A Bayesian model of learning to learn by sampling from multiple tasks is presented. The multiple tasks are themselves generated by sampling from a distribution over an environment of related tasks. Such an environment is shown to be naturally modelled within a Bayesian context by the concept of an objective prior distribution. It is argued that for many common machine learning problems, although in general we do not know the true (objective) prior for the problem, we do have some idea of a set of possible priors to which the true prior belongs. It is shown that under these circumstances a learner can use Bayesian inference to learn the true prior by learning sufficiently many tasks from the environment. In addition, bounds are given on the amount of information required to learn a task when it is simultaneously learnt with several other tasks. The bounds show that if the learner has little knowledge of the true prior, but the dimensionality of the true prior is small, then sampling multiple tasks is highly advantageous. The theory is applied to the problem of learning a common feature set or equivalently a low-dimensional-representation (LDR) for an environment of related tasks.
Abu-Mostafa, Y.S. (1989). Learning from Hints in Neural Networks. Journal of Complexity, 6:192–198.
Anthony, Martin & Bartlett, Peter. (1995). Function learning from interpolation. In Proceedings of the Second European Conference on Computational Learning Theory, Barcelona. Springer-Verlag.
Barron, Andrew & Clarke, Bertrand. (1994). Jeffreys' Prior is Asymptotically Least Favourable under Entropy Risk. Journal of Statistical Planning and Inference, 41:37–60.
Bartlett, Peter, Long, Philip & Williamson, Bob. (1994). Fat-Shattering and the Learnability of Real-Valued Functions. In Proccedings of the Seventh ACM Conference on Computational Learning Theory, New York. ACM Press.
Baxter, Jonathan. (1995a). A Model of Bias Learning. Technical Report LSE-MPS-97, London School of Economics, Centre for Discrete and Applicable Mathematics. Submitted for publication.
Baxter, Jonathan. (1995b). Learning Internal Representations. In Proceedings of the Eighth International Conference on Computational Learning Theory, pages 311–320, Santa Cruz, California. ACM Press.
Baxter, Jonathan. (1996a). A Bayesian/Information Theoretic Model of Bias Learning. In Proccedings of the Ninth ACM Conference on Computational Learning Theory, New York. ACM Press.
Baxter, Jonathan. (1996b). Learning Model Bias. In Advances in Neural Information Processing Systems 8, pages 169–175.
Berger, James O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York.
Berger, James O. (1986) Multivariate Estimation: Bayes, Empirical Bayes, and Stein Approaches. SIAM.
Bridle, J.S. (1989). Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In F Fogelman-Soulie and J Herault, editors, Neurocomputing: Algorithms, Architectures. Springer Verlag, New York.
Caruana, Richard. (1993). Learning Many Related Tasks at the Same Time with Backpropagation. In Advances in Neural Information Processing 5.
Clarke, Bertrand & Barron, Andrew. (1990). Information-Theoretic Asymptotics of Bayes Methods. IEEE Transactions on Information Theory, 36:453–471.
Cover, T.M. & Thomas, J.A. (1991). Elements of Information Theory. John Wiley & Sons, Inc., New York.
Fefferman, Charles. (1994). Reconstructing a neural network from its output. Rev. Mat. Iberoamericana, 10:507–555.
Good, I.J. (1980). Some History of the Hierarchical Bayesian Methodology. In J M Bernado, M H De Groot, D V Lindley, and A F M Smith, editors, Bayesian Statistics II. University Press, Valencia.
Haussler, David & Opper, Manfred. (1995a). General Bounds on the Mutual Information Between a Parameter and n Conditionally Independent Observations. In Proccedings of the Eighth ACM Conference on Computational Learning Theory, New York. ACM Press.
Haussler, David & Opper, Manfred. (1995b). Mutual Information, Metric Entropy and Risk in Estimation of Probability Distributions. Submitted to Annals of Statistics.
Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural Networks, 4:251–257.
Mackay, David. (1991). Bayesian Interpolation. Neural Computation, 4:415–447.
Mackay, David. (1991). The Evidence Framework Applied to Classification Networks. Neural Computation, 4:698–714.
Mitchell, Tom M. (1990). The need for biases in learning generalisations. In Tom G Dietterich and Jude Shavlik, editors, Readings in Machine Learning. Morgan Kaufmann.
Mitchell, Tom M. & Thrun, Sebastian. (1994). Learning One More Thing. Technical Report CMU-CS-94-184, CMU.
Pratt, Lori Y. (1992). Discriminability-based transfer between neural networks. In Stephen J Hanson, Jack D Cowan, and C Lee Giles, editors, Advances in Neural Information Processing Systems 5, pages 204–211, San Mateo. Morgan Kaufmann.
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Baxter, J. A Bayesian/Information Theoretic Model of Learning to Learn via Multiple Task Sampling. Machine Learning 28, 7–39 (1997). https://doi.org/10.1023/A:1007327622663
- Hierarchichal Bayesian Inference
- Bias learning
- Feature Learning
- Neural Networks
- Information Theory