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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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48 results for shuffle product

Power of network tests degrades when vertices are misaligned.

problem Power loss in network hypothesis testing due to vertex shuffling.
method Theoretical analysis and simulations of Frobenius norm differences in random dot product and stochastic block models.
result Shuffling vertices can significantly reduce the power of network tests.

OmniMatch algorithm perfectly matches graphs without edge correlation.

problem Graph matching in the absence of edge correlation.
method OmniMatch algorithm for seeded multiple graph matching.
result OmniMatch aligns O(sα)O(s^α) unseeded vertices across multiple networks efficiently and perfectly.

New method uses exponential family priors to handle shuffled data problems.

problem Handling mismatch errors in record linkage of two data files.
method Flexible exponential family prior on the permutation group for regularization.
result The proposed method outperforms competing methods in synthetic and real data.

Develops shuffling gradient-based methods for nonconvex-concave minimax optimization.

problem Nonconvex-concave minimax optimization problems.
method Two shuffling gradient-based algorithms for nonconvex-linear and nonconvex-strongly concave settings.
result Achieves state-of-the-art oracle complexity in nonconvex optimization and best-known complexity bounds for nonconvex-strongly concave setting.

A new algorithm improves convergence rates for convex optimization problems.

problem Convex optimization problems with finite-sum structure.
method Nesterov Accelerated Shuffling Gradient (NASG) integrating Nesterov's acceleration with different shuffling schemes.
result Improved convergence rate of O(1/T) for unified shuffling schemes.

A new Gaussian mechanism for differential privacy in the shuffle model is introduced.

problem Improving differential privacy in distributed learning environments.
method Characterization and upper-bounding of Rényi differential privacy (RDP) for the shuffle Gaussian mechanism.
result The shuffle Gaussian mechanism provides improved privacy guarantees compared to existing methods.

Improves privacy amplification by shuffling for differential privacy.

problem Enhancing privacy guarantees in systems with anonymous data contributions.
method Theoretical and numerical analysis of Rényi differential privacy parameters and privacy amplification by shuffling.
result First asymptotically optimal analysis of Rényi differential privacy parameters for shuffled outputs.

New shuffling methods improve convergence without Lipschitz smoothness.

problem Lack of convergence guarantees for shuffling methods under non-Lipschitz conditions.
method Revisit shuffling methods, prove convergence under general bounded variance condition.
result Matched current best-known convergence rates without Lipschitz smoothness.

This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields…

2019-03-07abs ↗pdf ↗

A new method resolves permutation issues in shuffled linear regression for large-scale applications.

problem Estimating latent features through linear transformation with unknown permutations.
method Spectral matching method to align spectral components of measurement and feature covariances.
result Achieves accurate estimates in shuffled LS and LASSO settings with sufficient samples.

DS-Sync improves distributed DNN training efficiency by 94% with minimal accuracy loss.

problem Network bottlenecks in distributed DNN training.
method Divide workers into non-overlapping groups for independent synchronization, then shuffle workers among groups iteratively.
result DS-Sync achieves up to 94% improvement in training time with minimal accuracy loss.

BUDS balances privacy and utility by shuffling data, achieving strong privacy with minimal loss.

problem Balancing privacy and utility in crowd-sourced statistical databases.
method One-hot encoding, iterative shuffling, loss estimation, risk minimization.
result Achieves ε=0.02ε= 0.02 for privacy, maintaining a privacy bound of ε=ln[t/((n11)S)]ε= ln [t/((n_1 - 1)^S)].

Unified analysis of asynchronous-SGD algorithms for distributed learning.

problem Analyzing asynchronous-SGD in heterogeneous settings with varying speeds and data distributions.
method Unified convergence theory for non-convex smooth functions, including pure asynchronous SGD and its modifications.
result Unified convergence rates for various asynchronous algorithms, including novel methods.

New convergence rates for shuffling gradient methods without strong convexity.

problem Theoretical gap between shuffling gradient methods' empirical success and established convergence rates.
method Proved last-iterate convergence rates for shuffling gradient methods using function value gap.
result First last-iterate convergence rates for shuffling gradient methods without strong convexity.

New convergence bounds for shuffling-based SGD methods in distributed learning.

problem Analyzing the performance of shuffling-based variants of SGD in distributed learning.
method Study of minibatch and local Random Reshuffling methods, proving convergence bounds and lower bounds.
result Shuffling-based variants converge faster than with-replacement sampling methods, and the bounds are tight.

Proposes methods to recover labels from shuffled networks using graph averages.

problem Recovering labels from a shuffled network using graph averages.
method Cluster networks into classes, then match the new graph to cluster-averages, minimizing the graph matching objective function.
result Higher fidelity matching performance when clustering networks into different classes.

An exciting new development in differential privacy is the shuffled model, in which an anonymous channel enables non-interactive, differentially private protocols with error much smaller than what is possible in the local model, while relying on weaker trust assumptions than in the central model. In this paper, we stud…

2019-08-29abs ↗pdf ↗

Improved shuffling technique amplifies privacy guarantees for anonymous data contributions.

problem Enhancing privacy in systems where data is contributed anonymously.
method Developed a new approach to random shuffling that amplifies differential privacy guarantees.
result Achieved asymptotically optimal privacy amplification with nearly optimal dependence in ε.

