The study characterizes diffusion model generalization using data-dependent ridge manifolds.
problem Understanding where diffusion model-generated samples lie when not memorizing the training set.
method Introduced a time-dependent family of log-density ridge manifolds to characterize reverse-time inference.
result Generated samples evolve by a reach-align-slide mechanism, controlled by normal and tangential components of training error.
A new trading strategy using reinforcement learning for statistical arbitrage.
problem Traditional statistical arbitrage models rely on model assumptions and price deviations from a long-term mean.
method Empirical reversion time metric, reinforcement learning framework, and state space optimization.
result Optimal mean reversion strategy identified through reinforcement learning.
LatentFlow simplifies conditioning of stochastic processes without training.
problem Intractable conditional laws for complex stochastic models.
method Writing stochastic process as latent innovation, reducing conditioning to latent-space inference.
result Exact conditional sampling across various model classes.
The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.
problem Understanding and controlling errors in discrete-time DDPMs.
method Structural analysis of score functions, Schrödinger's problem, and FBSDEs.
result Explicit upper bound for total variation distance between sampling and target distributions.
Adaptive learning of SPDE solutions using score-based diffusion models.
problem Model errors and reduced accuracy in SPDE solutions due to incomplete physical knowledge and environmental variability.
method Score-based diffusion models with recursive Bayesian inference, incorporating simulation data and observational information.
result Accuracy and robustness of the proposed method demonstrated on benchmark SPDEs.
New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.
problem Numerical stability issues in diffusion sampling despite small forward-marginal error.
method Constructing a smooth score field with arbitrarily small forward-marginal L2 error, showing nonexplosive behavior and moments of every order. result Euler--Maruyama discretizations can converge in probability even when moments diverge, demonstrating failure of weak convergence.
Generative model uses SDEs to transform data distributions.
problem Creating data from complex distributions.
method Stochastic differential equations (SDEs) for data transformation.
result Achieved record-breaking performance in image generation.
Improved variational inference for geophysical inverse problems with data correction.
problem High computational cost and accuracy issues in Bayesian inference for geophysical inverse problems.
method Amortized variational inference with latent distribution correction using physics-based priors.
result Improved robustness of amortized variational inference under data distribution shifts.
Modeling continuous-time physiological processes that manifest a patient's evolving clinical states is a key step in approaching many problems in healthcare. In this paper, we develop the Hidden Absorbing Semi-Markov Model (HASMM): a versatile probabilistic model that is capable of capturing the modern electronic healt…
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A precise characterization of the hedging cost, the replication cost caused by th…
SSDMs generate quantum states directly, outperforming classical methods.
problem Generating pure-state quantum representations efficiently.
method Score-based generative model on complex projective manifold.
result SSDMs match target pure-state ensembles by orders of magnitude.
Improved sampling efficiency for inverse problems using variance-reduced diffusion methods.
problem Efficiently estimating noisy scores in inverse problems.
method Developed a nonparametric self-normalized importance sampling estimator and a state-dependent blending rule.
result Improved sample quality for fixed simulation budgets in synthetic targets and PDE-governed inverse problems.
Machine learning infers time-reversible dynamics from data.
problem Learn time-reversible dynamics constrained by initial and final conditions.
method Machine learning algorithms solve boundary value problems for deterministic and stochastic dynamics.
result Inferred time-reversible dynamics for various types of systems.
DualVDT improves time-series forecasting with a novel dual reparametrized structure.
problem Time-series forecasting with improved performance and analytical rigor.
method Dual reparametrized variational mechanisms on VAE, latent score based generative model, reverse time stochastic differential equation, variational ancestral sampling, KL divergence reduction.
result Advanced performance in time-series forecasting with reduced KL divergence.
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere…
Continuous time framework for discrete data denoising models.
problem Efficient training and sampling for discrete data denoising models.
method Formulated as Continuous Time Markov Chains (CTMCs), efficient training using continuous time ELBO, high-dimensional CTMC simulation, novel theoretical error bound.
result Continuous time treatment enables novel theoretical error bound between generated and true data distributions.
DiPhon generates scalable graphs via diffusion on graphons.
problem Scaling diffusion models to large graphs.
method Formulated a continuous diffusion process on graphon space via Jacobi SDE, discretized for finite graphs.
result DiPhon matches the first moment of graphon dynamics and approximates the second moment.
In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncom…
QTD integrates quantization with diffusion for efficient data generation.
problem Challenges in continuous diffusion models, especially long-range transitions and biases.
method Quantized Transition Diffusion (QTD) integrates data quantization with discrete diffusion dynamics.
result QTD achieves efficient data generation with minimal score evaluations.
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
Generative Fractional Diffusion Models improve image diversity and quality.
problem Diffusion models struggle with diversity, mode-collapse, and slow convergence.
method Replaces light-tailed BM with fractional Brownian motion (fBM) and its Markov approximation (MA-fBM).
result GFDM achieves greater diversity and quality in image generation.
Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since associations among adjacent scalars are not modeled. In this paper, we propose a n…
Paper analyzes stability and forgetting in score-based generative models.
problem Understanding the stability and long-time behavior of generative models.
method Quantitative bounds on sampling error using stability and forgetting properties of the Markov chain.
result Provides practical consequences of stability and contraction mechanism in sampling.
