A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Derives Lagrangian for minimal surfaces, proving tangential variations vanish.
Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.
This tutorial derives the VAE loss function under Gaussian assumptions.
Derives equations for systems with external forces using variational methods.
Derives a new variational approach to information bottleneck.
Derive Dirichlet scalar curvature energy functional variation formula
New statistical biharmonic maps derived from a variation problem.
Derives optimal control conditions using calculus of variations.
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
Derives new optimization methods using variational integrators.
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a part…
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…
Paper derives formulas for surface variations in shell theory.
New method scales Gaussian processes with derivatives using variational inference.
Paper derives invariantised Euler-Lagrange equations for Herglotz problems.
Derives VMP for LDA, simplifying inference for topic modeling.
Survey on probabilistic models and variational inference in deep RL.
Simplified Variational Bayes for easier inference.
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as the geometry varies in a particular way, which we call a conformal variation. This…
Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of mod…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well a…
VIND reduces gradient variance for non-Gaussian approximations.
This work gives an in-depth derivation of the trainable evidence lower bound obtained from the marginal joint log-Likelihood with the goal of training a Multi-Modal Variational Autoencoder (MVAE).
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily …
We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second variational derivative to vanish, {\em via} the Second Noether Theorem we find t…
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
In this short paper, we re-derive the Bochner formula for the Laplacian by considering local variations of volume. The derivation is rooted in the fact that the Laplacian of a function measures the volume variation along the flow of the gradient vector of the function. Possible extensions of this approach/technique are…
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are approximated by Gaussian sampling. These approaches are of particular interest …
Survey of factor analysis, PCA, variational inference, and VAE.
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The treatment of the distributions' subsets as variational parameters distinguishes …
We derive a formula for the first variation of horizontal perimeter measure for hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for var…
Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.
Euler derived elastica equation using modern mathematical concepts.
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational fo…
Inspired by the seminal work on Stein Variational Inference and Stein Variational Policy Gradient, we derived a method to generate samples from the posterior variational parameter distribution by \textit{explicitly} minimizing the KL divergence to match the target distribution in an amortize fashion. Consequently, we a…
A new method for efficient Gaussian process regression reduces complexity and improves scalability.
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expect…
Marginal MAP problems are notoriously difficult tasks for graphical models. We derive a general variational framework for solving marginal MAP problems, in which we apply analogues of the Bethe, tree-reweighted, and mean field approximations. We then derive a "mixed" message passing algorithm and a convergent alternati…
Study high-dimensional Bayesian linear regression using variational inference.
This paper bridges variational inference and Wasserstein gradient flows.
We derive asymptotic expansions for option data to detect infinite variation volatility.
New method reduces training cost by using approximate gradients.
We study a functional that derives from the classical Yang-Mills functional and Born-Infeld theory. We establish its first variation formula and prove the existence of critical points. We also obtain the second variation formula.
Variational inference has experienced a recent surge in popularity owing to stochastic approaches, which have yielded practical tools for a wide range of model classes. A key benefit is that stochastic variational inference obviates the tedious process of deriving analytical expressions for closed-form variable updates…
Derives FPDE for equity-linked insurance pricing.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
New variational principle found for PDEs with symmetries and conservation laws.
New quantum algorithm simplifies complex financial derivatives pricing.