A new meta-analysis model detects and accommodates outliers.
problem Outliers in meta-analysis studies can skew results.
method Proposes a novel tMeta model using the t distribution for robustness. result Demonstrates superior performance in detecting and accommodating outliers.
The paper derives formulas for moments of a Student t distribution and applies them to quantify Lp-quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between Lp-quantiles. result For a Student t distribution, the Ln−j+1-quantile and Lj-quantile coincide at any confidence level. European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the greeks for Gosset and Bla…
Cluster GARCH model improves multivariate GARCH for high-dimensional asset returns.
problem Modeling high-dimensional asset returns with flexible tail dependencies and cluster structures.
method Introduced a novel multivariate GARCH model with flexible convolution-t distributions, tractable likelihood and derivatives for dynamic correlation structure.
result Cluster GARCH model outperforms existing models in daily returns of 100 assets, both in-sample and out-of-sample.
TDistNNs improve prediction intervals for neural networks by using t-distributions.
problem Traditional neural networks provide only point estimates, lacking predictive uncertainty.
method TDistNNs generate t-distributed outputs with adjustable degrees of freedom, enhancing robustness to non-Gaussian data.
result TDistNNs produce narrower prediction intervals with proper coverage compared to Gaussian-based PNNs.
This paper improves PPCA robustness using t-distributions.
problem Improving robustness of probabilistic PCA.
method Using multivariate t-distributions and a hierarchical model. result Clarified the correct correspondence between the multivariate t-PPCA framework and the hierarchical model. Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
Modified Jones-Faddy skew t-distribution captures asymmetry in stock returns.
problem Negative skew and positive mean in stock returns due to broken symmetry of stochastic volatility.
method Modified Jones-Faddy skew t-distribution applied to split gains and losses, using stochastic differential equations for stock returns and volatility.
result The modified distribution effectively captures the asymmetry in daily S&P500 returns, including its tails.
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of th…
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a …
Generative Adversarial Networks (GANs) have a great performance in image generation, but they need a large scale of data to train the entire framework, and often result in nonsensical results. We propose a new method referring to conditional GAN, which equipments the latent noise with mixture of Student's t-distributio…
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
RFPCA improves robustness of FPCA for matrix data.
problem Outliers in matrix data degrade the performance of FPCA.
method RFPCA uses matrix-variate t-distribution and EM algorithm for robust estimation.
result RFPCA outperforms other methods in detecting matrix-valued outliers.
Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns
problem Optimal option portfolios under Sharpe Ratio maximization
method Formulation for explicit portfolio weights
result Different optimal portfolios for Sharpe Ratio and return-to-Value-at-Risk (VaR) ratio
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-var…
A new operator based on t-distributions improves NN classifiers' robustness to out-of-distribution samples.
problem NN classifiers assign extreme probabilities to out-of-distribution samples, leading to unreliable predictions.
method Derive a novel operator using t-distributions to model uncertainty more accurately.
result Classifiers using the new operator are more robust to out-of-distribution samples.
Adaptive t-distribution estimates nonstationary time series using moving moments.
problem Nonstationary time series with varying dependence structure.
method Moving estimator optimizing a weighted log-likelihood, using exponential moving averages for moments.
result Evolution of ν parameter in Student's t-distribution, capturing tail behavior and extreme events.
A new filter adapts to heavy-tailed data without tuning, improving performance in challenging conditions.
problem Degraded performance of Kalman and EnKF in heavy-tailed distributions.
method Generalizes EnKF using t-distributions, estimating parameters via EM algorithm.
result Improves performance on challenging filtering problems with heavy-tailed noise.
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of th…
Improved image reconstruction using VAEs with Student's t-prior.
problem Improving the robustness of VAEs in image reconstruction.
method Proposed a VAE with Student's t-distribution as prior, trained all distribution parameters.
result Better image reconstruction achieved with Student's t-prior compared to Gaussian priors.
The probability distribution of log-returns of financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of time series on futures. Then, we show that the t-distribution with ν≃3 gives…
Proposes a robust factor analysis for matrix data.
problem Robust factor analysis for matrix data with heavy-tailed or contaminated data.
method Bilinear factor analysis based on the matrix-variate t distribution. result Significantly higher breakdown point than traditional methods.
Paper studies t-SNE convergence with generalized kernels.
problem Understanding convergence of t-SNE with generalized kernels.
method Concrete formulation of generalized kernels, proving convergence to an equilibrium distribution.
result t-SNE converges to an equilibrium distribution under certain conditions for generalized kernels.
