Student- processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student- processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the h…
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48 results for “Student-t Priors”
Bayesian neural networks approximate Student-t processes in the infinite-width limit.
problem Modeling uncertainty in neural networks with greater flexibility.
method Extending asymptotic properties of Gaussian processes to Student-t processes in the infinite-width limit of BNNs.
result Posterior BNNs converge to Student-t processes in the infinite-width limit.
New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
A VB method for high-dimensional regression with student-t priors achieves nearly optimal performance and computational efficiency.
problem High-dimensional linear model inferences with heavy-tailed shrinkage priors.
method Variational Bayesian (VB) procedure for high-dimensional linear models with student-t priors.
result The VB method achieves nearly optimal contraction rate and computational efficiency, outperforming MCMC methods.
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 -divergence.
result Our models generate rare and extreme events more effectively than standard diffusion models.
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear reg…
In this paper, a generalized multivariate Student-t mixture model is developed for classification and clustering of Low Probability of Intercept radar waveforms. A Low Probability of Intercept radar signal is characterized by a pulse compression waveform which is either frequency-modulated or phase-modulated. The propo…
Online Student- Processes with an Overall-local Scale Structure for Modelling Non-stationary Datastat.ML
Proposes a new Bayesian mixture of student-t processes for modeling non-stationary data.
problem Non-stationary data with non-Gaussian errors.
method Bayesian mixture of student-t processes with an overall-local scale structure, using SMC for online inference.
result Superior performance compared to Gaussian processes on real-world data.
Paper develops methods for estimating and simulating a Student-t Lévy regression model.
problem Estimation and simulation of Student-t Lévy process with arbitrary degrees of freedom.
method Develops a two-step estimation procedure and simulates increments using inverse Fourier transform.
result Efficient estimation and simulation methods for Student-t Lévy process.
Inter-order relations between moments of a Student distribution, with an application to -quantilesmath.ST
The paper derives formulas for moments of a Student t distribution and applies them to quantify -quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between -quantiles.
result For a Student t distribution, the -quantile and -quantile coincide at any confidence level.
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…
Proposes a VAE with Student- mixture model for authorship attribution.
problem Traditional authorship attribution in closed-set scenarios.
method Extends variational autoencoder with embedded Student- mixture model.
result Superior performance over existing methods on Amazon review dataset.
Minimal Variance Hedging of Options with Student-t Underlyingcond-mat.stat-mech
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 …
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several approximative methods have been proposed. The expectation propagation (EP) has been found …
Method introduces topological regularization using information filtering networks.
problem Sparse probabilistic modeling and multicollinear regression.
method Topological regularization via information filtering network.
result Direct application to -norm regularized problems.
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.
A robust loss for anomaly mitigation and unsupervised contamination classification
problem Detecting and mitigating contamination in supervised and unsupervised settings
method Neural Bayesian Anomaly Mitigation (NBAM)
result Recovering the structure of contamination and identifying label-flip pairs
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
Extended PELCoV for bivariate Student-t copulas to monitor foreign exchange risk.
problem Monitoring financial risk under asymmetric co-movements and tail dependence.
method Extending PELCoV to Student-t copulas, tracking dynamic risk spillovers.
result Potential to detect early signs of risk underestimation during financial stress.
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
Researchers derived formulas for joint moments of elliptical distributions.
problem Calculating joint moments of elliptical distributions.
method Used Stein's lemma and two different methods to derive expressions.
result New formulae for expectations of product of normally distributed random variables and simplified expressions for other distributions.
AIS algorithm improves heavy-tailed distribution estimation.
problem Inconsistent estimators and slow convergence in AIS for heavy-tailed distributions.
method Adapts Student-t proposal distributions by matching escort moments and minimizing α-divergence.
result Improves estimation accuracy for heavy-tailed distributions.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
COS method convergence conditions expanded for heavy-tailed distributions.
problem Ensuring convergence of the COS method for various densities.
method Analyzing truncation error and providing conditions for convergence.
result Conditions for COS method convergence extended to include heavy-tailed distributions.
Bayesian realized EGARCH models improve tail risk forecasting.
problem Forecasting tail risks in financial markets.
method Developed a Bayesian framework for realized EGARCH models, incorporating multiple realized volatility measures and using robust adaptive Metropolis algorithm for estimation.
result Standardized skewed Student-t distribution and sub-sampled realized range models outperform other models in tail risk forecasting.
This note presents an operational measure of fat-tailedness for univariate probability distributions, in where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size needed to establish a comparative needed for statistical significance, 2) allows…
In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM…
Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable a…
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…
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.
Develops a robust model for skewed and heavy-tailed data in periodontal studies.
problem Skewed and heavy-tailed data in periodontal pocket depth measurements.
method Flexible two-piece scale Student-t error distribution and deep neural network with monotonicity constraints.
result Robust mode-based estimation resistant to outliers with clinical interpretability.
DSPM models control noise volatility, improving financial data analysis.
problem Financial returns exhibit volatility clustering, challenging traditional models.
method DSPM uses a tempered-stable subordinator to control noise volatility, preserving kurtosis and autocorrelation.
result DSPM models accurately capture volatility clustering and noise mechanisms.
MCMC complexity matches optimization for large and .
problem Lack of theoretical understanding of MCMC complexity for large and .
method Comparison of MCMC, LA, and VI complexities for linear, logistic, and Poisson regression.
result MCMC complexity matches optimization complexity for .
Enhances neural processes for better context handling.
problem Real-world context sets are complex, requiring richer prior distributions.
method Introduces a graphical model for a richer prior on latent variables, enabling end-to-end optimization.
result Improves function modeling and test-time robustness with mixture and Student-t assumptions.
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.
This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and inference, and are governed by interpretable hyperparameters. However, GP models…
Tail Risk of Electricity Futuresq-fin.RM
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.
Bayesian optimization has recently attracted the attention of the automatic machine learning community for its excellent results in hyperparameter tuning. BO is characterized by the sample efficiency with which it can optimize expensive black-box functions. The efficiency is achieved in a similar fashion to the learnin…
Some Remarks on T-copulasq-fin.RM
We examine three methods of constructing correlated Student- random variables. Our motivation arises from simulations that utilise heavy-tailed distributions for the purposes of stress testing and economic capital calculations for financial institutions. We make several observations regarding the suitability of the …
Neural GARCH models financial time series with time-varying coefficients.
problem Modeling conditional heteroskedasticity in financial time series.
method Neural network adaptation of GARCH and BEKK models with time-varying coefficients parameterized by a recurrent neural network.
result Neural Students t model consistently outperforms other models on financial time series.
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noi…
We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic samplers, in particular with heavy-tailed simulation noise and low signal-to-no…
Paper presents a new probabilistic approach for high-dimensional quantile prediction.
problem High-dimensional quantile prediction challenges in robust statistical methods.
method Pseudo-Bayesian framework with scaled Student-t prior and Langevin Monte Carlo.
result Demonstrates strong theoretical guarantees and competitive performance in simulations and real-world data.
We employ and examine vine copulas in modeling symmetric and asymmetric dependency structures and forecasting financial returns. We analyze the asset allocations performed during the 2008-2009 financial crisis and test different portfolio strategies such as maximum Sharpe ratio, minimum variance, and minimum conditiona…
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…
BayPrAnoMeta tackles few-shot industrial image anomaly detection with Bayesian methods.
problem Challenges in industrial image anomaly detection, especially class imbalance and scarcity of labeled samples.
method Bayesian Proto-MAML approach with probabilistic normality models and Bayesian posterior predictive likelihood.
result Consistent and significant AUROC improvements over existing methods in few-shot anomaly detection.