We improve optimization for data with varying variance.
problem Optimizing data with varying variance.
method Generalized learning and optimization frameworks for data-driven optimization.
result Asymptotic and finite sample guarantees for stochastic programs.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
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.
New bounds show linear predictors rarely overfit with certain optimization methods.
problem Bounding test error for linear predictors with stochastic optimization methods.
method Coupling argument for fixed point methods like stochastic and batch mirror descent.
result Locally-adapted rates that depend on predictor properties, not global problem structure.
Novel framework discovers SPDEs from limited data.
problem Discovering SPDEs from limited data.
method Combines stochastic calculus, variational Bayes, and sparse learning.
result Accurately identifies SPDEs from limited data.
BNP extends Neural Processes using bootstrap to better model uncertainty.
problem Limitation of NP in modeling stochastic processes with a single latent variable.
method Introduces BNP by incorporating bootstrap to estimate uncertainty without assuming a specific form.
result Demonstrates improved flexibility and robustness of BNP on various data types.
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.
New algorithm improves on EM for streaming data, outperforming existing methods.
problem Processing high-volume, streaming data efficiently.
method Incremental stochastic Majorization-Minimization (MM) algorithm.
result The algorithm converges to a stationary point with vanishing gradient.
Improved noise estimation in latent neural SDEs enhances model accuracy.
problem Latent neural SDEs underestimate noise, limiting their stochastic dynamics modeling.
method Explicit additional noise regularization in the loss function.
result Model accurately captures diffusion component of stochastic time series data.
Stochastic neural ODEs outperform deterministic ones on image classification tasks.
problem Improving generalization in continuous-time models like neural ODEs.
method Empirical study of stochastically regularized neural ODEs using SDEs.
result Data augmentation negates the benefits of stochastic regularization, making neural ODEs and SDEs nearly equivalent.
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.
GenFormer uses deep learning to generate complex stochastic data.
problem Creating synthetic stochastic data that matches real-world statistical properties.
method Transformer-based deep learning model that maps Markov state sequences to time series values.
result GenFormer preserves target marginal distributions and other statistical properties in multivariate spatio-temporal data.
Method extracts governing laws from non-Gaussian stochastic systems data.
problem Modeling complex dynamics with non-Gaussian Lévy noise.
method Data-driven method to extract stochastic dynamical systems from noisy data.
result Established a theoretical framework and numerical algorithm to compute Lévy jump measure, drift, and diffusion.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
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…
Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.
problem Challenging identification of governing equations from noisy and partial observations.
method Jointly learns inference model and governing laws using variational deep learning.
result Framework generalizes state-of-the-art methods and accounts for stochastic variabilities.
Neural networks model financial data with Lévy processes.
problem Forecasting chaotic financial time series with big jumps.
method Lévy-induced stochastic differential equation network approximated by neural networks.
result The method improves prediction accuracy using non-Gaussian Lévy processes.
The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.
problem Stochastic optimization in a streaming setting with time-dependent and biased gradient estimates.
method Analysis of several first-order methods including SGD, mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
result Time-varying mini-batch SGD methods can break long- and short-range dependence structures, and biased SGD methods can achieve comparable performance to their unbiased counterparts.
Doubly-stochastic normalization improves robustness to heteroskedastic noise.
problem Robustness to heteroskedastic noise in affinity matrix construction.
method Doubly-stochastic normalization of the Gaussian kernel.
result Doubly-stochastic normalization converges to clean matrix with rate m−1/2 under heteroskedastic noise. A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
Improved convergence for nonconvex optimization with dependent data.
problem Constrained smooth nonconvex optimization with dependent data.
method Stochastic projected gradient methods under a general dependent data sampling scheme.
result Achieved worst-case rate of convergence ildeO(t−1/4) and complexity ildeO(ε−4). Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
problem Stochastic optimization with Markovian data and state-dependent transition kernels.
method Projection-based and projection-free algorithms for constrained nonconvex problems.
result The number of oracle calls to achieve an ε-stationary point is O(1/ε2.5). Method extracts stochastic systems with Lévy noise from data.
problem Identifying stochastic dynamical systems with Lévy noise from short data.
method Estimate Lévy jump measure and noise intensity, approximate drift coefficient.
result Accurate and effective method for discovering stochastic laws.
