arXiv subjects

Tsachy Weissman

Publications and source records attributed to Tsachy Weissman.

At least 37 records · Page 2Linked to original sources

arXiv2023

Exact Optimality of Communication-Privacy-Utility Tradeoffs in Distributed Mean Estimation

We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed \emph{order}-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits), \emph{exact} optimality (in the non-asymptotic setting) still has not been achieved. In this work, we take a step towards characterizing the \emph{exact}-optimal approach in the presence of shared randomness (a random variable shared between the server and the user) and identify several conditions for \emph{exact} optimality. We prove that one of the conditions is to utilize a rotationally symmetric shared random codebook. Based on this, we propose a randomization mechanism where the codebook is a randomly rotated simplex -- satisfying the properties of the \emph{exact}-optimal codebook. The proposed mechanism is based on a $k$-closest encoding which we prove to be \emph{exact}-optimal for the randomly rotated simplex codebook.

cs.LG↗

arXiv2023

Toward Textual Transform Coding

Inspired by recent work on compression with and for young humans, the success of transform-based approaches to information processing, and the rise of powerful language-based AI, we propose \emph{textual transform coding}. It shares some of its key properties with traditional transform-based coding underlying much of our current multimedia compression technologies. It can form the basis for compression at bit rates until recently considered uselessly low, and for boosting human satisfaction from reconstructions at more traditional bit rates.

cs.IT↗

arXiv2023

PIM: Video Coding using Perceptual Importance Maps

Human perception is at the core of lossy video compression, with numerous approaches developed for perceptual quality assessment and improvement over the past two decades. In the determination of perceptual quality, different spatio-temporal regions of the video differ in their relative importance to the human viewer. However, since it is challenging to infer or even collect such fine-grained information, it is often not used during compression beyond low-level heuristics. We present a framework which facilitates research into fine-grained subjective importance in compressed videos, which we then utilize to improve the rate-distortion performance of an existing video codec (x264). The contributions of this work are threefold: (1) we introduce a web-tool which allows scalable collection of fine-grained perceptual importance, by having users interactively paint spatio-temporal maps over encoded videos; (2) we use this tool to collect a dataset with 178 videos with a total of 14443 frames of human annotated spatio-temporal importance maps over the videos; and (3) we use our curated dataset to train a lightweight machine learning model which can predict these spatio-temporal importance regions. We demonstrate via a subjective study that encoding the videos in our dataset while taking into account the importance maps leads to higher perceptual quality at the same bitrate, with the videos encoded with importance maps preferred $1.8 \times$ over the baseline videos. Similarly, we show that for the 18 videos in test set, the importance maps predicted by our model lead to higher perceptual quality videos, $2 \times$ preferred over the baseline at the same bitrate.

eess.IV↗

arXiv2023

Lossy Compression of Noisy Data for Private and Data-Efficient Learning

Storage-efficient privacy-preserving learning is crucial due to increasing amounts of sensitive user data required for modern learning tasks. We propose a framework for reducing the storage cost of user data while at the same time providing privacy guarantees, without essential loss in the utility of the data for learning. Our method comprises noise injection followed by lossy compression. We show that, when appropriately matching the lossy compression to the distribution of the added noise, the compressed examples converge, in distribution, to that of the noise-free training data as the sample size of the training data (or the dimension of the training data) increases. In this sense, the utility of the data for learning is essentially maintained, while reducing storage and privacy leakage by quantifiable amounts. We present experimental results on the CelebA dataset for gender classification and find that our suggested pipeline delivers in practice on the promise of the theory: the individuals in the images are unrecognizable (or less recognizable, depending on the noise level), overall storage of the data is substantially reduced, with no essential loss (and in some cases a slight boost) to the classification accuracy. As an added bonus, our experiments suggest that our method yields a substantial boost to robustness in the face of adversarial test data.

