Dynamics of Student’s t-distributions part1(Machine Learning 2024)
Getting started
- Adaptive Student’s t-distribution with method of moments moving estimator for nonstationary time series(arXiv)
Author : Jarek Duda
Abstract : The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid such bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time t finding parameters optimizing e.g. Ft=∑τ<t(1−η)t−τln(ρθ(xτ)) moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments E[|x−μ|p] evolving for one or multiple powers p∈R+ using mp,t+1=mp,t+η(|xt−μt|p−mp,t). Application of such general adaptive methods of moments will be presented on Student’s t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of μ and σ, here we also get evolution of ν describing ρ(x)∼|x|−ν−1 tail shape, probability of extreme events — which might turn out catastrophic, destabilizing the marke
2. Reliable Multimodality Eye Disease Screening via Mixture of Student’s t Distributions(arXiv)
Author : Ke Zou, Tian Lin, Xuedong Yuan, Haoyu Chen, Xiaojing Shen, Meng Wang, Huazhu Fu
Abstract : Multimodality eye disease screening is crucial in ophthalmology as it integrates information from diverse sources to complement their respective performances. However, the existing methods are weak in assessing the reliability of each unimodality, and directly fusing an unreliable modality may cause screening errors. To address this issue, we introduce a novel multimodality evidential fusion pipeline for eye disease screening, EyeMoSt, which provides a measure of confidence for unimodality and elegantly integrates the multimodality information from a multi-distribution fusion perspective. Specifically, our model estimates both local uncertainty for unimodality and global uncertainty for the fusion modality to produce reliable classification results. More importantly, the proposed mixture of Student’s t distributions adaptively integrates different modalities to endow the model with heavy-tailed properties, increasing robustness and reliability. Our experimental findings on both public and in-house datasets show that our model is more reliable than current methods. Additionally, EyeMost has the potential ability to serve as a data quality discriminator, enabling reliable decision-making for multimodality eye disease screening.
