| Minka, T.P. Automatic Choice of Dimensionality for PCA Advances in Neural Information Processing Systems 2000 :598-604 [pdf] |
| A central issue in principal component analysis PCA is choosing the number of principal components to be retained By interpreting PCA as density estimation this paper shows how to use Bayesian model selection to determine the true dimensionality of the data The resulting estimate is simple to compute yet guaranteed to pick the correct dimensionality given enough data The estimate involves an integral over the Steifel manifold of k frames which is di cult to compute exactly But after choosing an appropriate parameterization and applying Laplace s method an accurate and practical estimator is obtained In simulations it is more accurate than cross validation and other proposed algorithms plus it runs much faster |
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| Philipona, D., O'Regan, J.K., Nadal, J.-P. , Coenen, O.J.-M. Perception of the structure of the physical world using unknown sensors and effectors Advances in Neural Information Processing Systems 2004 (15) [pdf] |
| Is there a way for an algorithm linked to an unknown body to infer by itself information about this body and the world it is in? Taking the case of space for example, is there a way for this algorithm to realize that its body is in a three dimensional world? Is it possible for this algorithm to discover how to move in a straight line? And more basically: do these questions make any sense at all given that the algorithm only has access to the very high-dimensional data consisting of its sensory inputs and motor outputs? We demonstrate in this article how these questions can be given a positive answer. We show that it is possible to make an algorithm that, by analyzing the law that links its motor outputs to its sensory inputs, discovers information about the structure of the world regardless of the devices constituting the body it is linked to. We present results from simulations demonstrating a way to issue motor orders resulting in fundamental movements of the body as regards the structure of the physical world. |
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