Polynomial time relatively computable triangular arrays for almost sure convergence

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

Download Full-text

Polynomial Time Joint Structural Inference for Sentence Compression

10.3115/v1/p14-2054 ◽

2014 ◽

Cited By ~ 4

Author(s):

Xian Qian ◽

Yang Liu

Keyword(s):

Polynomial Time ◽

Structural Inference ◽

Sentence Compression

Download Full-text

The Impossibility of Polynomial Time Solutions for Conjunctive Expressions with Binary Variables

SSRN Electronic Journal ◽

10.2139/ssrn.2996544 ◽

2017 ◽

Author(s):

Grigor Mulla

Keyword(s):

Polynomial Time ◽

Binary Variables

Download Full-text

On the Markov Transition Kernels for First Passage Percolation on the Ladder

Journal of Applied Probability ◽

10.1017/s0021900200007932 ◽

2011 ◽

Vol 48 (02) ◽

pp. 366-388 ◽

Cited By ~ 1

Author(s):

Eckhard Schlemm

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Asymptotic Variance ◽

Almost Sure Convergence ◽

First Passage Percolation ◽

First Passage ◽

Percolation Problem ◽

Vertex Set ◽

Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

Download Full-text