Modeling exchange rates and options using entropic dynamics.
problem Modeling the dynamics of exchange rates and European options.
method Entropic Dynamics, entropic inference, scale invariance, logarithm of exchange rate.
result Derives the Geometric Brownian Motion and the Garman-Kohlhagen model for European options.
New method improves approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
Entropic framework models stock and option dynamics.
problem Modeling stock and option dynamics with incomplete information.
method Entropic inference framework, scale invariance, Fokker-Planck equation, risk-neutral measure.
result Derives dynamics of stock and option prices using entropic inference.
A new method for inferring latent states in Markov jump processes.
problem Intractable exact inference for Markov jump processes.
method Entropic matching within expectation propagation.
result Superior performance in approximating the mean of the posterior process.
Entropic herding generates smooth distributions for probabilistic modeling.
problem Generating smooth distributions for probabilistic modeling.
method Derives entropic herding as optimization of maximum entropy principle.
result Entropic herding generates smoother distributions than original herding.
The paper proposes a method to estimate joint probability from unpaired data using entropic transport kernels.
problem Estimating joint probability from unpaired data with unknown internal ordering.
method Maximum-likelihood inference, entropic optimal transport kernels, EMML algorithm.
result The method can recover true density from empirical approximations as the number of blocks increases.
Estimates conditional Brenier maps using entropic optimal transport.
problem Non-parametric estimation of conditional Brenier maps.
method Entropic optimal transport for scalable non-parametric estimation.
result Entropic optimal transport maps asymptotically converge to conditional Brenier maps.
A new method for efficient inference and model selection in SBMs using OT.
problem Efficient inference and model selection in stochastic block models.
method Interpreting MLVI as srGW with entropic regularization, then unregularizing for sparse solutions, and adding a sparsity-promoting regularizer.
result The method consistently recovers SBM parameters and selects the number of clusters in finite samples.
Introduces entropic tribrackets and their applications in link distinguishing.
problem Distinguishing links with the same counting invariant.
method Definition and study of entropic tribrackets and their homsets.
result Homsets of entropic tribrackets form new entropic tribrackets.
SDPA is shown to be an optimal transport problem in deep learning.
problem The mathematical foundation and optimization perspective of SDPA.
method SDPA is shown to be the exact solution to a degenerate, one-sided Entropic Optimal Transport (EOT) problem.
result The SDPA mechanism is a principled mechanism where the forward pass performs optimal inference and the backward pass implements a rational, manifold-aware learning update.
We define link and graph invariants from entropic magmas modeling them on the Kauffman bracket and Tutte polynomial. We define the homology of entropic magmas. We also consider groups that can be assigned to the families of compatible entropic magmas.
This work presents entropic constraints from DAGs with hidden variables.
problem Characterizing causal relations in systems with hidden variables.
method Entropic inequality constraints derived from e-separation relations. result These constraints can learn about true causal models from observed data.
New loss improves OOD detection without extra data or tuning.
problem Improving OOD detection without additional data or tuning.
method Proposed IsoMax loss and entropic score to replace SoftMax loss.
result Training with IsoMax loss significantly improves OOD detection performance.
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.
problem Optimal transportation between Gaussian distributions with different dimensions.
method Entropic Gromov-Wasserstein and inner product Gromov-Wasserstein, with closed-form expressions and von Neumann's trace inequality.
result Closed-form expressions for the entropic IGW and its unbalanced variant between Gaussian distributions.
Kernel SVGD improves high-dimensional inference with noise adaptation.
problem Challenges in high-dimensional inference with SVGD.
method Noise Conditional Kernel SVGD (NCK-SVGD) with entropic regularization.
result NCK-SVGD produces samples comparable to GANs and SGLD on computer vision benchmarks.
Paper proves causal direction can be inferred from data with limited randomness.
problem Inferring causal direction from observational data with limited randomness.
method Entropy measurement and structural causal models.
result Causal direction is identifiable for most causal models with limited entropy.
Improved neural framework for scaling entropic MOT with significant computational gains.
problem High computational overhead in multimarginal optimal transport.
method Neural Entropic MOT (NEMOT) using mini-batch training to reduce complexity.
result Significant speedups and feasibility improvements for multimarginal data.
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
This paper uses entropy to derive stock price dynamics and option valuation.
problem Deriving stock price dynamics and option valuation from information constraints.
method Develops an entropic inference framework to derive stochastic processes from information constraints, representing price changes through two channels: continuous and jump.
result The derived dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit.
The paper studies convergence rates of Tsallis entropic regularization in optimal transport.
problem Optimal transport with regularization.
method Γ-convergence and quantization/shadow arguments.
result Derives convergence rate of Tsallis entropic regularization.
Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.
problem Formulating both Bakry-Émery and entropic curvature simultaneously.
method Generalization of Bakry-Émery calculus, new measure optimality criterion, dimension parameter in entropic curvature.
result Diameter estimates for Markov chains with strictly positive entropic curvature and spectral gap.
Paper explores entropic curvature in Markov chains, comparing it to other curvatures.
problem Comparing entropic curvature to other curvatures in Markov chains.
method Adapted Γ-calculus for θ-curvatures, explicit lower bounds, curvature perturbation.
result Entropic curvature differs significantly from other curvature notions.
ERTS uses Thompson sampling for Gaussian entropic risk bandits, achieving regret bounds.
problem Risk in decision making complicates reward maximization in MAB problems.
method ERTS (Entropic Risk Thompson Sampling) using Thompson sampling with an entropic risk measure.
result Regret bounds for ERTS under entropic risk measure provided.
