New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
The paper proves that certain price paths with jumps have consistent quadratic variation.
problem Understanding the quadratic variation of price paths with jumps in financial models.
method Proving the quadratic variation is consistent across different partitions of time.
result The quadratic variation of model-free price paths with mild jumps is consistent and independent of partitions.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
The paper shows that almost every path structure is not variational.
problem Determining if a path structure is variational.
method Generalized Douglas's result to higher dimensions and analyzed path geometries with infinitesimal symmetries.
result Almost every path structure is not variational.
Unified approach to DP problems using Gumbel distribution and variational Bayesian inference.
problem Solving classical optimal path problems in a probabilistic framework.
method Gumbel distribution and variational Bayesian inference for latent optimal paths.
result Unified approach transforms DP problems into directed acyclic graphs with Gibbs distribution.
This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume t…
A new method for stochastic integration using superhedging.
problem Existence of quadratic variation in stochastic processes.
method Using Vovk's outer measure to show the existence of quadratic variation for typical price paths.
result Developed a model-free Itô integration method based on robust quadratic variation.
Extends tracking guarantees for time-varying variational inequalities.
problem Tracking solutions of time-varying variational inequalities.
method Extends existing results to sublinear solution paths and periodic problems.
result Discrete dynamical systems of periodic time-varying VI can exhibit chaotic behavior or converge to the solution.
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…
Deep nets' complexity and risk are quantified using total path variation.
problem Quantifying the complexity and risk of deep neural networks.
method Using total path variation, the paper establishes relationships between network complexity and statistical risk.
result The statistical risk and metric entropy of deep nets are proportional to the total variation of path weights.
The paper studies metrics that match prescribed geodesics and introduces a variational problem.
problem Finding Riemannian metrics whose geodesics match given paths.
method Introduces a functional E on Riemannian metrics and computes its variational equations.
result Existence of conformally critical metrics in certain cases.
The paper extends first-order asymptotics for path-dependent derivatives in multiscale stochastic volatility.
problem Analyzing path-dependent derivatives in a multiscale stochastic volatility environment.
method First-order asymptotics analysis using Dupire's functional Ito calculus.
result Market parameters calibrated to vanilla options can price path-dependent derivatives to the same order.
Optimizes diffusion processes for target distributions.
problem Efficiently generating target distributions from point masses.
method Stochastic interpolant framework with conditional expectation drift.
result Optimal diffusion coefficient minimizes path-space KL divergence.
Study improves oracle inequality for tree graphs using total variation regularization.
problem Improving oracle inequality for tree graphs with total variation regularization.
method Generalized Fused Lasso result to tree graphs, using harmonic mean of distances.
result Proved a lower bound on compatibility constant for total variation penalty.
New control theory for self-path-dependent problems solves unique constraints.
problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.
New methods use machine learning to simulate rare transitions in molecular systems.
problem Simulating rare transitions between metastable states in molecular dynamics.
method Generative models and reinforcement learning for importance sampling.
result Efficiently generated transition paths linking metastable states.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths, where the qualification "typical" means that there is a trading strategy that risks …
Variational Bi-LSTM improves Bi-LSTM performance by jointly optimizing forward and backward paths.
problem Improving performance of Bi-LSTMs by capturing richer data representation.
method Proposes a Variational Bi-LSTM architecture that connects forward and backward paths during training.
result Shows state-of-the-art performance on various benchmarks.
Adaptive algorithm learns latent dynamical systems from sequential data.
problem Learning low-dimensional latent dynamical systems from high-dimensional sequential data.
method Combines amortized inference with path integral control to approximate inference.
result Proposed method leads to tighter lower bounds in sequential data learning.
New analysis of annealing paths in sampling and estimation.
problem Sampling from complex distributions and estimating normalization constants.
method Extending known results on Bregman divergence to quasi-arithmetic means under monotonic embedding.
result Analogous result for quasi-arithmetic means, highlighting the interplay between means, parametric families, and divergence functionals.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
Unified approach to stochastic control, filtering, and stopping using rough paths.
problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.
Derives FPDE for equity-linked insurance pricing.
problem Calculating prices for insurance policies with complex payment histories.
method Variational techniques in functional Itô calculus.
result Derives a functional partial differential equation.
Neural Diffusion Intensity Models simplify Cox processes inference.
problem Intractable nonparametric estimation and posterior inference of latent stochastic intensity in Cox processes.
method Variational framework using neural SDEs, with theoretical guarantee of ELBO maximization coinciding with maximum likelihood estimation.
result Accurate recovery of latent intensity dynamics and posterior paths with significant speedup.
A new path gradient estimator speeds up normalizing flows without sacrificing accuracy.
problem High computational cost and limited scalability of path gradient estimators for normalizing flows.
method Proposed a fast path gradient estimator that improves computational efficiency and scalability.
result The new estimator achieves superior performance and reduced variance across various applications.
PVI improves variational inference by constraining optimization paths.
problem Variational inference's sensitivity to initialization and local optima.
method Proximity Variational Inference (PVI) constrains optimization paths to find better local optima.
result PVI consistently finds better local optima and improves predictive performance.
