Search Results for author:
Found 16 papers, 4 papers with code
Taming the Interacting Particle Langevin Algorithm -- the superlinear case
Recent advances in stochastic optimization have yielded the interactive particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently sample from approximate posterior densities.
On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
As a result, we obtain the best known upper bound estimates in terms of key quantities of interest, such as the dimension and rates of convergence, for the Wasserstein-2 distance between the data distribution (Gaussian with unknown mean) and our sampling algorithm.
Taming under isoperimetry
In this article we propose a novel taming Langevin-based scheme called $\mathbf{sTULA}$ to sample from distributions with superlinearly growing log-gradient which also satisfy a Log-Sobolev inequality.
Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation
We achieve this by formulating a continuous-time interacting particle system which can be seen as a Langevin diffusion over an extended state space of parameters and latent variables.
Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz.
Langevin dynamics based algorithm e-TH$\varepsilon$O POULA for stochastic optimization problems with discontinuous stochastic gradient
We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks.
Statistical Finite Elements via Langevin Dynamics
Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model.
Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function
To illustrate the applicability of the main results, we consider an example from transfer learning with ReLU neural networks, which represents a key paradigm in machine learning.
Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks
We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models.
A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating
We are thus able to provide theoretical guarantees for the algorithm's convergence in (standard) Wasserstein distances for both convex and non-convex objective functions.
Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms
We offer a new learning algorithm based on an appropriately constructed variant of the popular stochastic gradient Langevin dynamics (SGLD), which is called tamed unadjusted stochastic Langevin algorithm (TUSLA).
Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization
We provide a nonasymptotic analysis of the convergence of the stochastic gradient Hamiltonian Monte Carlo (SGHMC) to a target measure in Wasserstein-2 distance without assuming log-concavity.
Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization
In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization.
Optimising portfolio diversification and dimensionality
It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree.
On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017).
Model-Independent Price Bounds for Catastrophic Mortality Bonds
In this paper, we are concerned with the valuation of Catastrophic Mortality Bonds and, in particular, we examine the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets.
