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Warren D. Smith

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

5 papers
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5

FOCS Conference 2000 Conference Paper

Testing that distributions are close

  • Tugkan Batu
  • Lance Fortnow
  • Ronitt Rubinfeld
  • Warren D. Smith
  • Patrick White

Given two distributions over an n element set, we wish to check whether these distributions are statistically close by only sampling. We give a sublinear algorithm which uses O(n/sup 2/3//spl epsiv//sup -4/ log n) independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the distributions is small (less than max(/spl epsiv//sup 2//32/sup 3//spl radic/n, /spl epsiv//4/spl radic/n=)) or large (more than /spl epsiv/) in L/sub 1/-distance. We also give an /spl Omega/(n/sup 2/3//spl epsiv//sup -2/3/) lower bound. Our algorithm has applications to the problem of checking whether a given Markov process is rapidly mixing. We develop sublinear algorithms for this problem as well.

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FOCS Conference 1998 Conference Paper

Geometric Separator Theorems & Applications

  • Warren D. Smith
  • Nicholas C. Wormald

We find a large number of "geometric separator theorems" such as: I: Given N disjoint isooriented squares in the plane, there exists a rectangle with /spl les/2N/3 squares inside, /spl les/2N/3 squares outside, and /spl les/(4+0(1))/spl radic/N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at /spl les/(4/spl middot/3/sup 1/4/+0(1))/spl radic/N points, having /spl les/2N/3 sites inside and outside. These theorems yield a large number of applications, such as subexponential algorithms for traveling salesman tour and rectilinear Steiner minimal tree in R/sup d/, new point location algorithms, and new upper and lower bound proofs for "planar separator theorems".

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AIJ Journal 1997 Journal Article

A Bayesian approach to relevance in game playing

  • Eric B. Baum
  • Warren D. Smith

The point of game tree search is to insulate oneself from errors in the evaluation function. The standard approach is to grow a full width tree as deep as time allows, and then value the tree as if the leaf evaluations were exact. The alpha-beta algorithm implements this with great computational efficiency. This approach has been effective in many games. Our approach is to form a Bayesian model of our uncertainty. We adopt an evaluation function that returns a probability distribution estimating the probability of various errors in valuing each position. These estimates are obtained by training from data. We thus use additional information at each leaf not available to the standard approach. We utilize this information in three ways: to evaluate which move is best after we are done expanding, to allocate additional thinking time to moves where additional time is most relevant to game outcome, and, perhaps most importantly, to expand the tree along the most relevant lines. Our measure of the relevance of expanding a given leaf provably approximates a measure of the impact of expanding the leaf on expected payoff, including the impact of the outcome of the leaf expansion on later expansion decisions. Our algorithms run (under reasonable assumptions) in time linear in the size of the final tree and hence except for a small constant factor, are as time efficient as alpha-beta. Our algorithm focuses on relevant lines, on which it can in principle grow a tree several times as deep as alpha-beta in a given amount of time. We have tested our approach on a variety of games, including Othello, Kalah, Warri, and others. Our probability independence approximations are seen to be significantly violated, but nonetheless our tree valuation scheme was found to play significantly better than minimax or the Probability Product rule when both competitors search the same tree. Our full search algorithm was found to outplay a highly ranked, directly comparable alpha-beta Othello program even when the alpha-beta program was given sizeable time odds, and also performed well against the three top Othello programs on the Internet Othello Server.

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