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price path, without making any stochastic assumptions. It is shown that typical price …
Optimal transport with path constraints for distributions of different masses.
problem Comparing distributions with different total masses under path constraints.
method Introduces a model for unbalanced optimal transport with path constraints, proving existence of solutions.
result Existence of solutions to path constrained unbalanced optimal transport for various constraints.
Paper introduces a new gradient estimator for SNNs.
problem High variance in score function gradient estimator impedes SNNs training.
method Developed a differentiable point process to derive path-wise gradient estimator.
result Demonstrated effectiveness of path-wise gradient estimator through simulations.
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform estimates, have widespread application and have simplified proofs of basic questions fr…
Inference for SDEs using variational methods and neural networks.
problem Parameter inference for stochastic differential equations is challenging due to latent diffusion processes.
method Variational inference with a mean-field approximation for parameters and a recurrent neural network for diffusion paths.
result Accurate parameter estimates for SDE systems, demonstrated on Lotka-Volterra and epidemic models.
Foundation for robust finance using rough path theory.
problem Mathematical models of financial markets under Knightian uncertainty.
method Introducing Property (RIE) for càdlàg paths, proving existence of rough integrals, verifying admissibility of trading strategies.
result Existence and stability of rough path integrals for non-gradient integrands.
Develops diffusion samplers for target distributions with efficient score and density estimates.
problem Estimating scores and densities for time-varying distributions.
method Sequential Monte Carlo with diffusion paths and control variates.
result Effective samplers for time-varying distributions with theoretical guarantees and practical applications.
This paper bridges variational inference and Wasserstein gradient flows.
problem Combining variational inference and Wasserstein gradient flows for more efficient approximations.
method Recasting Bures-Wasserstein gradient flow as a Euclidean gradient flow and using path-derivative gradient estimator.
result A new gradient estimator for f-divergences that can be implemented using machine learning libraries. We derive a curvature-variation formula for a path of left-invariant metrics on a compact Lie group, beginning at a bi-invariant metric. We prove rigidity theorems for paths which remain nonnegatively curved, and we make progress towards a classification of the left-invariant metrics with nonnegative curvature on SO(4)…
New relation on paths is not transitive.
problem Extending tree-like property to non-Lipschitz paths.
method Analyzing a fractal construction in the plane.
result The resulting relation is not an equivalence relation.
The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.
problem Finding optimal paths on manifolds avoiding obstacles.
method Study of sufficient conditions for optimality on Riemannian manifolds and Lie groups.
result New conditions for optimality are provided in terms of matrix invertibility.
Optimizes online learning with noisy gradient feedback for slowly changing minimizers.
problem Optimizing online learning performance with noisy gradient feedback for slowly changing minimizers.
method Introduces a path variation metric to analyze dynamic regret under true and noisy gradient feedback.
result Achieves optimal dynamic regret bounds under various feedback scenarios.
We find approximate geodesics in deep models using graph shortest paths.
problem Computational complexity of finding geodesics in high-dimensional latent spaces.
method Approximate geodesics via shortest paths in a finite graph of samples.
result Applicable to high-dimensional problems, e.g., visual data.
Introduces q-paths for generalizing geometric annealing paths in machine learning.
problem Limited applicability of existing path methods in machine learning.
method Develops a family of paths derived from a generalized mean, including geometric and arithmetic mixtures.
result Empirical gains in Bayesian inference and generative model evaluation.
PAN improves graph neural networks using path integrals.
problem Efficiency and performance of graph neural networks.
method PAN uses path integrals to generalize graph Laplacian, incorporating all paths between nodes.
result PAN achieves state-of-the-art performance on benchmark tasks.
The article calculates the most-likely path for Asian option pricing in local volatility models.
problem Approximating the price of Asian options in local volatility models.
method Path-integral approach using Brownian bridge and Laplace asymptotic formula.
result The most-likely path (MLP) is found to approximate the option price in the limit of small sampling time.
In this paper we consider two generalizations of the Skyrme model. One is a variational problem for maps from a compact three-manifold to a compact Lie group. The other is a variational problem for flat connections. We describe the path components of the configuration spaces of smooth fields for each of the variational…
New algorithms minimize dynamic regret in non-stationary online learning.
problem Universal dynamic regret minimization under exp-concave and smooth losses.
method Strongly Adaptive algorithms with a path variational based on second order differences of the comparator sequence.
result Achieve a dynamic regret of ildeO(d2n1/5Cn2/5∨d2), optimal modulo dependencies. Paper proposes financial schemes that exploit the Axiom of Choice for quick gains.
problem Financial quick gains through non-degenerate price paths.
method Trading schemes based on the Axiom of Choice, considering continuous and positive price paths.
result Schemes can lead to infinite wealth under certain conditions, but are impractical due to the Axiom of Choice.
Study singular curves on subriemannian spaces that don't affect homotopy types.
problem Understanding how singular curves affect the topology of horizontal paths.
method Analyzing the subriemannian energy and endpoint map to identify homotopically invisible curves.
result For d≥3, generic subriemannian structures have only homotopically invisible singular curves. Paper approximates Gaussian process regression using variational methods.
problem Approximating Gaussian process regression efficiently.
method Represented as a stochastic differential equation, variational inference used for approximation.
result Approximations are as good as full Gaussian process regression.