cs.IT↗

arXiv2023

Neural Network Compression for Noisy Storage Devices

Compression and efficient storage of neural network (NN) parameters is critical for applications that run on resource-constrained devices. Despite the significant progress in NN model compression, there has been considerably less investigation in the actual \textit{physical} storage of NN parameters. Conventionally, model compression and physical storage are decoupled, as digital storage media with error-correcting codes (ECCs) provide robust error-free storage. However, this decoupled approach is inefficient as it ignores the overparameterization present in most NNs and forces the memory device to allocate the same amount of resources to every bit of information regardless of its importance. In this work, we investigate analog memory devices as an alternative to digital media -- one that naturally provides a way to add more protection for significant bits unlike its counterpart, but is noisy and may compromise the stored model's performance if used naively. We develop a variety of robust coding strategies for NN weight storage on analog devices, and propose an approach to jointly optimize model compression and memory resource allocation. We then demonstrate the efficacy of our approach on models trained on MNIST, CIFAR-10 and ImageNet datasets for existing compression techniques. Compared to conventional error-free digital storage, our method reduces the memory footprint by up to one order of magnitude, without significantly compromising the stored model's accuracy.

cs.LG↗

arXiv2023

Sparse Random Networks for Communication-Efficient Federated Learning

One main challenge in federated learning is the large communication cost of exchanging weight updates from clients to the server at each round. While prior work has made great progress in compressing the weight updates through gradient compression methods, we propose a radically different approach that does not update the weights at all. Instead, our method freezes the weights at their initial \emph{random} values and learns how to sparsify the random network for the best performance. To this end, the clients collaborate in training a \emph{stochastic} binary mask to find the optimal sparse random network within the original one. At the end of the training, the final model is a sparse network with random weights -- or a subnetwork inside the dense random network. We show improvements in accuracy, communication (less than $1$ bit per parameter (bpp)), convergence speed, and final model size (less than $1$ bpp) over relevant baselines on MNIST, EMNIST, CIFAR-10, and CIFAR-100 datasets, in the low bitrate regime under various system configurations.

cs.LG↗

arXiv2022

Leveraging the Hints: Adaptive Bidding in Repeated First-Price Auctions

With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-price auctions to first-price auctions for online display ads. This shift immediately motivated the intellectually challenging question of how to bid in first-price auctions, because unlike in second-price auctions, bidding one's private value truthfully is no longer optimal. Following a series of recent works in this area, we consider a differentiated setup: we do not make any assumption about other bidders' maximum bid (i.e. it can be adversarial over time), and instead assume that we have access to a hint that serves as a prediction of other bidders' maximum bid, where the prediction is learned through some blackbox machine learning model. We consider two types of hints: one where a single point-prediction is available, and the other where a hint interval (representing a type of confidence region into which others' maximum bid falls) is available. We establish minimax optimal regret bounds for both cases and highlight the quantitatively different behavior between the two settings. We also provide improved regret bounds when the others' maximum bid exhibits the further structure of sparsity. Finally, we complement the theoretical results with demonstrations using real bidding data.

cs.GT↗

arXiv2022

Upper bounds on the Rate of Uniformly-Random Codes for the Deletion Channel

We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for small and large $d.$ We give simulation results which suggest that our upper bound is within 0.05 of the exact value for all $d$, and within $0.01$ for $d>0.75$. Despite our upper bounds, based on simulations, we conjecture that a positive rate is achievable with uniformly-random codes for all deletion probabilities less than 1. Our results imply impossibility results for the (equivalent) problem of compression of i.i.d. sources correlated via the deletion channel, a relevant model for DNA storage.

cs.IT↗

arXiv2022

An Interactive Annotation Tool for Perceptual Video Compression

Human perception is at the core of lossy video compression and yet, it is challenging to collect data that is sufficiently dense to drive compression. In perceptual quality assessment, human feedback is typically collected as a single scalar quality score indicating preference of one distorted video over another. In reality, some videos may be better in some parts but not in others. We propose an approach to collecting finer-grained feedback by asking users to use an interactive tool to directly optimize for perceptual quality given a fixed bitrate. To this end, we built a novel web-tool which allows users to paint these spatio-temporal importance maps over videos. The tool allows for interactive successive refinement: we iteratively re-encode the original video according to the painted importance maps, while maintaining the same bitrate, thus allowing the user to visually see the trade-off of assigning higher importance to one spatio-temporal part of the video at the cost of others. We use this tool to collect data in-the-wild (10 videos, 17 users) and utilize the obtained importance maps in the context of x264 coding to demonstrate that the tool can indeed be used to generate videos which, at the same bitrate, look perceptually better through a subjective study - and are 1.9 times more likely to be preferred by viewers. The code for the tool and dataset can be found at https://github.com/jenyap/video-annotation-tool.git

