arXiv research

High-probability bound for distributed stochastic approximation tracking error.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

Stochastic algo learns from evolving data, achieving optimal performance.

Unified view of federated learning and distributed RL using local stochastic approximation.

Study on Wasserstein distance for numerical approximations of stochastic differential equations.

Paper uses averaging from many particle filters to approximate posterior predictive distributions.

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust …

New algorithms for approximating stochastic processes efficiently.

New method uses PDMPs with sub-sampling for efficient sampling from posterior distributions.

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method can be used to approximate any posterior distribution, provided that it is given i…

A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.

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

Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using …

New method assesses financial and cyber risks under uncertainty.

Robust algorithm for distributed optimization resistant to Byzantine failures.

This work tackles resource allocation in asynchronous and stochastic systems.

Improved Bayesian neural network inference by selectively removing redundant modes.

Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing literature, although their practical applicability has been limited by the difficulty…

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

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 …

Bayesian inference using stochastic neural networks ensembles.

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumptio…

DASA speeds up SA with delayed agents, achieving N-fold speedup.

Motivated by machine learning applications in networks of sensors, internet-of-things (IoT) devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a network of nodes---each one of which has a stream of data arriving at a constant …

Develops a martingale expansion for stochastic volatility models.

New algorithm approximates continuous Wasserstein barycenters efficiently.

A new method interpolates between sampling and variational inference using stochastic mixtures.

Paper shows $L^\infty$-positivity and stochastic completeness are equivalent.

This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but n…

Deep learning approximates SPDE solutions from noise trajectories.

This paper approximates SA iterates using Gaussian distributions for tail bounds.

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this poli…

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…

FSGLD improves federated data sampling by correcting noisy gradients.

The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variatio…

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Efficiently simulates SABR model with novel sampling methods.

We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabl…

A new TS-SA method alleviates non-stationarity in TS algorithms for bandits.

New error bounds for flow matching methods using deterministic sampling.

The paper analyzes fixed step-size SA schemes on Riemannian manifolds.

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks represent mappings from a set of inputs to a set of probability distributions o…

New framework improves stochastic optimization for variational inference.

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence structure in the model. Incorporating sparsity in the precision matrix allows the Gaus…

Derives error bounds for stochastic iterative algorithms using Stein's method.

Paper analyzes CLT for TTSA with Markovian noise, broadening its applications.

Heavy-tailed distributions emerge in SGD's parameter evolution.