Study entropic regularization of Gaussian measures and processes on Hilbert space.
problem Regularizing 2-Wasserstein distance for infinite-dimensional Gaussian measures and processes.
method Minimum Mutual Information property, closed form formulas, Fréchet differentiability, Sinkhorn barycenter equation.
result Entropic 2-Wasserstein distance and Sinkhorn divergence are Fréchet differentiable in Hilbert space.
Researchers calculated EVaR for various distributions using Lambert function.
problem Difficulty in finding analytical representation of EVaR measure.
method Used Lambert function to calculate EVaR for multiple distributions.
result Successfully calculated EVaR for 7 specific distributions.
In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter λ≥0. Our method unifies hard and soft clustering, the Expectation-Maximization (EM) algorithm being exactly recovered for λ=1. The family of cl…
Efficiently computes optimal policies for Entropic Risk Measures.
problem Optimizing risk-sensitive metrics in MDPs is computationally expensive.
method Uses Entropic Risk Measures and novel structural analysis for efficient computation.
result Achieves strong performance in various decision-making scenarios.
Efficiently estimates optimal transport maps with rigorous guarantees.
problem Estimating optimal transport maps between distributions efficiently.
method Entropic version of Brenier's theorem, Sinkhorn's algorithm.
result Estimator is parallelizable and efficient for massive data sets.
New risk measures incorporate economic states to assess crude oil derivatives.
problem Assessing risk in crude oil derivatives with varying economic conditions.
method Introduced regime switching entropic risk measures using Markov chains.
result Closed formulae for risk measures derived, showing term structure and mean-reverting convenience yield.
The paper connects tempering and entropic mirror descent for sampling.
problem Sampling from a target distribution with known unnormalized density.
method Establishes the connection between tempering SMC and entropic mirror descent, deriving convergence rates and geometric insights.
result Tempering SMC iterates correspond to entropic mirror descent on the reverse KL divergence, providing new optimization perspectives.
Sparse attention model reduces long-context inference time with exponential accuracy guarantees.
problem Efficiently processing long-context queries in large language models.
method Formalizes attention as a projection onto key vectors, analyzes entropic relaxation, and introduces Vashista Sparse Attention.
result Sparse attention concentrates on a constant-size active face, leading to exponential decay of inactive tokens' mass and linear scaling of active face error.
We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially o…
Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long maturities. We show that forward …
The paper improves convergence for linear systems using entropic mirror descent with Polyak stepsizes.
problem Convergence analysis for linear systems with unbounded domain.
method Entropic mirror descent with Polyak stepsizes, sublinear and linear convergence results.
result Generalized convergence result for arbitrary convex functions.
In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL). A Tsallis MDP provides a unified framework for the original RL problem and RL with various types of entropy, includin…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial constraints on the observed distribution. Here, we propose an information-theoretic appr…
New method corrects bias in estimating entropic risk for better decision-making.
problem Underestimation of entropic risk when data are limited.
method Parametric bootstrap procedure to overestimate entropic risk.
result Corrected method provides better risk estimates, leading to improved decision-making.
Solving linear programs by using entropic penalization has recently attracted new interest in the optimization community, since this strategy forms the basis for the fastest-known algorithms for the optimal transport problem, with many applications in modern large-scale machine learning. Crucial to these applications h…
The paper develops efficient algorithms for variational inference with mixtures of isotropic Gaussians.
problem Efficiently approximating multimodal Bayesian posteriors.
method Develops a variational framework and efficient algorithms for mixtures of isotropic Gaussians.
result The approach provides accurate approximations of multimodal Bayesian posteriors while being memory and computationally efficient.
sEM uses optimal transport to improve EM algorithm for better convergence and avoiding local optima.
problem Improving the EM algorithm for better convergence and avoiding local optima.
method sEM uses entropic optimal transport to compute responsibilities in the expectation step, leading to better global convergence guarantees and avoiding local optima.
result sEM learns cell labels significantly better than other approaches, improving convergence and avoiding local optima.
Unified framework for optimal transport on curved spaces using neural potentials.
problem Optimal transport on curved Riemannian manifolds.
method Entropic RNOT combines entropic regularization with neural pullback parameterization.
result Unified framework recovers entropic optimal coupling in strong probabilistic metrics.
Upper bound derived for informed traders' gains in a model, akin to thermodynamics.
problem Informed traders' gains in a financial model with finite horizon.
method Bayesian inference and entropic inequality.
result Upper bound for expected gain, analogous to thermodynamics.
The study finds a diameter bound for graphs with positive entropic Ricci curvature, with optimal bounds for arithmetic mean.
problem Finding diameter bounds for graphs with positive entropic Ricci curvature.
method Using a localized gradient estimate and an equivalent definition of entropic Ricci curvature, the study derives a Bonnet-Myers type diameter bound.
result The derived diameter bound is optimal for arithmetic mean, but not for logarithmic mean.
ePF improves PF for ITS by balancing exploration and exploitation, outperforming baselines.
problem Premature exploitation in PF leads to suboptimal solutions under constrained budgets.
method Integrates Entropic Annealing and Look-ahead Modulation to preserve diversity and evaluate potential.
result Significant improvement in task reward (up to 50% relative) on math benchmarks.
Paper proposes risk-averse reinforcement learning algorithms.
problem Managing model uncertainty in reinforcement learning.
method Entropic risk constrained policy gradient and actor-critic algorithms.
result Demonstrates usefulness of risk-averse algorithms on various domains.
New curvature measure improves graph neural network performance.
problem Oversmoothing and oversquashing in GNNs due to local edge comparisons.
method Introduces Entropic Curvature, a global transport-based curvature.
result Entropic Curvature unifies oversmoothing and oversquashing as opposite ends of a curvature spectrum.
Simplified explanation of ML for mixtures and OT.
problem Maximum likelihood estimation for mixture models.
method Optimal transport with entropic regularization.
result EM algorithm is a block-coordinate descent on OT loss.