Novel Fourier-based estimator reveals stochastic leverage effect in high-frequency data.
problem Analyzing the stochastic leverage effect in high-frequency data.
method A novel Fourier-based estimator of the stochastic leverage effect is defined and proven consistent.
result The magnitude of the stochastic leverage effect is detectable at high-frequency.
New method estimates stochastic intervention effects in decision-making domains.
problem Current causal inference methods are limited to deterministic treatment, unable to handle stochastic policies.
method Developed a new stochastic propensity score and stochastic intervention effect estimator (SIE) with a customized genetic algorithm (Ge-SIO).
result Empirical study shows significant performance improvement over state-of-the-art baselines.
Dropout introduces both explicit and implicit regularization effects.
problem Understanding the full impact of dropout regularization.
method Disentangled explicit and implicit regularization effects through experiments and analytic simplifications.
result Explicit and implicit regularization effects of dropout are distinct and can be characterized analytically.
Develops a new theory for neural systems stability and width effects.
problem Stability and finite-width effects in deep neural systems.
method Gauge-covariant stochastic effective field theory using classical commuting fields.
result Predicts the edge of chaos and low-frequency spectral deformation.
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
Anomalous scaling explained by Joseph, Noah, and Moses effects.
problem Understanding and quantifying anomalous scaling in stochastic processes.
method Defined and measured scaling exponents for Joseph, Noah, and Moses effects.
result Intraday financial data shows anomalous scaling due to Moses effect.
Derives effective continuous dynamics for adaptive SGD methods.
problem Analyzing noise in adaptive SGD methods.
method Stochastic modified equations framework and Malladi's scaling rules.
result Sampling-induced noise in SGD limits to independent Brownian motions.
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Corrects Bayesian inference for stochastic interventions to improve accuracy.
problem Uncalibrated posterior uncertainty in estimating stochastic intervention effects.
method Develops a post-processing correction for nonparametric Bayesian models.
result Corrected posterior yields asymptotically efficient inference and valid frequentist coverage.
Study examines Bitcoin's volatility and returns using stochastic volatility model.
problem Characterizing Bitcoin as a financial asset and its volatility patterns.
method Asymmetric stochastic volatility model applied to Bitcoin data from 2013-2019.
result Bitcoin shows weak post-holiday effects and no asymmetry effect in returns and volatility.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
A new model connects stochastic effects to economic inequality.
problem Understanding economic inequality through stochastic effects.
method Introducing stochastic effects into a kinetic model based on Langevin and Fokker-Planck formalisms.
result Positive correlations between Gini index and total wealth indicate growing inequality.
We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows us to fully estimate all parameters involved and it will entail a deeper study on…
A scalable Bayesian inference method for mixed-effects models in systems biology.
problem Scalable Bayesian inference for complex hierarchical mixed-effects models in systems biology.
method Constructing amortized approximations of likelihood and posterior distributions, refined for each individual dataset.
result Our method is both fast and competitive in statistical accuracy compared to exact pseudomarginal Bayesian inference.
We propose an efficient method for estimating covariate effects in doubly-stochastic spatial models.
problem Computational demands and restrictive assumptions in existing doubly-stochastic spatial models.
method Penalized regression method for estimating covariate effects in doubly-stochastic point processes.
result Consistency and asymptotic normality of the covariate effect estimates achieved despite model misspecification.
Investigates spontaneous symmetry breaking in non-equilibrium systems.
problem Spontaneous symmetry breaking of ergodicity in non-equilibrium systems.
method Mathematical and effective field theory approaches to investigate symmetry breaking.
result Symmetry breaking phenomena observed in stochastic processes.
Efficiently simulates slow dynamics of high-dimensional stochastic systems.
problem Simulating high-dimensional stochastic systems with slow dynamics and fast modes.
method Designs an algorithm to estimate an invariant manifold and its dynamics, averaging out fast modes.
result Efficient simulator of effective dynamics on low-dimensional invariant manifold.
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
The Zumbach effect is significant under rough Heston but negligible in classical Heston.
problem Identifying the Zumbach effect in stochastic volatility models.
method Explicit computations of the Zumbach effect under rough Heston model.
result The Zumbach effect is negligible in the classical Heston model but significant under rough Heston.
Optimal bounds for exp-concave stochastic minimization in terms of effective dimension.
problem Finding optimal statistical and computational complexity for exp-concave stochastic minimization.
method Derives optimal bounds using effective dimension and sketching techniques.
result Reveals connections between algorithmic stability and ridge leverage scores.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.
New algorithms mitigate impairment effect in stochastic bandits.
problem Impairment effect in stochastic multi-armed bandits.
method Developed two novel algorithms with bucketing to address impairment and temporal constraints.
result Achieved sublinear regret, explicitly capturing impairment cost.
This work refutes the conventional wisdom and shows acceleration can be made robust for least squares regression.
problem The challenge of using fast gradient methods for stochastic optimization due to instability and error accumulation.
method Introduced an accelerated stochastic gradient method for least squares regression.
result Proves accelerated stochastic gradient descent achieves minimax optimal statistical risk faster than SGD.
