62,351 research outputs found

    Cascading Randomized Weighted Majority: A New Online Ensemble Learning Algorithm

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    With the increasing volume of data in the world, the best approach for learning from this data is to exploit an online learning algorithm. Online ensemble methods are online algorithms which take advantage of an ensemble of classifiers to predict labels of data. Prediction with expert advice is a well-studied problem in the online ensemble learning literature. The Weighted Majority algorithm and the randomized weighted majority (RWM) are the most well-known solutions to this problem, aiming to converge to the best expert. Since among some expert, the best one does not necessarily have the minimum error in all regions of data space, defining specific regions and converging to the best expert in each of these regions will lead to a better result. In this paper, we aim to resolve this defect of RWM algorithms by proposing a novel online ensemble algorithm to the problem of prediction with expert advice. We propose a cascading version of RWM to achieve not only better experimental results but also a better error bound for sufficiently large datasets.Comment: 15 pages, 3 figure

    A Las Vegas Algorithm for the Ordered Majority Problem

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    In this thesis, we study the majority problem using ordered comparisons under the Las Vegas randomized algorithm model. The majority problem asks whether a given set of n elements, each with some colour, has a colour which appears on more than half of the elements. We focus on algorithms for this problem whose fundamental operation is to compare two elements, and in particular the comparison returns one of {}. Additionally, we are interested specifically in Las Vegas randomized algorithms for this problem, which solve the problem correctly in all cases but whose running time is a random variable. Interestingly, most previous work studying this problem considers a different model where comparisons return just whether two elements are equal or not, instead of providing ordered information. Our contribution is a novel Las Vegas algorithm that uses only n + o(n) comparisons in the expectation, compared to 7n/6 + o(n) comparisons required in the expectation by the previous best algorithm for this problem

    Randomized Algorithms for Determining the Majority on Graphs

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    Every node of an undirected connected graph is colored white or black. Adjacent nodes can be compared and the outcome of each comparison is either 0 (same color) or 1 (different colors). The aim is to discover a node of the majority color, or to conclude that there is the same number of black and white nodes. We consider randomized algorithms for this task and establish upper and lower bounds on their expected running time. Our main contribution are lower bounds showing that some simple and natural algorithms for this problem cannot be improved in general

    Quantum Algorithms for Learning Symmetric Juntas via the Adversary Bound

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    In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function f on n variables that only depends on k variables, and, when restricted to them, equals some predefined function h. The task is to identify the variables the function depends on.When h is the XOR or the OR function, this gives a restricted variant of the Bernstein–Vazirani or the combinatorial group testing problem, respectively. We analyze the general case using the adversary bound and give an alternative formulation for the quantum query complexity of this problem. We construct optimal quantum query algorithms for the cases when h is the OR function (complexity is Θ(√k) ) or the exact-half function (complexity is O(k[supercript 1/4])). The first algorithm resolves an open problem from Ambainis & Montanaro (Quantum Inf Comput 14(5&6): 439–453, 2014). For the case when h is the majority function, we prove an upper bound of O(k[supercript 1/4]). All these algorithms can be made exact. We obtain a quartic improvement when compared to the randomized complexity (if h is the exact-half or the majority function), and a quadratic one when compared to the non-adaptive quantum complexity (for all functions considered in the paper).National Science Foundation (U.S.) (Scott Aaronson’s Alan T. Waterman Award

    Three Puzzles on Mathematics, Computation, and Games

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    In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure
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