By Jyrki Kivinen, Csaba Szepesvári, Esko Ukkonen, Thomas Zeugmann (auth.), Jyrki Kivinen, Csaba Szepesvári, Esko Ukkonen, Thomas Zeugmann (eds.)
This e-book constitutes the refereed complaints of the twenty second foreign convention on Algorithmic studying conception, ALT 2011, held in Espoo, Finland, in October 2011, co-located with the 14th overseas convention on Discovery technology, DS 2011.
The 28 revised complete papers offered including the abstracts of five invited talks have been conscientiously reviewed and chosen from quite a few submissions. The papers are divided into topical sections of papers on inductive inference, regression, bandit difficulties, on-line studying, kernel and margin-based equipment, clever brokers and different studying models.
Read or Download Algorithmic Learning Theory: 22nd International Conference, ALT 2011, Espoo, Finland, October 5-7, 2011. Proceedings PDF
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Extra resources for Algorithmic Learning Theory: 22nd International Conference, ALT 2011, Espoo, Finland, October 5-7, 2011. Proceedings
Even though a Boltzmann Machine is a parametric model when we consider the dimensionality nh of h to be ﬁxed, in practice one allows nh to vary, making it a non-parametric model. With nh large enough, one can model any discrete distribution: Le Roux and Bengio (2008) showed that Restricted Boltzmann Machines (described below) are universal approximators, and since they are special cases 28 Y. Bengio and O. Delalleau of Boltzmann Machines, Boltzmann Machines also are universal approximators.
Show that the number of unique √ products found in the expanded polynomial representation of f ∈ Fn is 2 n−1 . 2. Prove that the only possible architecture for a shallow sum-product network to compute f is to have a hidden layer made of product units, with a sum unit as output. 3. Conclude that the number of hidden units in step 2 must be at least the number of unique products computed in step 1. For family G, we obtain that a shallow sum-product network computing gin ∈ Gin must have at least (n−1)i hidden units.
RBMs are typically trained by stochastic gradient descent, using a noisy (and generally biased) estimator of the above log-likelihood gradient. , 2006), and it has a particularly simple form: the negative phase gradient is obtained by starting a very short chain (usually just one step) at the observed x and replacing the above expectations by the corresponding samples. , 2010) or unsupervised (Hinton and Salakhutdinov, 2006) neural network. Another common way to train RBMs is based on the Stochastic Maximum Likelihood (SML) estimator (Younes, 1999) of the gradient, also called Persistent Contrastive Divergence (PCD; Tieleman, 2008) when it was introduced for RBMs.
Algorithmic Learning Theory: 22nd International Conference, ALT 2011, Espoo, Finland, October 5-7, 2011. Proceedings by Jyrki Kivinen, Csaba Szepesvári, Esko Ukkonen, Thomas Zeugmann (auth.), Jyrki Kivinen, Csaba Szepesvári, Esko Ukkonen, Thomas Zeugmann (eds.)