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
New neural network method simplifies high-dimensional data.
problem Scalability issues in nonlinear sufficient dimension reduction.
method Stochastic neural network with adaptive gradient algorithm.
result Proposed method outperforms existing methods on large-scale data.
New method recovers BSDE from financial data without ergodicity.
problem Discovering probabilistic laws from financial data.
method Stochastic SINDy method under risk-neutral measure.
result Recovery of BSDE from limited financial data.
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…
SON learns SPDE solutions and uncertainty from noisy data.
problem Uncertainty quantification in SPDEs with unknown model uncertainties.
method Combining DeepONet and SNNs, SON models stochasticity and predicts uncertainty.
result SON accurately captures solution structure and quantifies predictive uncertainty.
Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm i…
How to model distribution of sequential data, including but not limited to speech and human motions, is an important ongoing research problem. It has been demonstrated that model capacity can be significantly enhanced by introducing stochastic latent variables in the hidden states of recurrent neural networks. Simultan…
We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as…
Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic s…
Improved loss scaling for stochastic momentum algorithms in high dimensions.
problem Improving loss scaling for stochastic momentum algorithms in high dimensions.
method Dimension-adapted Nesterov acceleration (DANA) scales momentum hyperparameters based on model size and data complexity.
result DANA improves loss scaling exponents across various data and target complexities.
Study on statistical inference for nonlinear stochastic approximation with Markovian data.
problem Statistical inference for nonlinear stochastic approximation algorithms with Markovian data.
method Established a functional central limit theorem for the partial-sum process of the target parameter estimate, providing asymptotic pivotal statistics for constructing confidence intervals.
result Valid and efficient asymptotic inference method for nonlinear stochastic approximation algorithms with Markovian data.
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…
PASTIS selects minimal models from stochastic dynamics data.
problem Overfitting in model selection for stochastic dynamics.
method Combining likelihood-estimation statistics with extreme value theory.
result PASTIS reliably identifies minimal models, even with low sampling rates or error.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical D…
Develops robust methods for infinite-dimensional stochastic processes.
problem Measuring covariations in stochastic evolution equations in infinite dimensions.
method Asymptotic theory for jump robust measurement of covariations.
result Identifies scaling limits for realized covariations.
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and calibration of implied volatility is the addition of a few other factors to the volatil…
NDDV estimates data point value from a single stochastic trajectory.
problem Estimating marginal contributions of data points over stochastic training paths.
method Introduces Neural Dynamic Data Valuation (NDDV) using stochastic state and adjoint equations.
result NDDV provides a one-run, trajectory-conditioned estimator of data point value.
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Usin…
Stochastic methods improve data assimilation with high-frequency sensor data.
problem Computational challenges in data assimilation with high-frequency sensor data.
method Adapted stochastic approximation methods to handle high-frequency observations.
result Produces high-quality estimates using all observations without compromising statistical accuracy.
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
SORSCNs improve nonstationary data modeling by self-organizing and adjusting network parameters.
problem Nonstationary data challenges traditional models in continuous learning.
method SORSCNs autonomously adjust network parameters and structure in real-time using adaptive algorithms.
result SORSCNs outperform other models in generalizing to nonstationary data.
ICSGLD improves efficiency in posterior sampling for big data.
problem Efficient posterior sampling for large datasets.
method Embarrassingly parallel multiple-chain CSGLD with efficient interactions.
result ICSGLD is more efficient than a single-chain CSGLD.
Stochastic gradient descent on manifolds improves low-rank approximation.
problem Efficiently approximate large matrices with lower rank.
method Stochastic gradient descent on a manifold.
result Algorithm outperforms Euclidean space methods on Netflix Prize data.
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.