AI models collapse when trained on recursively generated data

I Shumailov, Z Shumaylov, Y Zhao, N Papernot… - Nature, 2024 - nature.com
Stable diffusion revolutionized image creation from descriptive text. GPT-2 (ref.), GPT-3 (.
5)(ref.) and GPT-4 (ref.) demonstrated high performance across a variety of language tasks …

[HTML][HTML] Absolute moments of the variance-gamma distribution

RE Gaunt - Journal of Mathematical Analysis and Applications, 2025 - Elsevier
We obtain exact formulas for the absolute raw and central moments of the variance-gamma
distribution, as infinite series involving the modified Bessel function of the second kind and …

The product distribution of more-than-two correlated normal variables: A didactic review with some new findings

H Ogasawara - Communications in Statistics-Theory and Methods, 2024 - Taylor & Francis
Some reviews of the distribution of the product of two correlated normal random variables
and the corresponding more-than-two uncorrelated cases are given with a historical …

Log Heston Model for Monthly Average VIX

J Park, A Sarantsev - arxiv preprint arxiv:2410.22471, 2024 - arxiv.org
We model time series of VIX (monthly average) and monthly stock index returns. We use log-
Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight …

[HTML][HTML] On the moments of the variance-gamma distribution

RE Gaunt - Statistics & Probability Letters, 2023 - Elsevier
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Multivariate Mat\'ern Models--A Spectral Approach

D Yarger, S Stoev, T Hsing - arxiv preprint arxiv:2309.02584, 2023 - arxiv.org
The classical Mat\'ern model has been a staple in spatial statistics. Novel data-rich
applications in environmental and physical sciences, however, call for new, flexible vector …

On the cumulative distribution function of the variance-gamma distribution

RE Gaunt - Bulletin of the Australian Mathematical Society, 2024 - cambridge.org
We obtain exact formulas for the cumulative distribution function of the variance-gamma
distribution, as infinite series involving the modified Bessel function of the second kind and …

Introducing a Family of Distributions by Using the Class of Normal Mean–Variance Mixture

M Darijani, H Zakerzadeh, AA Jafari - Journal of Statistical Theory and …, 2024 - Springer
In this study, we present a new family of asymmetric distributions by taking into consideration
the multivariate normal mean–variance (NMV) mixture model. These models are created …

[HTML][HTML] On the gamma difference distribution

PJ Forrester - Statistics & Probability Letters, 2024 - Elsevier
The gamma difference distribution is defined as the difference of two independent gamma
distributions, with in general different shape and rate parameters. Starting with knowledge of …

The VIX as Stochastic Volatility for Corporate Bonds

J Park, A Sarantsev - arxiv preprint arxiv:2410.22498, 2024 - arxiv.org
Classic stochastic volatility models assume volatility is unobservable. We use the VIX for
consider it observable, and use the Volatility Index: S\&P 500 VIX. This index was designed …