arXiv research

Stochastic reservoir computing is shown to be a universal approximator.

Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments c…

Storchastic improves stochastic AD for complex models in RL and VI.

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity…

Enhances SGLD for log-concave posteriors with asynchronous computation.

Quantum computing speeds up analysis of financial stochastic processes.

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.

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…

Method learns software resource usage from snapshots.

A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…

AdaSub optimizes with second-order info in low-dims subspace.

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning scenarios. In this paper, we provide dynamic programming algorithms for the comput…

Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-compute noisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic g…

Stochastic Q-learning tackles large action spaces with reduced computation.

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradien…

MindFlayer SGD improves parallel SGD for heterogeneous, random compute times.

The paper uses machine learning to compute rare event probabilities in stochastic systems.

Paper introduces a new deep-learning method for quantum mechanics.

Stochastic Volatility in Mean models with heavy-tailed distributions using Hidden Markov Models

In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …

Diamonds help compute volatility models efficiently.

We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- su…

Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate, due to high variance introduced by the stochastic updates. The popular Stochastic …

The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.

Study on test risk dynamics in learning theory with stochastic gradient flow.

Study approximates rough stochastic volatility models using diffusion processes.

SVD-based methods reduce computational cost for stochastic systems.

Stochastic variational inference (SVI) employs stochastic optimization to scale up Bayesian computation to massive data. Since SVI is at its core a stochastic gradient-based algorithm, horizontal parallelism can be harnessed to allow larger scale inference. We propose a lock-free parallel implementation for SVI which a…

New method estimates SDE parameters efficiently using WCE and SGD.

GPU speeds up Monte Carlo simulations for large time steps.

Quantum computing techniques applied to Monte Carlo simulations in finance.

Signature kernel handles sequential data with theoretical and practical advantages.

Efficient method for high confidence level inference using parallel stochastic optimization.

Bayesian optimization reduces hyperparameter tuning cost for stochastic models.

Unified treatment of RC in stochastic and deterministic settings.

Improved first-order algorithm for entropy regularized OT with faster convergence.

Investigates portfolio selection with transaction costs and stochastic volatility, using deep learning for computation.

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…

Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.

Study on stochastic hypergradient computation for machine learning problems.

This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function for two market models featuring joint normally distributed jumps, stochastic vol…

A new method speeds up quantum state estimation.

For large matrix factorisation problems, we develop a distributed Markov Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics (SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling properties with increasing data size and is comparable in terms of computational requiremen…

Matrix approximation method for Bachelier option pricing and Greeks under stochastic volatility models

This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Mall…

ICSGLD improves efficiency in posterior sampling for big data.

This work tackles resource allocation in asynchronous and stochastic systems.