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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Renyi to Renyi -- Source Coding under Siege
Michael B. Baer · 2006-02-18 · via cs.DS updates on arXiv.org

A novel lossless source coding paradigm applies to problems of unreliable lossless channels with low bit rates, in which a vital message needs to be transmitted prior to termination of communications. This paradigm can be applied to Alfred Renyi's secondhand account of an ancient siege in which a spy was sent to scout the enemy but was captured. After escaping, the spy returned to his base in no condition to speak and unable to write. His commander asked him questions that he could answer by nodding or shaking his head, and the fortress was defended with this information. Renyi told this story with reference to prefix coding, but maximizing probability of survival in the siege scenario is distinct from yet related to the traditional source coding objective of minimizing expected codeword length. Rather than finding a code minimizing expected codeword length $\sum_{i=1}^n p(i) l(i)$, the siege problem involves maximizing $\sum_{i=1}^n p(i) θ^{l(i)}$ for a known $θ\in (0,1)$. When there are no restrictions on codewords, this problem can be solve using a known generalization of Huffman coding. The optimal solution has coding bounds which are functions of Renyi entropy; in addition to known bounds, new bounds are derived here. The alphabetically constrained version of this problem has applications in search trees and diagnostic testing. A novel dynamic programming algorithm -- based upon the oldest known algorithm for the traditional alphabetic problem -- optimizes this problem in $O(n^3)$ time and $O(n^2)$ space, whereas two novel approximation algorithms can find a suboptimal solution faster: one in linear time, the other in $O(n \log n)$. Coding bounds for the alphabetic version of this problem are also presented.