Recasting gradient-based meta-learning as hierarchical bayes

6th International Conference on Learning Representations, ICLR 2018 - Conference Track Proceedings

Volumn , Issue , 2018, Pages

  Grant, Erin ^a,b   Finn, Chelsea ^a   Levine, Sergey ^a,b   Darrell, Trevor ^a,b   Griffiths, Thomas ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN NETWORKS; COMPUTATIONAL EFFICIENCY; GRADIENT METHODS; INFERENCE ENGINES; LEARNING SYSTEMS;

APPROXIMATE INFERENCE; BAYESIAN HIERARCHICAL MODEL; COMPUTATIONAL STRATEGY; CURVATURE ESTIMATION; HIERARCHICAL BAYESIAN MODELING; IMPROVING PERFORMANCE; PROBABILISTIC INFERENCE; THEORETICAL FRAMEWORK;

LEARNING ALGORITHMS;

EID: 85083953531     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (59)

1. Daniel Alspach and Harold Sorenson. Nonlinear Bayesian estimation using Gaussian sum approximations. IEEE Transactions on Automatic Control, 17(4):439–448, 1972.
2. Shun-Ichi Amari. Natural gradient works efficiently in learning. Neural computation, 10(2):251–276, 1998.
3. Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, and Nando de Freitas. Learning to learn by gradient descent by gradient descent. In Advances in Neural Information Processing Systems (NIPS) 29, pp. 3981–3989, 2016.
4. Samy Bengio, Yoshua Bengio, Jocelyn Cloutier, and Jan Gecsei. On the optimization of a synaptic learning rule. In Proceedings of the Conference on Optimality in Artificial and Biological Neural Networks, pp. 6–8, 1992.
5. Yoshua Bengio, Samy Bengio, and Jocelyn Cloutier. Learning a synaptic learning rule. In Proceedings of the International Joint Conference on Neural Networks (IJCNN), volume 2, 1991.
6. J.M. Bernardo and A.F.M. Smith. Bayesian Theory. Wiley Series in Probability and Statistics. John Wiley & Sons Canada, Limited, 2006.
7. Christopher M Bishop. Regularization and complexity control in feed-forward networks. In Proceedings of the International Conference on Artificial Neural Networks (ICANN), pp. 141–148, 1995.
8. Léon Bottou and Vladimir Vapnik. Local learning algorithms. Neural computation, 4(6):888–900, 1992. Rich Caruana. Multitask learning. In Learning to learn, pp. 95–133. Springer, 1998.
9. Hal Daumé III. Bayesian multitask learning with latent hierarchies. In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 135–142, 2009.
10. David Duvenaud, Dougal Maclaurin, and Ryan Adams. Early stopping as nonparametric variational inference. In Proceedings of the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 1070–1077, 2016.
11. Harrison Edwards and Amos Storkey. Towards a neural statistician. In Proceedings of the 5th International Conference on Learning Representations (ICLR), 2017.
12. Li Fei-Fei et al. A Bayesian approach to unsupervised one-shot learning of object categories. In Proceedings of the 9th Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1134–1141. IEEE, 2003.
13. Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. In Proceedings of the 34th International Conference on Machine Learning (ICML), 2017.
14. Ronald Aylmer Fisher. Theory of statistical estimation. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 22, pp. 700–725. Cambridge University Press, 1925.
15. Jing Gao, Wei Fan, Jing Jiang, and Jiawei Han. Knowledge transfer via multiple model local structure mapping. In Proceedings of the 14th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), pp. 283–291. ACM, 2008.
16. Andrew Gelman, John B Carlin, Hal S Stern, David B Dunson, Aki Vehtari, and Donald B Rubin. Bayesian data analysis, volume 2. Chapman and Hall, 2014.
17. Gene H. Golub and Charles F. Van Loan. Matrix computations. The Johns Hopkins University Press, 1983.
18. Bharath Hariharan and Ross Girshick. Low-shot visual object recognition. In Proceedings of the International Conference on Computer Vision (ICCV), 2017.
19. Tom Heskes. Solving a huge number of similar tasks: A combination of multi-task learning and a hierarchical Bayesian approach. In Proceedings of the 15th International Conference on Machine Learning (ICML), pp. 233–241, 1998.
20. Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In Proceedings of the 32nd International Conference on Machine Learning (ICML), pp. 448–456, 2015.
21. Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Proceedings of the 3rd International Conference on Learning Representations (ICLR), 2014.
22. Gregory Koch. Siamese neural networks for one-shot image recognition. Master’s thesis, University of Toronto, 2015.
23. Brenden M Lake, Ruslan Salakhutdinov, Jason Gross, and Joshua B Tenenbaum. One shot learning of simple visual concepts. In Proceedings of the 33rd Annual Meeting of the Cognitive Science Society (CogSci), 2011.
24. Brenden M Lake, Tomer D Ullman, Joshua B Tenenbaum, and Samuel J Gershman. Building machines that learn and think like people. Behavioral and Brain Sciences, pp. 1–101, 2016.
25. Pierre Simon Laplace. Memoir on the probability of the causes of events. Statistical Science, 1(3):364–378, 1986.
26. Neil D Lawrence and John C Platt. Learning to learn with the informative vector machine. In Proceedings of the 21st International Conference on Machine Learning (ICML), pp. 65, 2004.
27. Ke Li and Jitendra Malik. Learning to optimize. In Proceedings of the 5th International Conference on Learning Representations (ICLR), 2017a.
28. Ke Li and Jitendra Malik. Learning to optimize neural nets. In Proceedings of the 34th International Conference on Machine Learning (ICML), 2017b.
