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About 804 papers for “Machine epsilon”

Epsilon*: Privacy Metric for Machine Learning Models

Diana M. Negoescu, Humberto González, Saad Eddin Al Orjany et al. · arXiv (Cornell University) · 2023

We introduce Epsilon*, a new privacy metric for measuring the privacy risk of a single model instance prior to, during, or after deployment of privacy mitigation strategies. The metric requires only black-box access to model predictions, does not require training data re-sampling or model re-training, and can be used to measure the privacy risk of models not trained with differential privacy. Epsilon* is a function of true positive and false positive rates in a hypothesis test used by an adversary in a membership inference attack. We distinguish between quantifying the privacy loss of a trained model instance, which we refer to as empirical privacy, and quantifying the privacy loss of the training mechanism which produces this model instance. Existing approaches in the privacy auditing literature provide lower bounds for the latter, while our metric provides an empirical lower bound for the former by relying on an ($ε$, $δ$)-type of quantification of the privacy of the trained model instance. We establish a relationship between these lower bounds and show how to implement Epsilon* to avoid numerical and noise amplification instability. We further show in experiments on benchmark public data sets that Epsilon* is sensitive to privacy risk mitigation by training with differential privacy (DP), where the value of Epsilon* is reduced by up to 800% compared to the Epsilon* values of non-DP trained baseline models. This metric allows privacy auditors to be independent of model owners, and enables visualizing the privacy-utility landscape to make informed decisions regarding the trade-offs between model privacy and utility.

Cited by 0Open access

Revisiting epsilon serializabilty to improve the database state machine

Correia, Alfrânio, Sousa, António, Soares, L. et al. · RepositóriUM (Universidade do Minho) · 2004

Recently, a large body of research has been exploiting group communication based techniques to improve the dependability and performance of synchronously replicated database systems.

Cited by 0Open access

Epsilon Sampling Rocks: Investigating Sampling Strategies for Minimum Bayes Risk Decoding for Machine Translation

Markus Freitag, Behrooz Ghorbani, Patrick Fernandes · 2023

Recent advances in machine translation (MT) have shown that Minimum Bayes Risk (MBR) decoding can be a powerful alternative to beam search decoding, especially when combined with neural-based utility functions. However, the performance of MBR decoding depends heavily on how and how many candidates are sampled from the model. In this paper, we explore how different sampling approaches for generating candidate lists for MBR decoding affect performance. We evaluate popular sampling approaches, such as ancestral, nucleus, and top-k sampling. Based on our insights into their limitations, we experiment with the recently proposed epsilon-sampling approach, which prunes away all tokens with a probability smaller than epsilon, ensuring that each token in a sample receives a fair probability mass. Through extensive human evaluations, we demonstrate that MBR decoding based on epsilon-sampling significantly outperforms not only beam search decoding, but also MBR decoding with all other tested sampling methods across four language pairs.

Cited by 6Open access

Refinement of Hierarchies of Time Bounded Computations

Juris Hartmanis, John E. Hopcroft · eCommons (Cornell University) · 1968

It is shown that for any "slowly growing" time function $T(n)$ and any $\epsilon > 0$ there exists a computation which can be performed by a multitape Turing machine in time $T(n)\log^{\epsilon}T(n)$ and cannot be performed by any multitape Turing machine in time $T(n)$.

Cited by 0Open access

Inferring planar disorder in close-packed structures <i>via</i> ∊-machine spectral reconstruction theory: structure and intrinsic computation in zinc sulfide

D. P. Varn, Geoffrey Canright, James P. Crutchfield · Acta Crystallographica Section B Structural Science · 2007

We apply epsilon-machine spectral reconstruction theory to analyze structure and disorder in four previously published zinc sulfide diffraction spectra and contrast the results with the most common alternative theory, the fault model. In each case we find that the reconstructed epsilon-machine provides a more comprehensive and detailed understanding of the stacking structure, often detecting stacking structures not previously found. Using the epsilon-machines reconstructed for each spectrum, we calculate a number of physical parameters - such as configurational energies, configurational entropies and hexagonality - and several quantities - including statistical complexity and excess entropy - that describe the intrinsic computational properties of the stacking structures.

