Download Algorithmic Learning Theory: 26th International Conference, by Kamalika Chaudhuri, CLAUDIO GENTILE, Sandra Zilles PDF

By Kamalika Chaudhuri, CLAUDIO GENTILE, Sandra Zilles

This publication constitutes the court cases of the twenty sixth foreign convention on Algorithmic studying conception, ALT 2015, held in Banff, AB, Canada, in October 2015, and co-located with the 18th foreign convention on Discovery technological know-how, DS 2015. The 23 complete papers offered during this quantity have been rigorously reviewed and chosen from forty four submissions. additionally the e-book comprises 2 complete papers summarizing the invited talks and a couple of abstracts of invited talks. The papers are prepared in topical sections named: inductive inference; studying from queries, instructing complexity; computational studying idea and algorithms; statistical studying concept and pattern complexity; on-line studying, stochastic optimization; and Kolmogorov complexity, algorithmic info theory.

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Extra info for Algorithmic Learning Theory: 26th International Conference, ALT 2015, Banff, AB, Canada, October 4-6, 2015, Proceedings

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20]). 32 A. Anandkumar et al. The following theorem implies that if T has an orthogonal decomposition as given in (4), then the set of robust eigenvectors of T are precisely the set {v1 , v2 , . . vk }, implying that the orthogonal decomposition is unique. ) Theorem 6. Let T have an orthogonal decomposition as given in (4). 1. The set of θ ∈ Rn which do not converge to some vi under repeated iteration of (6) has measure zero. 2. The set of robust eigenvectors of T is equal to {v1 , v2 , . .

We start with the simpler case where all of the covariances are identical; this probabilistic model is closely related to the (non-probabilistic) k-means clustering problem [24]. We then consider the case where the spherical variances may differ. Common Covariance. Let wi be the probability of choosing component i ∈ [k], {μ1 , μ2 , . . , μk } ⊂ Rd be the component mean vectors, and σ 2 I be the common covariance matrix. An observation in this model is given by x := μh + z, where h is the discrete random variable with Pr[h = i] = wi for i ∈ [k] (similar to the exchangeable single topic model), and z ∼ N (0, σ 2 I) is an independent multivariate Gaussian random vector in Rd with zero mean and spherical covariance σ 2 I.

AA is supported in part by the NSF Award CCF-1219234, AFOSR Award FA9550-10-1-0310 and the ARO Award W911NF-12-1-0404. References 1. : Tensor decompositions for learning latent variable models. Journal of Machine Learning Research 15, (2014) Tensor Decompositions for Learning Latent Variable Models 37 2. : A spectral algorithm for latent Dirichlet allocation. In: Advances in Neural Information Processing Systems 25, (2012) 3. : Learning mixtures of tree graphical models. In: Advances in Neural Information Processing Systems 25 (2012) 4.

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