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved…
DistillKac generates images quickly using damped wave equations.
problem Generating high-quality images efficiently.
method Uses damped wave equations and Kac dynamics for finite speed transport.
result Fast image generation with high quality and numerical stability.
A new method detects changes in data sequences by comparing backward and forward confidence sequences.
problem Detecting changes in data sequences over time.
method Constructing and comparing backward and forward confidence sequences.
result The method successfully detects changes with strong nonasymptotic guarantees.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
Boomerang generates nonidentical images similar to input on image manifolds.
problem Generating nonidentical images similar to input on image manifolds.
method Adding noise to input image, moving closer to latent space, and mapping back through partial reverse diffusion.
result Boomerang generates nonidentical images similar to input on image manifolds.
Generative model for hypergraphs captures complex interactions without pairwise reductions.
problem Challenges in generating realistic hypergraphs with pairwise reductions.
method Structured stochastic diffusion on relaxed incidence matrices.
result Generative model preserves structure-aware noising and yields explicit Gaussian law.
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
Introduces DF framework for sampling decisions from target distributions.
problem Sampling from target distributions with additional guidance.
method DF framework based on MDP and Path Integral Diffusion.
result DF enhances guided sampling across various applications.
A new sampling method estimates scores without training or nested MCMC.
problem Efficient sampling from complex, unnormalised distributions.
method Multiscale averaging in SDEs for score estimation.
result Empirical results show competitive accuracy and efficiency.
ScoreGrad predicts multivariate time series with energy-based models, achieving state-of-the-art results.
problem Predicting multivariate time series with generative models while considering noise and distribution.
method ScoreGrad uses continuous energy-based generative models with a feature extraction and score matching module.
result ScoreGrad achieves state-of-the-art results on six real-world datasets.
Within the context of multivariate time series segmentation this paper proposes a method inspired by a posteriori optimal trading. After a normalization step time series are treated channel-wise as surrogate stock prices that can be traded optimally a posteriori in a virtual portfolio holding either stock or cash. Line…
New method uses TT approximations to solve HJB equations for efficient sampling.
problem Efficiently sampling from complex probability densities.
method Direct time integration of HJB equations using Tensor Train compression.
result Sample-free, dimensionality-avoiding integration method.
The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.
problem Developing a mathematical framework for denoising diffusion models in noncommutative settings.
method Formulating diffusion and reverse processes governed by operator-valued stochastic dynamics, using tools from free stochastic analysis.
result Establishing an information-geometric link between entropy production, transport, and deconvolution.
New method controls classifier guidance in diffusion models.
problem Improving classifier guidance in diffusion models.
method Cross-entropy control of classifier gradients.
result Effective guidance vectors with mean squared error O(dε). A new first-order sampler improves diffusion probabilistic model sampling quality.
problem The belief that first-order methods are inherently slower for diffusion probabilistic model sampling.
method A novel training-free, first-order sampler that approximates the forward-value evaluation via a one-step lookahead predictor.
result The proposed sampler provably approximates the ideal forward-value trajectory while retaining first-order convergence and can improve sample quality under the same NFE budget.
DSB approximates SB problem for faster generative modeling.
problem Fast generation from complex data distributions.
method Entropy-regularized optimal transport on path spaces.
result DSB yields faster convergence to data distribution.
Generative model uses DDPMs for risk-neutral derivative pricing.
problem Derivative pricing using arbitrage-free models.
method Developed a framework using DDPMs to generate risk-neutral asset price dynamics.
result Empirically validated the method for both European and path-dependent derivatives.
One of the most fundamental questions one can ask about a pair of random variables X and Y is the value of their mutual information. Unfortunately, this task is often stymied by the extremely large dimension of the variables. We might hope to replace each variable by a lower-dimensional representation that preserves th…
TabSODA improves imputation of surveys with skips and ordinal data.
problem Handling structural skips and ordinal responses in survey data.
method TabSODA uses an Elucidated Diffusion Model with skip pattern detection and ordinal awareness.
result TabSODA reduces ordinal missing-at-random (MACE) by up to 23.7% and improves categorical accuracy by up to 9%.
Empirical analysis of financial market trends and reversions across various time scales.
problem Understanding trends and reversions in financial markets over different time scales.
method Analysis of 14 years of futures tick data, 30 years of daily futures prices, 330 years of monthly asset prices, and yearly financial data since medieval times.
result Markets exhibit trending and reversion regimes with different time scales, explaining trends persistence and reversions.
Kernel-smoothed scores improve diffusion models by reducing memorization.
problem Diffusion models can memorize training data, leading to biased samples.
method Interpret empirical score as noisy version of true score, kernel-smoothed.
result Kernel-smoothing reduces variance and improves generalization.
New error bound for diffusion models without dimensionality constraints.
problem Error estimation in diffusion generative models without dimensionality constraints.
method Derive dimension-free error bound using a smooth test functional.
result Explicit, dimension-free bound on generated vs true data distributions.
Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computatio…
Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key problem faced by practitioners is measuring the accuracy of an approximate infe…
This work frames active inference through control as inference, offering robust control algorithms.
problem Active inference framework lacks practical sensorimotor control algorithms.
method Frame active inference through control as inference, presenting trajectory optimization as inference.
result AI may be framed as partially-observed CaI when the cost function is defined in observation states.