1. [PDF] Bayesian Learning via Stochastic Gradient Langevin Dynamics
Abstract. In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches.
2. Bayesian learning via stochastic gradient langevin dynamics
ABSTRACT · References · Index Terms
3. [PDF] Bayesian Learning via Stochastic Gradient Langevin Dynamics
▷ A very simple twist to standard stochastic gradient ascent. ▷ Turns it into a Bayesian algorithm which samples from the full posterior distribution rather ...
4. Bayesian Learning via Stochastic Gradient Langevin Dynamics
This paper proposes a new framework for learning from large scale datasets based on iterative learning from small mini-batches by adding the right amount of ...
This paper proposes a new framework for learning from large scale datasets based on iterative learning from small mini-batches by adding the right amount of noise to a standard stochastic gradient optimization algorithm and shows that the iterates will converge to samples from the true posterior distribution as the authors anneal the stepsize. In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches. By adding the right amount of noise to a standard stochastic gradient optimization algorithm we show that the iterates will converge to samples from the true posterior distribution as we anneal the stepsize. This seamless transition between optimization and Bayesian posterior sampling provides an inbuilt protection against overfitting. We also propose a practical method for Monte Carlo estimates of posterior statistics which monitors a "sampling threshold" and collects samples after it has been surpassed. We apply the method to three models: a mixture of Gaussians, logistic regression and ICA with natural gradients.
5. Bayesian Learning via Stochastic Gradient Langevin Dynamics and ...
Feb 8, 2023 · At a high level, it transforms the sampling of a target probability distribution into a physics problem with Hamiltonian dynamics. Intuitively, ...
After a long digression, I'm finally back to one of the main lines of research that I wanted to write about. The two main ideas in this post are not that recent but have been quite impactful (one of
6. [PDF] Bayesian Learning via Stochastic Gradient Langevin Dynamics
In stochastic optimization you update the MAP estimate by estimating the parameter's change with each batch. At each update t, we choose a subset of size n ...
7. Bayesian inference with Stochastic Gradient Langevin Dynamics
May 14, 2020 · The authors of the Bayesian Learning via Stochastic Gradient Langevin Dynamics paper show that we can interpret the optimization trajectory of ...
Modern machine learning algorithms can scale to enormous datasets and reach superhuman accuracy on specific tasks. Yet, they are largely incapable of answering “I don’t know” when queried with new data. Taking a Bayesian approach to learning lets models be uncertain about their predictions, but classical Bayesian methods do not scale to modern settings. In this post we are going to use Julia to explore Stochastic Gradient Langevin Dynamics (SGLD), an algorithm which makes it possible to apply Bayesian learning to deep learning models and still train them on a GPU with mini-batched data.
8. [PDF] Decentralized Langevin Dynamics for Bayesian Learning
Motivated by decentralized approaches to machine learning, we propose a collab- orative Bayesian learning algorithm taking the form of decentralized Langevin ...
9. Bayesian Learning via Stochastic Gradient Langevin Dynamics
In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches.
Implemented in one code library.
10. [PDF] hybrid deterministic-stochastic gradient langevin dynamics for ...
This work focuses on Bayesian learning based on a hybrid deterministic-stochastic gradient descent Langevin dynamics. There has been increas- ing interest in ...
11. Can Stochastic Gradient Langevin Dynamics Provide ... - OpenReview
Jan 28, 2022 · Bayesian learning via Stochastic Gradient Langevin Dynamics (SGLD) has been suggested for differentially private learning.
Bayesian learning via Stochastic Gradient Langevin Dynamics (SGLD) has been suggested for differentially private learning. While previous research provides differential privacy bounds for SGLD when...
12. [PDF] Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
An algorithm based on the Langevin equation with stochastic gradi- ents (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leverag-.
13. Stochastic Gradient Langevin Dynamics Algorithms with Adaptive ...
Sep 20, 2020 · Abstract: Bayesian deep learning offers a principled way to address many issues concerning safety of artificial intelligence (AI), ...
Bayesian deep learning offers a principled way to address many issues concerning safety of artificial intelligence (AI), such as model uncertainty,model interpretability, and prediction bias. However, due to the lack of efficient Monte Carlo algorithms for sampling from the posterior of deep neural networks (DNNs), Bayesian deep learning has not yet powered our AI system. We propose a class of adaptive stochastic gradient Markov chain Monte Carlo (SGMCMC) algorithms, where the drift function is biased to enhance escape from saddle points and the bias is adaptively adjusted according to the gradient of past samples. We establish the convergence of the proposed algorithms under mild conditions, and demonstrate via numerical examples that the proposed algorithms can significantly outperform the existing SGMCMC algorithms, such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian Monte Carlo (SGHMC) and preconditioned SGLD, in both simulation and optimization tasks.
14. Can Stochastic Gradient Langevin Dynamics Provide ... - OpenReview
May 5, 2023 · TL;DR: The paper investigates, theoretically and empirically, whether SGLD can provide differential privacy for deep learning. Abstract: ...
The paper investigates, theoretically and empirically, whether SGLD can provide differential privacy for deep learning.