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
Improved VAE for heavy-tailed data using Student's t-distributions.
problem Over-regularization in VAEs with Gaussian priors.
method Proposed t3VAE framework with Student's t-distributions for prior, encoder, and decoder. result Significantly outperforms other models on heavy-tailed datasets.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
We propose a robust method to estimate heteroscedastic noise models using Student's t-distribution.
problem Identifying cause and effect from bivariate observational data with non-Gaussian noise.
method We propose a novel approach using Student's t-distribution to estimate heteroscedastic noise models, which is more robust and achieves better performance.
result Our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.
New diffusion models capture heavy-tailed distributions better.
problem Diffusion models struggle with rare or extreme events in heavy-tailed distributions.
method Repurposed diffusion framework using multivariate Student-t distributions, tailored perturbation kernel, and γ-divergence. result Our models generate rare and extreme events more effectively than standard diffusion models.
We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed between choices of risk function (e.g. VaR vs CVaR); choice of return distribution (p…
Volatility is a key measure of risk in financial analysis. The high volatility of one financial asset today could affect the volatility of another asset tomorrow. These lagged effects among volatilities - which we call volatility spillovers - are studied using the Vector AutoRegressive (VAR) model. We account for the p…
A new update rule for deep reinforcement learning reduces learning variance and variance in reference signals.
problem Learning variance and incorrect reference signals in deep reinforcement learning.
method t-soft update method inspired by student-t distribution, which reduces extreme updates and accelerates similar updates.
result The t-soft update method outperforms conventional methods in terms of return and variance in PyBullet robotics simulations.
Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.
problem Underestimation of Value-at-Risk by traditional models in asset pricing.
method Developed an econometric framework combining heavy-tailed Student's t distributions with behavioral probability weighting. result Student's t specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points. Explains SNE, t-SNE, and their variants for manifold learning.
problem Dimensionality reduction and manifold learning.
method Probabilistic approach using Gaussian and Student-t distributions.
result Out-of-sample extension and acceleration methods for t-SNE.
TAdam optimizes machine learning models to resist noise effectively.
problem Noise in data, especially in robotics, hinders model performance.
method Integrates robust student-t distribution into Adam optimizer.
result TAdam outperforms Adam in robustness across various tasks.
We present a Kalman smoothing framework based on modeling errors using the heavy tailed Student's t distribution, along with algorithms, convergence theory, open-source general implementation, and several important applications. The computational effort per iteration grows linearly with the length of the time series, a…
The study compares VaR and ES models for tail risk of electricity futures, finding AR(1)-GARCH(1,1) with Student-t distribution best.
problem Modeling tail risk of electricity futures contracts in various markets.
method Comparison of VaR and ES models using AR(1)-GARCH(1,1) with Student-t distribution, historical simulation, and quantile regression.
result AR(1)-GARCH(1,1) with Student-t distribution is the best-performing model for tail risk estimation.
Flow cytometry is a high-throughput technology used to quantify multiple surface and intracellular markers at the level of a single cell. This enables to identify cell sub-types, and to determine their relative proportions. Improvements of this technology allow to describe millions of individual cells from a blood samp…
The study tackles modeling high-frequency financial data using continuous distributions, finding them inadequate.
problem Challenges in modeling high-frequency integer price changes with continuous distributions.
method Proposed a modified maximum likelihood estimation procedure to account for the discreteness of high-frequency price changes.
result Traditional GARCH models are not suitable for high-frequency data due to the discreteness of price changes.
Optimizes option portfolios for skewed-t returns using VaR and variance measures.
problem Optimizing portfolios for skewed-t returns with heavy tails and skewness.
method Uses variance and VaR measures, departing from normal returns, and provides explicit portfolio weights.
result Optimal portfolio weights differ significantly from variance optimal weights due to skewness.
A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model o…
New method infers co-expression networks robustly from multiple studies.
problem Challenges in inferring co-expression networks from transcriptome data.
method Robust method based on multivariate t-distribution with shared precision matrix.
result Identifies co-expression matrix up to scaling factor.
A new method uses a product of experts with Dirichlet variables to approximate complex distributions.
problem Approximating complex distributions with tractable models.
method A product of experts with auxiliary Dirichlet variables, using a Feynman identity to sample and optimize.
result The method efficiently approximates complex distributions using a product of experts and Dirichlet variables.
The time development of the price of a financial asset is considered by constructing and solving Langevin equations for a homogeneously saturated model, and for comparison, for a standard model and for a logistic model. The homogeneously saturated model uses coupled rate equations for the money supply and for the price…
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…
I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with Student-t distributions. The results may serve as illustrative examples for option pricing …
Improved normalising flows using Student's t-distribution for robust training.
problem Training deep probabilistic models with robust statistics.
method Propose Student's t-distribution as a robust alternative to Gaussian in normalising flows.
result Improved robustness and reduced generalization gap with Student's t-distribution.
T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient imple…
In this paper, we generalize the parametric Delta-VaR methods from portfolios with elliptic distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of the mixtur…