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Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…

Numerical Analysis · Mathematics 2022-05-06 Qian Yan , Hanyu Li , Chengmei Niu

Let $P=(P_1, P_2, \ldots, P_n)$, $P_i \in \field{R}$ for all $i$, be a signal and let $C$ be a constant. In this work our goal is to find a function $F:[n]\rightarrow \field{R}$ which optimizes the following objective function: $$ \min_{F}…

Data Structures and Algorithms · Computer Science 2015-03-13 Gary L. Miller , Richard Peng , Russell Schwartz , Charalampos E. Tsourakakis

The Knill-Laflamme (KL) conditions distinguish exact quantum error correction codes, and it has played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not…

Quantum Physics · Physics 2024-06-21 Guo Zheng , Wenhao He , Gideon Lee , Liang Jiang

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well…

Statistics Theory · Mathematics 2020-02-21 Stéphane Guerrier , Mucyo Karemera , Samuel Orso , Maria-Pia Victoria-Feser

Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, maximum likelihood (ML) estimators are utilized to estimate both the…

Information Theory · Computer Science 2018-08-15 Guanyu Wang , Jiang Zhu , Rick S. Blum , Peter Willett , Stefano Marano , Vincenzo Matta , Paolo Braca

We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…

Optimization and Control · Mathematics 2020-03-17 Alejandra Peña-Ordieres , James R. Luedtke , Andreas Wächter

This paper identifies that a group of latest locally-differentially-private (LDP) algorithms for frequency estimation, including all the Hadamard-matrix-based algorithms, are equivalent to the private Count-Mean Sketch (CMS) algorithm with…

Cryptography and Security · Computer Science 2025-07-28 Mingen Pan

The randomized linear combination of unitaries (LCU) method with many applications to early fault-tolerant quantum computing algorithms has been proposed. This quantum algorithm computes the same expectation values as the original, fully…

Quantum Physics · Physics 2026-02-16 Kaito Wada , Hiroyuki Harada , Yasunari Suzuki , Yuuki Tokunaga , Naoki Yamamoto , Suguru Endo

The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…

Information Theory · Computer Science 2015-10-22 Masahito Hayashi , Vincent Y. F. Tan

We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…

Data Structures and Algorithms · Computer Science 2017-03-07 Ilias Diakonikolas , Daniel M. Kane , Vladimir Nikishkin

The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…

Information Theory · Computer Science 2016-11-17 Neri Merhav

This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…

Information Theory · Computer Science 2014-04-28 Jonathan Scarlett , Alfonso Martinez , Albert Guillén i Fàbregas

This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…

Statistics Theory · Mathematics 2025-09-08 Tetsuya Takabatake , Jun Yu , Chen Zhang

We give a simple deterministic $O(\log K / \log\log K)$ approximation algorithm for the Min-Max Selecting Items problem, where $K$ is the number of scenarios. While our main goal is simplicity, this result also improves over the previous…

Data Structures and Algorithms · Computer Science 2013-04-30 Benjamin Doerr

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…

In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A…

Methodology · Statistics 2018-01-04 Giacomo Aletti , Caterina May , Chiara Tommasi

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…

Formal Languages and Automata Theory · Computer Science 2022-10-03 Moses Ganardi , Louis Jachiet , Markus Lohrey , Thomas Schwentick

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…

Statistics Theory · Mathematics 2013-03-06 Vladimir Spokoiny

Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…

Disordered Systems and Neural Networks · Physics 2007-05-23 S. Knysh , V. N. Smelyanskiy , R. D. Morris