eess.IV↗

arXiv2022

Txt2Vid: Ultra-Low Bitrate Compression of Talking-Head Videos via Text

Video represents the majority of internet traffic today, driving a continual race between the generation of higher quality content, transmission of larger file sizes, and the development of network infrastructure. In addition, the recent COVID-19 pandemic fueled a surge in the use of video conferencing tools. Since videos take up considerable bandwidth (~100 Kbps to a few Mbps), improved video compression can have a substantial impact on network performance for live and pre-recorded content, providing broader access to multimedia content worldwide. We present a novel video compression pipeline, called Txt2Vid, which dramatically reduces data transmission rates by compressing webcam videos ("talking-head videos") to a text transcript. The text is transmitted and decoded into a realistic reconstruction of the original video using recent advances in deep learning based voice cloning and lip syncing models. Our generative pipeline achieves two to three orders of magnitude reduction in the bitrate as compared to the standard audio-video codecs (encoders-decoders), while maintaining equivalent Quality-of-Experience based on a subjective evaluation by users (n = 242) in an online study. The Txt2Vid framework opens up the potential for creating novel applications such as enabling audio-video communication during poor internet connectivity, or in remote terrains with limited bandwidth. The code for this work is available at https://github.com/tpulkit/txt2vid.git.

eess.IV↗

arXiv2022

An Information-Theoretic Justification for Model Pruning

We study the neural network (NN) compression problem, viewing the tension between the compression ratio and NN performance through the lens of rate-distortion theory. We choose a distortion metric that reflects the effect of NN compression on the model output and derive the tradeoff between rate (compression) and distortion. In addition to characterizing theoretical limits of NN compression, this formulation shows that \emph{pruning}, implicitly or explicitly, must be a part of a good compression algorithm. This observation bridges a gap between parts of the literature pertaining to NN and data compression, respectively, providing insight into the empirical success of model pruning. Finally, we propose a novel pruning strategy derived from our information-theoretic formulation and show that it outperforms the relevant baselines on CIFAR-10 and ImageNet datasets.

cs.LG↗

arXiv2021

Optimal Communication Rates and Combinatorial Properties for Common Randomness Generation

We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a publicly seen blackboard through which the players communicate with each other. We provide a tight representation of the optimal communication rates via linear programming, and more importantly, propose explicit algorithms for the optimal distributed simulation for a wide class of hypergraphs. In particular, the optimal communication rate in complete hypergraphs is still achievable in sparser hypergraphs containing a path-connected cycle-free cluster of topologically connected components. Some key steps in analyzing the upper bounds rely on two different definitions of connectivity in hypergraphs, which may be of independent interest.

cs.IT↗

arXiv2021

Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints

We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes an estimate of a desired parameter. We develop lower bounds for the minimax risk of estimating the underlying parameter for a large class of losses and distributions. Our results show that under mild regularity conditions, the communication constraint reduces the effective sample size by a factor of $d$ when $k$ is small, where $d$ is the dimension of the estimated parameter. Furthermore, this penalty reduces at most exponentially with increasing $k$, which is the case for some models, e.g., estimating high-dimensional distributions. For other models however, we show that the sample size reduction is re-mediated only linearly with increasing $k$, e.g. when some sub-Gaussian structure is available. We apply our results to the distributed setting with product Bernoulli model, multinomial model, Gaussian location models, and logistic regression which recover or strengthen existing results. Our approach significantly deviates from existing approaches for developing information-theoretic lower bounds for communication-efficient estimation. We circumvent the need for strong data processing inequalities used in prior work and develop a geometric approach which builds on a new representation of the communication constraint. This approach allows us to strengthen and generalize existing results with simpler and more transparent proofs.

