Probability Bounds

نویسنده

John Duchi

چکیده

This document starts from simple probalistic inequalities (Markov’s Inequality) and builds up through several stronger concentration results, developing a few ideas about Rademacher complexity, until we give proofs of the main Vapnik-Chervonenkis complexity for learning theory. Many of these proofs are based on Peter Bartlett’s lectures for CS281b at Berkeley or Rob Schapire’s lectures at Princeton. The aim is to have one self-contained document some of the standard uniform convergence results for learning theory.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverag...

متن کامل

Outage Probability Bound and Diversity Gain for Ultra-Wideband Multiple-Access Relay Channels with Correlated Noises

In this paper, Ultra-wideband (UWB) multiple access relay channel with correlated noises at the relay and receiver is investigated. We obtain outer and inner bounds for the IEEE 802.15.3a UWB multiple access relay channel, and also, a diversity gain bound. Finally, we evaluate some results numerically and show that noise correlation coefficients play important role in determining relay position.

متن کامل

Some Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables

In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.

متن کامل

Classes of lower bounds on outage error probability and MSE in Bayesian parameter estimation

In this paper, new classes of lower bounds on the outage error probability and on the mean-square-error (MSE) in Bayesian parameter estimation are proposed. The minima of the h-outage error probability and the MSE are obtained by the generalized maximum a-posteriori probability and the minimum MSE (MMSE) estimators, respectively. However, computation of these estimators and their corresponding ...

متن کامل

General Classes of Lower Bounds on the Probability of Error in Multiple Hypothesis Testing

In this paper, two new classes of lower bounds on the probability of error for m-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion, is usually not tractable. The new classes are derived using Hölder’s inequality and reverse Hölder’s inequality. The bounds in these classes provide good pr...

متن کامل