Mirror variational transport: a particle-based algorithm for distributional optimization on constrained domains
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Ahn, K., & Chewi, S. (2021). Efficient constrained sampling via the mirror-Langevin algorithm. Advances in Neural Information Processing Systems, 34, 28405–28418.
Arjovsky, M., Chintala, S., & Bottou, L. (2017). Wasserstein generative adversarial networks. In International conference on machine learning (pp. 214–223). PMLR.
Beck, A., & Teboulle, M. (2003). Mirror descent and nonlinear projected subgradient methods for convex optimization. Operations Research Letters, 31(3), 167–175.
Bowman, S. R., Vilnis, L., Vinyals, O., Dai, A. M., Jozefowicz, R., & Bengio, S. (2015). Generating sentences from a continuous space. arXiv preprint arXiv:1511.06349
Cheng, X., & Bartlett, P. (2018). Convergence of Langevin MCMC in KL-divergence. In Algorithmic learning theory (pp. 186–211). PMLR.
Cuturi, M. (2013). Sinkhorn distances: Lightspeed computation of optimal transport. Advances in Neural Information Processing Systems, 26.
Duchi, J., Shalev-Shwartz, S., Singer, Y., & Chandra, T. (2008). Efficient projections onto the l 1-ball for learning in high dimensions. In Proceedings of the 25th international conference on Machine learning (pp. 272–279).
Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., & Smola, A. (2012). A kernel two-sample test. The Journal of Machine Learning Research, 13(1), 723–773.
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.
Hsieh, Y.-P., Kavis, A., Rolland, P., & Cevher, V. (2018). Mirrored Langevin dynamics. Advances in Neural Information Processing Systems, 31.
Joo, W., Lee, W., Park, S., & Moon, I.-C. (2020). Dirichlet variational autoencoder. Pattern Recognition, 107, 107514.
Kingma, D. P., & Welling, M. (2013) Auto-encoding variational Bayes. arXiv preprint arXiv:1312.6114
Koziel, S., & Michalewicz, Z. (1998). A decoder-based evolutionary algorithm for constrained parameter optimization problems. In Parallel problem solving from nature-PPSN V: 5th International conference Amsterdam, 1998 Proceedings (Vol. 5, pp. 231–240). Springer.
Liu, L., Zhang, Y., Yang, Z., Babanezhad, R., & Wang, Z. (2021). Infinite-dimensional optimization for zero-sum games via variational transport. In International conference on machine learning (pp. 7033–7044). PMLR.
Liu, Q., & Wang, D. (2016). Stein variational gradient descent: A general purpose Bayesian inference algorithm. Advances in Neural Information Processing Systems, 29.
Ma, Y.-A., Chen, T., & Fox, E. (2015). A complete recipe for stochastic gradient MCMC. Advances in Neural Information Processing Systems, 28.
Michalewicz, Z., & Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1–32.
Nguyen, D. H., Nguyen, C. H., & Mamitsuka, H. (2021). Learning subtree pattern importance for Weisfeiler–Lehman based graph kernels. Machine Learning, 110, 1585–1607.
Nguyen, D. H., & Tsuda, K. (2023). On a linear fused Gromov–Wasserstein distance for graph structured data. Pattern Recognition (p. 109351).
Rosasco, L., Belkin, M., & De Vito, E. (2009). A note on learning with integral operators. In COLT. Citeseer.
Santambrogio, F. (2017). $$\{$$Euclidean, metric, and Wasserstein$$\}$$ gradient flows: An overview. Bulletin of Mathematical Sciences, 7(1), 87–154.
Shi, J., Liu, C., & Mackey, L. (2021). Sampling with mirrored stein operators. arXiv preprint arXiv:2106.12506
Welling, M., & Teh, Y. W. (2011). Bayesian learning via stochastic gradient Langevin dynamics. In Proceedings of the 28th international conference on machine learning (ICML-11) (pp. 681–688).
Wibisono, A. (2018). Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem. In Conference on learning theory (pp. 2093–3027). PMLR.
Xu, P., Chen, J., Zou, D., & Gu, Q. (2018). Global convergence of Langevin dynamics based algorithms for nonconvex optimization. Advances in Neural Information Processing Systems, 31.
Zhang, H., & Sra, S. (2016). First-order methods for geodesically convex optimization. In Conference on learning theory (pp. 1617–1638). PMLR.