Improved shuffling gradient methods converge faster for nonsmooth convex optimization.

problem Improving convergence rates for nonsmooth convex optimization problems.
method Analysis of shuffling gradient methods, focusing on Random Reshuffle and Single Shuffle strategies.
result Shuffling gradient methods, particularly Random Reshuffle and Single Shuffle, converge faster than Proximal Gradient Descent for nonsmooth convex optimization.

This paper presents a new method for solving systems with polynomial stiffness.

problem Finding analytical solutions to nonlinear differential equations with polynomial stiffness is challenging.
method The paper introduces a geometric/algebraic method using generating series and shuffle product.
result The method provides a recursive schematic that can be automated and applied to systems with polynomial stiffness.

New neural model processes 2D data with long-range dependencies efficiently.

problem Limited receptive field of convolutions for complex 2D tasks.
method Proposes Matrix Shuffle-Exchange network with O(logn)\mathcal{O}( \log{n}) layers and O(n2logn)\mathcal{O}( n^2 \log{n}) complexity.
result Exceeds convolutional and graph neural network baselines in long-range dependency modeling.

We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with replacement, we focus here on popular but poorly-understood heuristics, which i…

2019-07-31abs ↗pdf ↗

A new concept of Loday algebroid (and its pure algebraic version - Loday pseudoalgebra) is proposed and discussed in comparison with other similar structures present in the literature. The structure of a Loday pseudoalgebra and its natural reduction to a Lie pseudoalgebra is studied. Further, Loday algebroids are inter…

2011-03-30abs ↗pdf ↗

In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for nn-party real summation in the shuffle model of differential privacy with Oε,δ(1)O_{ε, δ}(1) error and Θ(εn)Θ(ε\sqrt{n}) one-bit messages per party. In contrast, every local model protocol for real summation must incur error Ω(1/n)Ω(1/\sqrt{n}), and there exist …

2019-06-20abs ↗pdf ↗

We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during the protocol. In this work, we propose a framework that treats the un…

2018-04-02abs ↗pdf ↗

Sampling without replacement speeds up optimization in minimax problems.

problem Optimizing minimax problems with faster convergence rates.
method Analysis of gradient descent ascent and proximal point method with two sampling strategies.
result Sampling without replacement leads to faster convergence rates in minimax optimization.

Paper proves privacy guarantees for shuffled and online PNSGD, reducing noise over time.

problem Privacy amplification in shuffled and online PNSGD settings.
method Iterative analysis of PNSGD with hidden updates, proving privacy guarantees for shuffled and online settings.
result Privacy guarantees for shuffled and online PNSGD with reduced noise over time.

The paper analyzes the variance of different shuffling methods in stochastic gradient descent.

problem Understanding the variance of different shuffling methods in stochastic gradient descent.
method Power spectral density analysis to study the noise sequences of stochastic gradients.
result The stationary variances of iterates decrease in the order of SGD, SGD-RR, and SGD-SO.

Proof of injection from double shuffle to Kashiwara-Vergne Lie algebra.

problem Injecting double shuffle Lie algebra into Kashiwara-Vergne Lie algebra.
method Inclusion of brunnian braids group on different genus 0 surfaces, using lower central series of brunnian Lie algebras, and explicit links between maps.
result Injection of double shuffle Lie algebra into symmetric Kashiwara-Vergne Lie algebra.

Is it possible to perform linear regression on datasets whose labels are shuffled with respect to the inputs? We explore this question by proposing several estimators that recover the weights of a noisy linear model from labels that are shuffled by an unknown permutation. We show that the analog of the classical least-…

2017-05-03abs ↗pdf ↗

Random Reshuffling outperforms Stochastic Gradient Descent in smooth convex optimization.

problem Theoretical limitations of Random Reshuffling in smooth convex optimization.
method Random Reshuffling (RR) as a variant of Shuffling Stochastic Gradient Descent (Shuffling SGD).
result Random Reshuffling (RR) dominates Stochastic Gradient Descent (SGD) in smooth convex optimization under any reasonable stepsize after any finite number of epochs.

Paper improves privacy bounds for shuffle model using novel numerical techniques.

problem Improving privacy guarantees in the shuffle model of differential privacy.
method Develops and evaluates numerical techniques for tighter (ε,δ)(\varepsilon,δ)-differential privacy bounds.
result Accurately evaluates privacy loss distribution for adaptive compositions of shufflers.

New algorithms for private generalized linear contextual bandits.

problem Private estimation and optimization for generalized linear models under differential privacy.
method Developed algorithms for stochastic and adversarial contexts under shuffle and joint differential privacy.
result Achieved private regret bounds for generalized linear models, differing from non-private rates by factors of d/ε\sqrt{d/\varepsilon} and d/ε\sqrt{d/\varepsilon} respectively.

This paper improves privacy bounds for DP algorithms using ff-DP.

problem Difficulty in analyzing randomness in DP algorithms due to mixture distributions.
method Derives a closed-form expression for trade-off functions and analyzes ff-DP.
result Enhances privacy of DP-GD with random initialization and shuffling models.

The paper explores privacy-preserving methods for counting unique elements in distributed settings.

problem Counting unique elements in a distributed setting while maintaining privacy.
method Analyzes and proves lower bounds for differentially private protocols in various settings.
result Achieves optimal error bounds for multi-message shuffle protocols in estimating distinct elements.