Cited by 18

Epsilon-Distortion Complexity for Cantor Sets

Claudio Bonanno, Jean-René Chazottes, Pierre Collet · arXiv (Cornell University) · 2007

We define the epsilon-distortion complexity of a set as the shortest program, running on a universal Turing machine, which produces this set at the precision epsilon in the sense of Hausdorff distance. Then, we estimate the epsilon-distortion complexity of various central Cantor sets on the line generated by iterated function systems (IFS's). In particular, the epsilon-distortion complexity of a C^k Cantor set depends, in general, on k and on its box counting dimension, contrarily to Cantor sets generated by polynomial IFS or random affine Cantor sets.

Cited by 0Open access

Accurate floating-point operation using controlled floating-point precision

A. Zaki, Mohamed H. El-Shafey, Ayman M. Bahaa-Eldin et al. · 2011

Rounding and accumulation of errors when using floating point numbers are important factors in computer arithmetic. Many applications suffer from these problems. The underlying machine architecture and representation of floating point numbers play the major role in the level and value of errors in this type of calculations. A quantitative measure of a system error level is the machine epsilon. In the current representation of floating point numbers, the machine epsilon can be as small as 9.63E-35 in the 128 bit version of IEEE standard floating point representation system. In this work a novel solution that guarantees achieving the desired minimum error regardless of the machine architecture is presented. The proposed model can archive a machine epsilon of about 4.94E-324. A new representation model is given and a complete arithmetic system with basic operations is presented. The accuracy of the proposed method is verified by inverting a high order, Hilbert matrix, an ill-conditioned matrix that cannot be solved in the traditional floating point standard. Finally some comparisons are given.

Cited by 3

The 300-500 GeV e&amp;quot;+e&amp;quot;- linear collider

Settles, R., Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut · OpenGrey (Institut de l'Information Scientifique et Technique) · 1993

This report is a brief review of the physics opportunities of a 300-500 GeV #epsilon#&amp;quot;+#epsilon#&amp;quot;- Linear Collider and of the state-of-the-art of the machine technology, subjects of detailed discussion at the ICFA Workshop on Physics and Experimentation at Linear Colliders held in Finland in September 1991. Theoretical and experimental aspects of a broad range of physics issues were studied about the Standard Model and beyond, a few examples of which are covered here. Highlights are given on the topics of the Top Quark, the Higgs Boson of the Standard Model and of its Minimal Supersymmetric extension, and the Discovery Potential. A summary is given of the status of Machine R and D as covered at Finland and as subsequently updated at The ECFA Workshop on #epsilon#&amp;quot;+#epsilon#&amp;quot;- Linear Colliders LC92 held in Bavaria in July 1992. (orig.)

Cited by 0

Finite ε-unit distance graphs

Mike Krebs · Journal of Algebra Combinatorics Discrete Structures and Applications · 2021

\nIn 2005, Exoo posed the following question. Fix $\\epsilon$ with $0\\leq\\epsilon&lt;1$. Let $G_\\epsilon$ be the graph whose vertex set is the Euclidean plane, where two vertices are adjacent iff the Euclidean distance between them lies in the closed interval $[1-\\epsilon,1+\\epsilon]$. What is the chromatic number $\\chi(G_\\epsilon)$ of this graph? The case $\\epsilon=0$ is precisely the classical ``chromatic number of the plane'' problem. In a 2018 preprint, de Grey shows that $\\chi(G_0)\\geq 5$; the proof relies heavily on machine computation. In 2016, Grytczuk et al. proved a weaker result with a human-comprehensible but nonconstructive proof: whenever $0&lt;\\epsilon&lt;1$, we have that $\\chi(G_\\epsilon)\\geq 5$. (This lower bound of $5$ was later improved by Currie and Eggleton to $6$.) The De Bruijn - Erd\\H{o}s theorem (which relies on the axiom of choice) then guarantees the existence, for each $\\epsilon$, of a finite subgraph $H_\\epsilon$ of $G_\\epsilon$ such that $\\chi(H_\\epsilon)\\geq 5$. In this paper, we explicitly construct such finite graphs $H_\\epsilon$. We find that the number of vertices needed to create such a graph is no more than $2\\pi(15+14\\epsilon^{-1})^2$. Our proof can be done by hand without the aid of a computer.\n

Cited by 0Open access