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Found 13 papers, 3 papers with code
Emergence of heavy tails in homogenized stochastic gradient descent
It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters.
Hyperbolic Deep Learning in Computer Vision: A Survey
In this paper, we provide a categorization and in-depth overview of current literature on hyperbolic learning for computer vision.
State space decomposition and classification of term structure shapes in the two-factor Vasicek model
Using the concept of envelopes we show how to divide the state space $\RR^2$ of the two-factor Vasicek model into regions of identical term-structure shape.
W-shaped implied volatility curves in a variance-gamma mixture model
In liquid option markets, W-shaped implied volatility curves have occasionally be observed.
Bartlett's Delta revisited: Variance-optimal hedging in the lognormal SABR and in the rough Bergomi model
We derive analytic expressions for the variance-optimal hedging strategy and its mean-square hedging error in the lognormal SABR and in the rough Bergomi model.
Strain-Minimizing Hyperbolic Network Embeddings with Landmarks
We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only the distance measurements to a few 'landmark nodes'.
Hyperbolic Busemann Learning with Ideal Prototypes
To be able to compute proximities to ideal prototypes, we introduce the penalised Busemann loss.
A Theory of Hyperbolic Prototype Learning
We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space.
The hyperbolic geometry of financial networks
Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative curvature, i. e., by hyperbolic geometry.
The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach
We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates.
Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data
We introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space.
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance
Distance covariance is a quantity to measure the dependence of two random vectors.
Probability Statistics Theory Statistics Theory
Distance multivariance: New dependence measures for random vectors
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance.
Probability Statistics Theory Statistics Theory 62H20, 60E10, 62G10, 62G15, 62G20