29. David MacKay. A practical Bayesian framework for backpropagation networks. Neural computation, 4(3): 448–472, 1992a.
30. David JC MacKay. The evidence framework applied to classification networks. Neural computation, 4(5): 720–736, 1992b.
31. Vikash K Mansinghka, Tejas D Kulkarni, Yura N Perov, and Josh Tenenbaum. Approximate bayesian image interpretation using generative probabilistic graphics programs. In Advances in Neural Information Processing Systems, pp. 1520–1528, 2013.
32. James Martens. New insights and perspectives on the natural gradient method. arXiv preprint arXiv:1412.1193, 2014.
33. James Martens. Second-order optimization for neural networks. PhD thesis, University of Toronto, 2016.
34. James Martens and Roger Grosse. Optimizing neural networks with Kronecker-factored approximate curvature. In Proceedings of the 32nd International Conference on Machine Learning (ICML), pp. 2408–2417, 2015.
35. Nikhil Mishra, Mostafa Rohaninejad, Xi Chen, and Pieter Abbeel. Meta-learning with temporal convolutions. arXiv preprint arXiv:1707.03141, 2017.
36. Nikhil Mishra, Mostafa Rohaninejad, Xi Chen, and Pieter Abbeel. A simple neural attentive meta-learner. In Proceedings of the 6th International Conference on Learning Representations (ICLR), 2018.
37. Tsendsuren Munkhdalai and Hong Yu. Meta networks. In Proceedings of the 34th International Conference on Machine Learning (ICML), 2017.
38. Devang K Naik and RJ Mammone. Meta-neural networks that learn by learning. In Proceedings of the International Joint Conference on Neural Networks (IJCNN), pp. 437–442, 1992.
39. Razvan Pascanu and Yoshua Bengio. Revisiting natural gradient for deep networks. In Proceedings of the 4th International Conference on Learning Representations (ICLR), 2014.
40. Rajat Raina, Andrew Y Ng, and Daphne Koller. Constructing informative priors using transfer learning. In Proceedings of the 23rd International Conference on Machine Learning (ICML), pp. 713–720, 2006.
41. Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. In Proceedings of the 5th International Conference on Learning Representations (ICLR), 2017.
42. Ruslan Salakhutdinov, Joshua Tenenbaum, and Antonio Torralba. One-shot learning with a hierarchical nonparametric bayesian model. In Proceedings of ICML Workshop on Unsupervised and Transfer Learning, pp. 195–206, 2012.
43. Ruslan Salakhutdinov, Joshua B Tenenbaum, and Antonio Torralba. Learning with hierarchical-deep models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(8):1958–1971, 2013.
44. Adam Santoro, Sergey Bartunov, Matthew Botvinick, Daan Wierstra, and Timothy Lillicrap. Meta-learning with memory-augmented neural networks. In Proceedings of the 33rd International Conference on Machine Learning (ICML), pp. 1842–1850, 2016.
45. Reginaldo J. Santos. Equivalence of regularization and truncated iteration for general ill-posed problems. Linear Algebra and its Applications, 236(15):25–33, 1996.
46. Jürgen Schmidhuber. Evolutionary principles in self-referential learning. PhD thesis, Institut für Informatik, Technische Universität München, 1987.
47. Jürgen Schmidhuber. Learning to control fast-weight memories: An alternative to dynamic recurrent networks. Neural Computation, 4(1):131–139, 1992.
48. Jonas Sjöberg and Lennart Ljung. Overtraining, regularization and searching for a minimum, with application to neural networks. International Journal of Control, 62(6):1391–1407, 1995.
49. Jake Snell, Kevin Swersky, and Richard S Zemel. Prototypical networks for few-shot learning. In Advances in Neural Information Processing Systems (NIPS) 30, 2017.
50. Harold W Sorenson and Daniel L Alspach. Recursive Bayesian estimation using Gaussian sums. Automatica, 7 (4):465–479, 1971.
51. Flood Sung, Yongxin Yang, Li Zhang, Tao Xiang, Philip H. S. Torr, and Timothy M. Hospedales. Learning to compare: Relation network for few-shot learning. CoRR, abs/1711.06025, 2017.
52. Joshua B Tenenbaum. A Bayesian framework for concept learning. PhD thesis, Massachusetts Institute of Technology, 1999.
53. Sebastian Thrun and Lorien Pratt. Learning to learn. Kluwer Academic Publishers, 1998.
54. Eleni Triantafillou, Richard Zemel, and Raquel Urtasun. Few-shot learning through an information retrieval lens. In Advances in Neural Information Processing Systems (NIPS) 30, 2017.
55. Charles F Van Loan. The ubiquitous Kronecker product. Journal of computational and applied mathematics, 123(1):85–100, 2000.
56. Oriol Vinyals, Charles Blundell, Tim Lillicrap, Daan Wierstra, et al. Matching networks for one shot learning. In Advances in Neural Information Processing Systems (NIPS) 29, pp. 3630–3638, 2016.
57. Jing Wan, Zhilin Zhang, Jingwen Yan, Taiyong Li, Bhaskar D Rao, Shiaofen Fang, Sungeun Kim, Shannon L Risacher, Andrew J Saykin, and Li Shen. Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer’s disease. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 940–947. IEEE, 2012.
58. Olga Wichrowska, Niru Maheswaranathan, Matthew W Hoffman, Sergio Gomez Colmenarejo, Misha Denil, Nando de Freitas, and Jascha Sohl-Dickstein. Learned optimizers that scale and generalize. In Proceedings of the 34th International Conference on Machine Learning (ICML), 2017.
59. Kai Yu, Volker Tresp, and Anton Schwaighofer. Learning Gaussian processes from multiple tasks. In Proceedings of the 22nd International Conference on Machine Learning (ICML), pp. 1012–1019, 2005.