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cs.DS updates on arXiv.org

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
Sample(x)=(a*x<=t) is a distinguisher with probability...
Mikkel Thorup · 2014-11-19 · via cs.DS updates on arXiv.org

A random sampling function Sample:U->{0,1} for a key universe U is a distinguisher with probability p if for any given assignment of values v(x) to the keys x in U, including at least one non-zero v(x)!=0, the sampled sum sum{ v(x) | x in U and Sample(x) } is non-zero with probability at least p. Here the key values may come from any commutative monoid (addition is commutative and associative and zero is neutral). Such distinguishers were introduced by Vazirani [PhD thesis 1986], and Naor and Naor used them for their small bias probability spaces [STOC'90]. Constant probability distinguishers are used for testing in contexts where the key values are not computed directly, yet where the sum is easily computed. A simple example is when we get a stream of key value pairs (x_1,v_1),(x_2,v_2),...,(x_n,v_n) where the same key may appear many times. The accumulated value of key x is v(x)=sum{v_i | x_i=x}. For space reasons, we may not be able to maintain v(x) for every key x, but the sampled sum is easily maintained as the single value sum{v_i | Sample(x_i)}. Here we show that when dealing with w-bit integers, if a is a uniform odd w-bit integer and t is a uniform w-bit integer, then Sample(x)=[ax mod 2^w <= t] is a distinguisher with probability 1/8. Working with standard units, that is, w=8, 16, 32, 64, we exploit that w-bit multiplication works modulo 2^w, discarding overflow automatically, and then the sampling decision is implemented by the C-code a*x<=t. Previous such samplers were much less computer friendly, e.g., the distinguisher of Naor and Naor [STOC'90] was more complicated and involved a 7-independent hash function.