The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling
By Michael Betancourt. 2015
25 citations recorded by the source corpus.
Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-dimensional target distributions. When confronted with data-intensive applications, however, the algorithm may be too expensive to implement, leaving us to consider the utility of approximations such as data subsampling. In this paper I demonstrate how data subsampling fundamentally compromises the efficient exploration of Hamiltonian flow and hence the scalable performance of Hamiltonian Monte Carlo itself.
Subfields: Mathematical Physics, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Boyan Beronov
- Christopher C. Holmes
- Trevor Campbell
- Zoltán Szabó
- Max Welling
- Dino Sejdinovic
- Arnaud Doucet
- Arthur Gretton
In Statistics and Probability
- Dino Sejdinovic
- Trevor Campbell
- Arthur Gretton
- Heiko Strathmann
- Boyan Beronov
- Arnaud Doucet
- Bharath K. Sriperumbudur
- Bernhard Schölkopf
Citations in the corpus
- Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, background): “Stochastic gradient based HMC methods, however, often suffer from low acceptance rates or additional bias that is hard to quantify [9].”
- Hamiltonian ABC (2015, background): “Recent work has shown that scaling HMC for large data applications may be fundamentally limited [4]: noise from mini-batches causes biases in trajectories, which require either increasing mini-batch sizes (in our case, running more simulations) or decreasing the step size.”
- What Are Bayesian Neural Network Posteriors Really Like? (2021, background): “In particular, Betancourt (2015) argues that HMC is incompatible with data subsampling.”
- On Markov chain Monte Carlo methods for tall data (2015, background): “Chen et al. (2014) propose a modification of HMC that is inspired by the SGLD with decreasing stepsize of Welling & Teh (2011), while Betancourt (2014) explores why naive approaches suffer from unacceptable biases.”
- Hamiltonian Monte Carlo Acceleration Using Neural Network Surrogate functions (2015, background): “However, in general applications, we cannot simply use random subsets for this purpose: the amount of information we lose as a result of random sampling leads to non-ignorable loss of accuracy, which in turn has a substantial negative impact on computational efficiency [11].”
- Sparse Variational Inference: Bayesian Coresets from Scratch (2019, methodology): “In practice, however, exact Bayesian inference is typically intractable, and we must use approximate inference algorithms such as Markov chain Monte Carlo (MCMC) [1; 2, Ch. 11,12] and variational inference (VI) [3, 4].”