[PDF] Top 20 Dimension-Free Error Bounds from Random Projections

... of error bounds for learning settings where such dependence is known to be essential in ...of random projections to take advan- tage of benign low complexity geometry – leveraged here in a ... See full document

... these dimension-free inequalities is that the spectral learning algorithm is consistent, even if the whole empirical Hankel matrix is used, suggesting that the choice of relevant sets of rows and columns is ... See full document

... the error rates of certain learning al- gorithms, with particular focus on refining logarithmic ...obtaining bounds on the error rates of sample-consistent classifiers with monotonic error ... See full document

... linear random projections is to multiply the original data matrix A ∈ R n × D with a random projection matrix R ∈ R D × k , resulting in a projected matrix B = AR ∈ R n × k ...distances) from ... See full document

... using random subsets In this section we present a general formulation of our method for obtaining lower bounds for the dimensions of sections of a set given a knowledge of the dimensions of ... See full document

... a random subclass of ...coordinate projections of this random subclass. Sharp generalization bounds can be obtained when the “size” of the set of coordinate projections of the ... See full document

... where the last equality follows from (3.11). This immediately implies that the opera- tor S maps K* into K*. Moreover, the operator S is continuous and completely contin- uous. Schauder ’ s fixed point theorem ... See full document

... The new approach developed in this paper is simple and easy to apply. It is based on first establishing an appropriate Dirichlet-type result (assuming it does not already exist) and then applying the Mass Transference ... See full document

... Proof: Suppose that d x g x ( , ( ) ) = − x g x ( ) for x ∈ k . By the mean-value theorem and the given condi- tion , g x ( ) is a contraction mapping of the complete metric space k into itself . Hence , by Corollary 1.4 ... See full document

... best error bound for quartic spline ...uniqueness, error bounds and convergence properties of deficient quartic spline interpolation which matches the given function of mesh points and mid points, ... See full document

... the free, mov- ing, unilateral, and equilibrium problems arising in elasticity, fluid flow through porous media, finance, economics, transportation, circuit, and structural analysis in a unified framework; see [1, ... See full document

... parameters from the observed ...of projections from different view angles are identical to each ...the projections with different view angles because the projec- tion data themselves are not ... See full document

... The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, ... See full document

... Abstract. This paper initiates the study of preserving differential pri- vacy (DP) when the data-set is sparse. We study the problem of con- structing efficient sanitizer that preserves DP and guarantees high utility for ... See full document

... This paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideratio[r] ... See full document

... much random error there is in a given ...distance from the equator to the North ...of random error that may be present in a study and how common pitfalls of handling random ... See full document

... Theorem 2.4 says that [f ≤ α] 6 = ∅ whenever τ := inf x∈[α<f<β] d ∗ (0, ∂f(x)) > 0 and that τ is the greatest positive number such that (GE) γβ holds for all α ≤ γ < β. Moreover, in that case, one has (GE) γβ ... See full document

... Shawe-Taylor and Cristianini (1998) and Bennett et al. (2000) obtain a generalization error bound for the special case in which the margin error is zero. The following theorem improves that bound and ... See full document

... Bayesian approaches to learning and estimation have played a significant role in the Statistics lit- erature over many years. While they are often provably optimal in a frequentist setting, and lead to excellent ... See full document

... results from the perturbation theory of symmetric matrices which are collected in the Appendix, while the estimates of the norm of the error matrices in Section 4 and 5 rely on standard large deviation ... See full document