) such as Gated Recurrent Units (GRUs) and Long-Short-Term-Memory Units (LSTMs) that are used for HAR. We use a Variational Information Bottleneck (VIB) t…
We model a dense wireless local area network where the access points (APs) employ carrier sense multiple access (CSMA)-type medium access control protocol. In our model, the spatial locations of the set of active APs are modeled using the random sequential adsorption (RSA) process, which is more accurate in terms of the density of active APs compared to the Matérn hard-core point process of type-II (MHPP-II) commonly used for modeling CSMA networks. Leveraging the theory of the RSA process from the statistical physics literature, we provide an approximate but accurate analytical result for the…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Facebook AI Research（脸书人工智能研究院）；University College London（伦敦大学学院）；University of Oxford（牛津大学）
Latent variable models have been successfully applied in lossless compression with the bits-back coding algorithm. However, bits-back suffers from an increase in the bitrate equal to the KL divergence between the approximate posterior and the true posterior. In this paper, we show how to remove this gap asymptotically by deriving bits-back coding algorithms from tighter variational bounds. The key idea is to exploit extended space representations of Monte Carlo estimators of the marginal likelihood. Naively applied, our schemes would require more initial bits than the standard bits-back coder,…
