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 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 …
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the assoc…
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. To reduce the large computation and storage cost of a deep convolutional neural network, the knowledge distillation based methods have pioneered to transfer the generalization ability of a large (teacher) deep network to a light-weight (student) network. However, these methods mostly focus on transferring the probabili…
Distilled models often fail to match teacher models, despite improving generalization.
problem The discrepancy between teacher and student predictive distributions remains large.
method Investigated the optimization difficulties and dataset details affecting student performance.
result Optimizing for matching the teacher does not always lead to better generalization.
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…
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.
Deep neural networks forecast financial return distributions accurately.
problem Forecasting probability distributions of financial returns.
method Used 1D CNN and LSTM architectures with custom loss functions to optimize distribution parameters.
result LSTM with skewed Student's t distribution outperformed classical models in multiple evaluation metrics.
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…
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…
Spaced repetition is among the most studied learning strategies in the cognitive science literature. It consists in temporally distributing exposure to an information so as to improve long-term memorization. Providing students with an adaptive and personalized distributed practice schedule would benefit more than just …
A new teacher-class network method compresses DNNs by distributing knowledge to multiple student networks.
problem Overwhelming size of Deep Neural Networks (DNNs).
method Single teacher with multiple student networks, transferring knowledge to each student.
result The combined knowledge of the class of students achieves better performance and reduces parameters.
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.
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.
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.
ReOPD uses pre-collected teacher trajectories to distill knowledge from multi-turn interactions.
problem The cost of fully online on-policy distillation for multi-turn interactions.
method ReOPD, an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes, addressing the prefix trap and distribution shift.
result ReOPD preserves or improves OPD-level accuracy, uses zero tool calls, and is at least 4imes faster per training step. 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.
Extracurricular learning closes the accuracy gap in knowledge distillation.
problem Accuracy gap between teacher and student models after knowledge distillation.
method Modeling student and teacher output distributions, sampling from an extended data distribution, and matching over this set.
result Extracurricular learning reduces the accuracy gap by 46% to 68%.
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. 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.
Paper uses econometrics time series model with T-student Distribution for short-term load forecasting.
problem Accurate short-term load forecasting for optimizing electrical sources and protecting energy.
method Uses SARIMA-GARCH model with T-student Distribution to forecast electric load.
result The proposed model outperforms the ARIMA model with Normal Distribution.
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 new distillation method transfers channel information from teacher to student.
problem Transfer knowledge from teacher to student with fewer parameters and calculations.
method Channel Distillation (CD) and Guided Knowledge Distillation (GKD) with loss decay.
result Achieved 27.68% top-1 error on ImageNet with ResNet18, outperforming state-of-the-art methods.
Study analyzes catastrophic forgetting in continual learning using teacher-student networks.
problem Catastrophic forgetting in continuously learning systems.
method Teacher-student learning framework, similarity of input distributions and target functions.
result Network can avoid catastrophic forgetting with small input distribution similarity and large target function similarity.
Study shows financial literacy, social capital, and financial tech positively impact financial inclusion of Indonesian students.
problem Financial literacy, social capital, and financial technology's impact on financial inclusion of Indonesian students.
method Quantitative research using questionnaires distributed to 100 students from 7 private colleges in Tangerang, Indonesia.
result Financial literacy, social capital, and financial technology have a positive and significant influence on financial inclusion.
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.
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.
Bayesian Dark Knowledge is a method for compressing the posterior predictive distribution of a neural network model into a more compact form. Specifically, the method attempts to compress a Monte Carlo approximation to the parameter posterior into a single network representing the posterior predictive distribution. Fur…
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…
Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the process underlying student choices. We propose a probabilistic approach to modellin…
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.
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 …
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…
This paper distills Bayesian posterior expectations for deep neural networks.
problem Improving deep neural network performance and uncertainty quantification.
method Develops a framework for distilling expectations from Bayesian posterior distributions using Monte Carlo samples.
result The framework successfully distills posterior predictive distribution and expected entropy.
Analyzes Hessian spectrum for neural networks near optimal learning.
problem Understanding learning dynamics near optimal points in neural networks.
method Characterizes Hessian eigenspectrum for teacher-student problems, using analytical and numerical methods.
result The rank of the Hessian matrix determines effective number of parameters for non-linear networks.
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 L0-norm regularized problems. Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
problem Limitations of inverse covariance matrix in non-Gaussian settings.
method Exploits local dependence function to define generalized precision matrix (GPM) for multivariate t-Student distribution.
result GPM leads to statistically significant lower out-of-sample variances in minimum-variance portfolios.
A new system recommends specific knowledge concepts in MOOCs based on student interests.
problem MOOCs recommend courses but ignore specific knowledge concepts interests.
method End-to-end graph neural network (ACKRec) that combines content and context information.
result ACKRec effectively recommends knowledge concepts to MOOC students.
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.
This note presents an operational measure of fat-tailedness for univariate probability distributions, in [0,1] 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 n needed for statistical significance, 2) allows…
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.
New theory explains how strong models can learn from weak ones.
problem Learning from weak, incomplete, or incorrect labels.
method New bounds based on data distribution and student hypothesis class.
result Existing weak supervision theory fails to account for pseudolabel correction and coverage expansion.
A new method predicts student skill success rates in real-time.
problem Accurate and explainable prediction of student skill success rates in real-time.
method Performance Distribution Tracing (PDT) using a Dynamic Bayesian Network with continuous random variables.
result PDT provides both explainability and accuracy in real-time predictions of student skill success rates.
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.
Under-parameterized networks can either copy or average teacher weights, leading to universal optimal solutions.
problem Approximating a teacher network with an under-parameterized student network.
method Analyzing shallow neural networks with erf activation function and unitary teacher weights, proving copy-average configurations are critical points and finding the optimal solution.
result The optimal solution for under-parameterized networks has a universal structure, whether copying or averaging teacher neurons.
A new method identifies a stable subnetwork in overparameterized student models.
problem Identifying a stable subnetwork in overparameterized student models.
method Spectral representation of linear transfer of information, focusing on eigenvalues and eigenvectors.
result A stable student substructure is isolated that mirrors the true complexity of the teacher.