Related papers: An Experimental Study of Distributed Quantile Esti…
As data volume grows extensively, data profiling helps to extract metadata of large-scale data. However, one kind of metadata, order statistics, is difficult to be computed because they are not mergeable or incremental. Thus, the limitation…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…
In this paper we consider the problem of estimating quantiles when data are received sequentially (data stream). For real life data streams, the distribution of the data typically varies with time making estimation of quantiles challenging.…
Very large datasets are often encountered in climatology, either from a multiplicity of observations over time and space or outputs from deterministic models (sometimes in petabytes= 1 million gigabytes). Loading a large data vector and…
This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
Quantile regression \parencite{Koenker1978} is a robust and practically useful way to efficiently model quantile varying correlation and predict varied response quantiles of interest. This article constructs and tests MM algorithms, which…
A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used…
Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
We present on-line algorithms for computing approximations of rank-based statistics that give high accuracy, particularly near the tails of a distribution, with very small sketches. Notably, the method allows a quantile $q$ to be computed…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…