Estimating the Fundamental Limits is Easier Than Achieving the Fundamental Limits

@article{Jiao2019EstimatingTF,
  title={Estimating the Fundamental Limits is Easier Than Achieving the Fundamental Limits},
  author={Jiantao Jiao and Yanjun Han and Irena Fischer-Hwang and Tsachy Weissman},
  journal={IEEE Transactions on Information Theory},
  year={2019},
  volume={65},
  pages={6704-6715}
}
We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct the explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under logarithmic loss, we show that in the finite space setting, when it is possible to construct an estimator of the limits with vanishing error with <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> samples, it may require at least… Expand
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References

SHOWING 1-10 OF 56 REFERENCES
Maximum Likelihood Estimation of Functionals of Discrete Distributions
TLDR
The worst case squared error risk incurred by the maximum likelihood estimator (MLE) in estimating the Shannon entropy is described and it is established that the MLE achieves the minimax optimal rate regardless of the alphabet size. Expand
Estimating Learnability in the Sublinear Data Regime
TLDR
It is often possible to accurately estimate this "learnability" even when given an amount of data that is too small to reliably learn any accurate model, as well as to establish that these sample complexities are optimal, to constant factors. Expand
Variational Minimax Estimation of Discrete Distributions under KL Loss
TLDR
In the sparse-data limit c → 0, it is found that the Dirichlet-Bayes (add-constant) estimator with parameter scaling like - c log(c) optimizes both the upper and lower bounds, suggesting an optimal choice of the "add- constant" parameter in this regime. Expand
Estimating the unseen: an n/log(n)-sample estimator for entropy and support size, shown optimal via new CLTs
We introduce a new approach to characterizing the unobserved portion of a distribution, which provides sublinear--sample estimators achieving arbitrarily small additive constant error for a class ofExpand
Minimax Estimation of Functionals of Discrete Distributions
TLDR
The minimax rate-optimal mutual information estimator yielded by the framework leads to significant performance boosts over the Chow-Liu algorithm in learning graphical models and the practical advantages of the schemes for the estimation of entropy and mutual information. Expand
Minimax rate-optimal estimation of KL divergence between discrete distributions
TLDR
A minimax rate-optimal estimator is constructed which is adaptive in the sense that it does not require the knowledge of the support size nor the upper bound on the likelihood ratio, and the effective sample size enlargement phenomenon holds. Expand
Risk bounds for statistical learning
We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of theExpand
Estimating the Unseen
TLDR
This work can be seen as introducing a robust, general, and theoretically principled framework that, for many practical applications, essentially amplifies the sample size by a logarithmic factor; it is expected that it may be fruitfully used as a component within larger machine learning and statistical analysis systems. Expand
Minimax Rates of Entropy Estimation on Large Alphabets via Best Polynomial Approximation
TLDR
It is shown that the minimax mean-square error is within the universal multiplicative constant factors of (k/n log k)2 t log2 k/n if n exceeds a constant factor of ( k/log k); otherwise, there exists no consistent estimator. Expand
The Power of Linear Estimators
  • G. Valiant, Paul Valiant
  • Mathematics, Computer Science
  • 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
  • 2011
TLDR
The main result is that for any property in this broad class of practically relevant distribution properties, there exists a near-optimal linear estimator, and a practical and polynomial-time algorithm for constructing such estimators for any given parameters. Expand
...
1
2
3
4
5
...