cs.DC↗

arXiv2021

Minimax Rate-Optimal Estimation of Divergences between Discrete Distributions

We study the minimax estimation of $α$-divergences between discrete distributions for integer $α\ge 1$, which include the Kullback--Leibler divergence and the $χ^2$-divergences as special examples. Dropping the usual theoretical tricks to acquire independence, we construct the first minimax rate-optimal estimator which does not require any Poissonization, sample splitting, or explicit construction of approximating polynomials. The estimator uses a hybrid approach which solves a problem-independent linear program based on moment matching in the non-smooth regime, and applies a problem-dependent bias-corrected plug-in estimator in the smooth regime, with a soft decision boundary between these regimes.

cs.IT↗

arXiv2021

Reducing latency and bandwidth for video streaming using keypoint extraction and digital puppetry

COVID-19 has made video communication one of the most important modes of information exchange. While extensive research has been conducted on the optimization of the video streaming pipeline, in particular the development of novel video codecs, further improvement in the video quality and latency is required, especially under poor network conditions. This paper proposes an alternative to the conventional codec through the implementation of a keypoint-centric encoder relying on the transmission of keypoint information from within a video feed. The decoder uses the streamed keypoints to generate a reconstruction preserving the semantic features in the input feed. Focusing on video calling applications, we detect and transmit the body pose and face mesh information through the network, which are displayed at the receiver in the form of animated puppets. Using efficient pose and face mesh detection in conjunction with skeleton-based animation, we demonstrate a prototype requiring lower than 35 kbps bandwidth, an order of magnitude reduction over typical video calling systems. The added computational latency due to the mesh extraction and animation is below 120ms on a standard laptop, showcasing the potential of this framework for real-time applications. The code for this work is available at https://github.com/shubhamchandak94/digital-puppetry/.

eess.IV↗

arXiv2020

LFZip: Lossy compression of multivariate floating-point time series data via improved prediction

Time series data compression is emerging as an important problem with the growth in IoT devices and sensors. Due to the presence of noise in these datasets, lossy compression can often provide significant compression gains without impacting the performance of downstream applications. In this work, we propose an error-bounded lossy compressor, LFZip, for multivariate floating-point time series data that provides guaranteed reconstruction up to user-specified maximum absolute error. The compressor is based on the prediction-quantization-entropy coder framework and benefits from improved prediction using linear models and neural networks. We evaluate the compressor on several time series datasets where it outperforms the existing state-of-the-art error-bounded lossy compressors. The code and data are available at https://github.com/shubhamchandak94/LFZip

eess.SP↗

arXiv2019

Optimal rates of entropy estimation over Lipschitz balls

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates $(n\ln n)^{-s/(s+d)} + n^{-1/2}$ for $0<s\leq 2$ for densities supported on $[0,1]^d$, where $s$ is the smoothness parameter and $n$ is the number of independent samples. We generalize the results to densities with unbounded support: given an Orlicz functions $Ψ$ of rapid growth (such as the sub-exponential and sub-Gaussian classes), the minimax rates for densities with bounded $Ψ$-Orlicz norm increase to $(n\ln n)^{-s/(s+d)} (Ψ^{-1}(n))^{d(1-d/p(s+d))} + n^{-1/2}$, where $p$ is the norm parameter in the Lipschitz ball. We also show that the integral-form plug-in estimators with kernel density estimates fail to achieve the minimax rates, and characterize their worst case performances over the Lipschitz ball. One of the key steps in analyzing the bias relies on a novel application of the Hardy-Littlewood maximal inequality, which also leads to a new inequality on the Fisher information that may be of independent interest.

math.ST↗

arXiv2019

Concentration Inequalities for the Empirical Distribution

We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes of sample size $n$ and alphabet size $k$, and the improvement becomes more significant when $k$ is large. We discuss the applications of our results in obtaining tighter concentration inequalities for $L_1$ deviations of the empirical distribution from the true distribution, and the difference between concentration around the expectation or zero. We also obtain asymptotically tight bounds on the variance of the KL divergence between the empirical and true distribution, and demonstrate their quantitatively different behaviors between small and large sample sizes compared to the alphabet size.

cs.IT↗