English
Related papers

Related papers: Tunable robustness in power-law inference

200 papers

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this…

Optimization and Control · Mathematics 2014-10-03 Zizhuo Wang , Peter Glynn , Yinyu Ye

We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…

Optimization and Control · Mathematics 2024-06-11 Ahmed Attia

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

Machine Learning · Statistics 2018-07-03 John Duchi , Peter Glynn , Hongseok Namkoong

Robustness analysis is an emerging field in the domain of uncertainty quantification. It consists of analysing the response of a computer model with uncertain inputs to the perturbation of one or several of its input distributions. Thus, a…

Statistics Theory · Mathematics 2020-12-16 Clement Gauchy , Jerome Stenger , Roman Sueur , Bertrand Iooss

Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source.…

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

Optimization and Control · Mathematics 2021-11-30 Romain Guillaume , Adam Kasperski , Pawel Zielinski

Calibrated predictions are useful because their numerical values can be interpreted as probabilities. Calibration errors are therefore widely used to evaluate, compare, and tune probabilistic predictors. Recently, Haghtalab et al. (2024)…

Machine Learning · Computer Science 2026-05-19 Yuxuan Lu , Yifan Wu , Jason Hartline , Lunjia Hu

We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for…

Machine Learning · Computer Science 2023-08-02 Yuqian Cheng , Daniel M. Kane , Zhicheng Zheng

It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…

Data Analysis, Statistics and Probability · Physics 2017-04-12 Rudolf Hanel , Bernat Corominas-Murtra , Bo Liu , Stefan Thurner

We study binary classification in the setting where the learner is presented with multiple corrupted training samples, with possibly different sample sizes and degrees of corruption, and introduce an approach based on minimizing a weighted…

Machine Learning · Statistics 2019-10-11 Clayton Scott , Jianxin Zhang

In many data analyses, each measurement may come with a simple yes/no correction; for example, belonging to one of two populations or being contaminated or not. Ignoring such binary effects may bias the results, while accounting for them…

Cosmology and Nongalactic Astrophysics · Physics 2026-05-13 Marcus Högås , Edvard Mörtsell

Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…

History and Philosophy of Physics · Physics 2022-04-26 Daniel Andrés Díaz-Pachón , Ola Hössjer , Robert J. Marks

Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…

Physics and Society · Physics 2014-11-11 Filippo Radicchi

A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio…

Machine Learning · Statistics 2019-11-05 Aditya Grover , Jiaming Song , Alekh Agarwal , Kenneth Tran , Ashish Kapoor , Eric Horvitz , Stefano Ermon

Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely…

Applications · Statistics 2012-09-07 Alvaro Corral , Anna Deluca , Ramon Ferrer-i-Cancho

We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…

Many objects studied in astronomy follow a power law distribution function, for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The…

Instrumentation and Methods for Astrophysics · Physics 2015-05-13 Thomas Maschberger , Pavel Kroupa

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We…

Machine Learning · Statistics 2019-08-28 Tim Coleman , Kimberly Kaufeld , Mary Frances Dorn , Lucas Mentch

Above the magnitude of completeness - the minimum threshold for which a 100\% detection rate is assumed - earthquake magnitudes are typically modeled as a continuous exponential distribution. In practice, however, earthquake catalogs report…

Geophysics · Physics 2026-03-03 Angela Stallone , Ilaria Spassiani

Traditional binned statistics such as $\chi^2$ suffer from information loss and arbitrariness of the binning procedure. We point out that the underlying statistical quantity (the log likelihood $L$) does not require any binning beyond the…