Study asset price bubbles using random matching and stochastic factors.
problem Understanding and modeling asset price bubbles through investor contagion.
method Developed a stochastic model of liquidity-based asset price bubbles using random matching mechanism.
result Derived conditions for arbitrage-free financial market models.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
New algorithms bound treatment effects with unmeasured confounding.
problem Estimating causal effects when confounding is unmeasured.
method Formulate causal effects as objective functions in optimization, using stochastic methods and Monte Carlo.
result Efficient algorithms for bounded treatment effects in complex settings.
Paper reduces communication in distributed machine learning.
problem Reduces burdensome communication in distributed machine learning.
method Introduces communication-censoring technique to reduce transmissions of variables.
result CSGD algorithm achieves same convergence rate as SGD but with significant communication reduction.
New method views residual networks as stochastic differential equations.
problem Improving generalization of neural networks.
method Applying modified equations to show residual networks as weak approximations of stochastic differential equations.
result Stochastic training of residual networks can be understood through the lens of optimal control of backward Kolmogorov's equations.
This paper contains a summary of mathematical researches of stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum--field top. Applications to interactively controlled stochastic computer-graphic dynamical systems are also discussed.
Stochastic reservoir computing is shown to be a universal approximator.
problem Theoretical justification for using stochastic reservoirs in machine learning.
method Investigated stochastic reservoir computing using probabilities of reservoir states as readout.
result Stochastic reservoir computers are universal approximating classes.
New flaw found in SAP defense, reducing its effectiveness to 0.1%.
problem Weakness in Stochastic Activation Pruning defense against adversarial attacks.
method Re-examined the implementation of SAP and introduced a new BPDA attack.
result SAP's effectiveness reduced to 0.1% when properly applied.
Gradient coding technique improves efficiency and accuracy in distributed machine learning.
problem Mitigating delays caused by slow nodes in distributed machine learning.
method Gradient coding via the stochastic block model.
result SBCs are efficient, accurate, and resistant to adversarial stragglers.
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
problem Slow computations for high-dimensional crossed random effects in mixed-effects models.
method Krylov subspace-based methods for generalized mixed-effects models with cross effects.
result Speedups by factors of up to 10,000 in computations for mixed-effects models.
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources…
Paper tackles non-convex inf-projection problems with stochastic optimization.
problem Non-convex and possibly non-smooth inf-projection minimization problems.
method Developed stochastic algorithms for finding (nearly) stationary solutions.
result Established first-order convergence for non-convex inf-projection problems.
Approximates derivative pricing under fractional stochastic volatility.
problem Derivative pricing under fractional stochastic volatility model.
method Approximate expression derived from deterministic functions and fractional Ornstein-Uhlenbeck process.
result Numerical simulations show the feasibility and effect of long-range dependencies on derivative prices.
Study shows how repetition affects learning in bandit settings, providing algorithms with sublinear regret.
problem Effect of persistence of engagement on learning in stochastic multi-armed bandit settings.
method Novel algorithms that achieve sublinear regret under temporal constraints.
result Additive effect of priming on regret upper bound, matching popular algorithms in absence of priming.
A new multi-factor model improves commodity pricing accuracy.
problem Enhancing accuracy in commodity pricing by integrating multiple risk factors.
method A four-factor model using Kalman filter for simultaneous estimation and state variable filtering.
result The four-factor model outperforms existing models in capturing futures term structures and crude oil pricing.
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
Develops polynomial diffusion models for multi-factor commodity futures dynamics.
problem Modeling futures prices using latent state variables for short and long-term stochastic factors.
method Polynomial diffusion models to incorporate non-linear effects, two filtering methods for estimation.
result Accurate estimation of futures prices despite parameter identification issues in polynomial diffusion models.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
problem Estimating higher-order interaction effects in stochastic processes with limited data.
method Additive Poisson Process (APP) combines information geometry and generalized additive models to model intensity functions in lower dimensions.
result The model can estimate higher-order intensity functions with sparse data.
Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
Stochastic Gradient Descent introduces noise in training, affecting model decision boundaries.
problem Understanding the impact of noise in SGD on model decision boundaries.
method Characterized SGD and persistent SGD dynamics in a neural network model, measuring noise magnitude in both under- and over-parametrized regimes.
result Noisier algorithms lead to wider decision boundaries in constraint satisfaction problems.
Paper develops SINNOs for approximating stochastic processes.
problem Approximating stochastic processes with neural networks.
method Developed stochastic interpolation neural network operators (SINNOs) with random coefficients.
result Established boundedness, interpolation accuracy, and approximation capabilities of SINNOs.
Optimizes trading in markets with unpredictable price impacts.
problem Optimizing trading strategies in markets with stochastic price impacts.
method Singular perturbation methods to approximate optimal control problem.
result Proves approximations are accurate to specified order using sub- and super-solutions.
New method extracts stochastic laws from data, including Lévy noise.
problem Extracting stochastic laws from data with non-Gaussian noise.
method Using normalizing flows to estimate transition density, then applying nonlocal Kramers-Moyal formulas.
result Can learn stochastic differential equations with Lévy motion.