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Sharper lower bounds on the performance of the empirical risk minimization algorithm
empirical risk minimization learning theory lower bound multidimensional central limit theorem uniform central limit theorem
2011/3/24
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
Fluctuation bounds for the asymmetric simple exclusion process
exclusion process particle current second class particle coupling moment bound fluctuations
2009/6/15
We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the order...
We slightly improve the upper bounds of disconnection exponents for planar Brownian motion that we derived in an earlier paper. We also give a proof of the lower bound $1/(2pi)$ for the disconnection ...
On Constrained Annealed Bounds for Pinning and Wetting Models
Disordered Systems Quenched Disorder Annealed Models Polymer Models
2009/4/24
The free energy of quenched disordered systems is bounded above by the free energy of the corresponding annealed system. This bound may be improved by applying the annealing procedure, which is just J...
Exponential tail bounds for max-recursive sequences
recursive algorithm exponential bounds divide and conquer algorithm
2009/4/23
Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in...