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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
Efficient Algorithm for Deterministic Search of Hot Elements
Dariusz R. Kowalski, Dominik Pajak · 2022-03-29 · via cs.DS updates on arXiv.org

When facing a very large stream of data, it is often desirable to extract most important statistics online in a short time and using small memory. For example, one may want to quickly find the most influential users generating posts online or check if the stream contains many identical elements. In this paper, we study streams containing insertions and deletions of elements from a possibly large set $N$ of size $|N| = n$, that are being processed by online deterministic algorithms. At any point in the stream the algorithm may be queried to output elements of certain frequency in the already processed stream. More precisely, the most frequent elements in the stream so far. The output is considered correct if the returned elements it contains all elements with frequency greater than a given parameter $\varphi$ and no element with frequency smaller than $\varphi-ε$. We present an efficient online deterministic algorithm for solving this problem using $O(\min(n, \frac{polylog(n)}ε))$ memory and $O(polylog(n))$ time per processing and outputting an element. It is the first such algorithm as the previous algorithms were either randomized, or processed elements in substantially larger time $Ω(\min(n, \frac{\log n}ε))$, or handled only insertions and required two passes over the stream (i.e., were not truly online). Our solution is almost-optimally scalable (with only a polylogarithmic overhead) and does not require randomness or scanning twice through the stream. We complement the algorithm analysis with a lower bound $Ω(\min(n, \frac{1}ε))$ on required memory.