Related papers: Non-parametric power-law surrogates

We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is primarily motivated by a natural approximation to the so-called…

The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show…

Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variations, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis…

Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of 'social particles',…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…

We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b…

In many application domains, time series are monitored to detect extreme events like technical faults, natural disasters, or disease outbreaks. Unfortunately, it is often non-trivial to select both a time series that is informative about…

Random multiplicative processes $w_t =\lambda_1 \lambda_2 ... \lambda_t$ (with < \lambda_j > 0 ) lead, in the presence of a boundary constraint, to a distribution $P(w_t)$ in the form of a power law $w_t^{-(1+\mu)}$. We provide a simple and…

We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…

One-shot decision making is required in situations in which we can evaluate a fixed number of solution candidates but do not have any possibility for further, adaptive sampling. Such settings are frequently encountered in neural network…

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to…

Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…

Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed datasets while using only minimal assumptions. However, such…

It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time…

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…

Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…

The emergence of heavy-tailed statistics in complex systems is conventionally attributed to non-local stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a…

It is generally believed that more observations provide more information. However, we observe that in the independence test for rare events, the power of the test is, surprisingly, determined by the number of rare events rather than the…