15. Stochastic gradient Langevin dynamics with adaptive drifts - PMC
Jul 27, 2021 · When the dataset is big, Bayesian learning is often conducted using the stochastic gradient Langevin dynamics (SGLD) algorithm [1], which is ...
We propose a class of adaptive stochastic gradient Markov chain Monte Carlo (SGMCMC) algorithms, where the drift function is adaptively adjusted according to the gradient of past samples to accelerate the convergence of the algorithm in simulations of ...
16. Test of time - Bayesian Inference via Stochastic Gradient Langevin ...
Jul 22, 2021 · Test of time - Bayesian Inference via Stochastic Gradient Langevin Dynamics · Speakers · Organizer · About ICML 2021 · Store presentation · Should ...
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
17. Bayesian Learning via Stochastic Gradient Langevin Dynamics. - DBLP
Apr 3, 2019 · Bibliographic details on Bayesian Learning via Stochastic Gradient Langevin Dynamics.
Bibliographic details on Bayesian Learning via Stochastic Gradient Langevin Dynamics.
18. GoAi #3: Bayesian Learning via Stochastic Gradient Langevin ...
Jul 30, 2016 · The Stochastic Gradient Langevin Dynamics combine both advantage of the followings. It can not only take mini batch gradient computation but ...
Reference: Bayesian Learning via Stochastic Gradient Langevin Dynamics
19. Bayesian Learning via Stochastic Gradient Langevin Dynamics
Aug 4, 2012 · This paper is using SGD to get close to the posterior modes (which will be the MAP estimate in a unimodal problem such as non-hierarchical ...
Posted on August 4, 2012 9:58 AM by Andrew
20. Non-convex Bayesian Learning via Stochastic Gradient Markov Chain ...
Dec 18, 2021 · A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical ...
The rise of artificial intelligence (AI) hinges on the efficient training of modern deep neural networks (DNNs) for non-convex optimization and uncertainty quantification, which boils down to a non-convex Bayesian learning problem. A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical guarantees. However, non-convex Bayesian learning in real big data applications can be arbitrarily slow and often fails to capture the uncertainty or informative modes given a limited time. As a result, advanced techniques are still required.In this thesis, we start with the replica exchange Langevin Monte Carlo (also known as parallel tempering), which is a Markov jump process that proposes appropriate swaps between exploration and exploitation to achieve accelerations. However, the na\"ive extension of swaps to big data problems leads to a large bias, and the bias-corrected swaps are required. Such a mechanism leads to few effective swaps and insignificant accelerations. To alleviate this issue, we first propose a control variates method to reduce the variance of noisy energy estimators and show a potential to accelerate the exponential convergence. We also present the population-chain replica exchange and propose a generalized deterministic even-odd scheme to track the non-reversibility and obtain an optimal round trip rate. Further approximations are conducted based on stochastic gradient descents, which yield a user-friendly nature for large-scale uncertainty approximation tasks without much tuning costs. In the second part of the thesis, we study scalable dynamic importance sampling algorithms based on stochastic approximation. Traditional dynamic importance sampling algorithms have achieved successes in bioinformatics and statistical physics, however, the lack of scalability has greatly limited their extensions to big data applications. To handle this scalability issue, we resolve the vanishing gradient problem and propose two dynamic importance sampling algorithms based on stochastic gradient Langevin dynamics. Theoretically, we establish the stability condition for the underlying ordinary differential equation (ODE) system and guarantee the asymptotic convergence of the latent variable to the desired fixed point. Interestingly, such a result still holds given non-convex energy landscapes. In addition, we also propose a pleasingly parallel version of such algorithms with interacting latent variables. We show that the interacting algorithm can be theoretically more efficient than the single-chain alternative with an equivalent computational budget.
21. [PDF] Bayesian Posterior Sampling via Stochastic Gradient Descent with ...
Dec 10, 2019 · Markov Chain Monte Carlo algorithms, with step proposals based on Hamiltonian or Langevin dynamics, are commonly used in Bayesian machine ...
22. [PDF] Low-Precision Stochastic Gradient Langevin Dynamics - ICML
Bayesian Learning via Stochastic Gradient Langevin Dynamics. Welling and Teh, 2011. Pros of sampling: ✓ Characterize complex and multi-modal DNN posteriors.
23. [PDF] Bayesian sparse learning with preconditioned stochastic gradient ...
Jan 2, 2021 · A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter ...
24. [PDF] Stochastic Gradient Descent as Approximate Bayesian Inference
Specifically, we use the stochastic-process perspective to compute the stationary distribution of Stochastic-Gradient Langevin Dynamics. (SGLD) by Welling and ...
25. [PDF] Preconditioned Stochastic Gradient Langevin Dynamics for Deep ...
2014). A Bayesian approach for learning neural networks in- corporates uncertainty into model learning, and can reduce. ∗Appendix is at ...
26. Stochastic Gradient Langevin Dynamics as proposed in Welling
Stochastic Gradient Langevin Dynamics as proposed in Welling, M., & Teh, Y. W. (n.d.). Bayesian Learning via Stochastic Gradient Langevin Dynamics. 8 ...
Stepsizes will be adapted according to