arXiv research

Optimal hedging framework with variational preferences under convex risk measures.

Solves a problem related to dual Orlicz curvature measure.

We derive a formula for the first variation of horizontal perimeter measure for $C^2$ hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For $C^2$ hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for var…

The abstract discusses extending learning objectives to measure theory for better generalization.

A new method for stochastic integration using superhedging.

The paper develops a new approach to conditional risk measures using modular convex analysis.

New concept of sparse regular variation for better understanding of extreme events.

A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.

Study shows how to reduce variational inference bias by concentrating likelihood ratio distribution.

New model resolves signal ambiguities in ill-posed systems.

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

First variation of fractional $k$-dimensional measure for submanifolds

We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of M…

This paper refines human labeling as a measurement process, revealing four sources of variation.

The paper studies the dimension of limit sets using variational principles and stationary measures.

Paper introduces hybrid curves moduli space and canonical measures.

The paper studies stability of mean-field variational inference for log-concave distributions.

New definition of disentanglement for non-independent factors of variation.

Bayesian hierarchical models are increasing popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide f…

This paper studies asymptotic multivariate expectiles in risk measures.

Proposes variance reduction techniques for sliced Wasserstein distance estimation.

Proves sufficiency of countable test plans for BV functions on metric spaces.

A new measure helps compute suboptimality in entropy-regularized methods.

We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Per…

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that…

A new method for efficient sampling from probability measures.

Paper presents a new VMBQC model with fewer parameters for better generative modeling.

Study improves convergence rates for GVI under prior misspecification.

This work proposes new methods for variational inference using gradient flows on Gaussian measures.

Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the…

GWI combines deep neural networks with Gaussian processes for better predictive performance and uncertainty quantification.

VSE estimates complex processes from noisy measurements without a model.

A new method using spherical harmonics approximates the Sliced-Wasserstein distance.

This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …

Proposes variational Wasserstein barycenters for geometric clustering.

CAVI converges for log-concave measures via optimal transport.

We determine necessary conditions for a non-horizontal submanifold of a sub-Riemannian stratified Lie group to be of minimal measure. We calculate the first variation of the measure for a non-horizontal submanifold and find that the minimality condition implies the tensor equation $H+σ=0$, where $H$ is analogous to the…

Paper uses VAEs to measure distance between high-dimensional datasets.

Optimizes kernel density ratios for better predictions and information measures.

The hermitian analog of Aleksandrov's area measures of convex bodies is investigated. A characterization of those area measures which arise as the first variation of unitarily invariant valuations is established. General smooth area measures are shown to form a module over smooth valuations and the module of unitarily …

Geometric framework analyzes bias in variational inference for posterior functionals.

Develops a new framework for analyzing MFVI algorithms.

A new algorithm solves sparse optimization problems on measures efficiently.

We propose a definition of the weighted $σ_k$-curvature of a smooth metric measure space and justify it in two ways. First, we show that the weighted $σ_k$-curvature prescription problem is governed by a fully nonlinear second order elliptic PDE which is variational when $k=1,2$ or the smooth metric measure space is lo…

We show that degenerate complex Monge-Ampere equations in a big cohomology class of a compact Kaehler manifold can be solved using a variational method independent of Yau's theorem. Our formulation yields in particular a natural pluricomplex analogue of the classical logarithmic energy of a measure. We also investigate…

New variational bounds improve posterior covariances and likelihoods.

Softplus normalization improves uncertainty estimation in Bayesian CNNs.

This paper develops bootstrap methods to assess uncertainty in variational inference.