Regret Minimization in Multi-objective Submodular Function MaximizationTasuku Soma
This document presents algorithms for minimizing regret ratio in multi-objective submodular function maximization. It introduces the concept of regret ratio for evaluating the quality of a solution set for multiple objectives. It then proposes two algorithms, Coordinate and Polytope, that provide upper bounds on regret ratio by leveraging approximation algorithms for single objective problems. Experimental results on a movie recommendation dataset show the proposed algorithms achieve significantly lower regret ratios than a random baseline.
Fast Deterministic Algorithms for Matrix Completion ProblemsTasuku Soma
This document summarizes research on fast deterministic algorithms for matrix completion problems. It presents new algorithms for:
1) Matrix completion by rank-one matrices, solving it faster than previous work in O((m+n)2.77) time rather than O(m4.37n) time, where m is the larger matrix dimension and n is the number of indeterminates.
2) Mixed skew-symmetric matrix completion, the first deterministic polynomial time algorithm for this problem.
3) Skew-symmetric matrix completion by rank-two skew-symmetric matrices, the first deterministic polynomial time algorithm for this problem. The algorithms work over an arbitrary field.
Regret Minimization in Multi-objective Submodular Function MaximizationTasuku Soma
This document presents algorithms for minimizing regret ratio in multi-objective submodular function maximization. It introduces the concept of regret ratio for evaluating the quality of a solution set for multiple objectives. It then proposes two algorithms, Coordinate and Polytope, that provide upper bounds on regret ratio by leveraging approximation algorithms for single objective problems. Experimental results on a movie recommendation dataset show the proposed algorithms achieve significantly lower regret ratios than a random baseline.
Fast Deterministic Algorithms for Matrix Completion ProblemsTasuku Soma
This document summarizes research on fast deterministic algorithms for matrix completion problems. It presents new algorithms for:
1) Matrix completion by rank-one matrices, solving it faster than previous work in O((m+n)2.77) time rather than O(m4.37n) time, where m is the larger matrix dimension and n is the number of indeterminates.
2) Mixed skew-symmetric matrix completion, the first deterministic polynomial time algorithm for this problem.
3) Skew-symmetric matrix completion by rank-two skew-symmetric matrices, the first deterministic polynomial time algorithm for this problem. The algorithms work over an arbitrary field.
Multicasting in Linear Deterministic Relay Network by Matrix CompletionTasuku Soma
This document presents a new algorithm for multicasting in linear deterministic relay networks (LDRNs) that is faster than previous algorithms. The algorithm works by first solving the unicast subproblems using an existing algorithm, then determining the linear encoding matrices for each layer simultaneously using mixed matrix completion. This allows the encoding matrices for an entire layer to be determined at once, rather than one node at a time. The new algorithm runs in O(dq(nr)^3 log(nr)) time, which is faster than the previous best algorithm when n = o(r).
Optimal Budget Allocation: Theoretical Guarantee and Efficient AlgorithmTasuku Soma
The document presents two main results:
1. A general framework for submodular function maximization over integer lattices with a (1-1/e)-approximation algorithm that runs in pseudo polynomial time. This extends budget allocation to more complex scenarios.
2. A faster algorithm for budget allocation when influence probabilities are non-increasing, running in almost linear time compared to previous polynomial time algorithms. Experiments on real and large synthetic graphs show it outperforms heuristics by up to 15%.
The low-rank basis problem for a matrix subspaceTasuku Soma
This document summarizes a presentation on finding low-rank bases for matrix subspaces. It introduces the low-rank basis problem, describes a greedy algorithm to solve it using two phases - rank estimation and alternating projection, and proves local convergence guarantees for the algorithm. Experimental results on synthetic and image data demonstrate the algorithm can recover known low-rank bases and separate mixed images. Comparisons are made to tensor decomposition methods for the special case of rank-1 bases.
Nonconvex Compressed Sensing with the Sum-of-Squares MethodTasuku Soma
This document presents a method for nonconvex compressed sensing using the sum-of-squares (SoS) method. It formulates q-minimization, which requires fewer samples than l1-minimization but is nonconvex, as a polynomial optimization problem. The SoS method is then applied to obtain a pseudoexpectation operator satisfying a pseudo robust null space property, guaranteeing stable signal recovery. Specifically, it shows that for a Rademacher measurement matrix, with the number of measurements scaling quadratically in the sparsity s, the SoS method finds a solution x^ satisfying ||x^-x||_q ≤ O(σs(x)q) + ε, providing nearly q-stable recovery.
Active Content-Based Crowdsourcing Task SelectionCarsten Eickhoff
Crowdsourcing has long established itself as a viable alternative to corpus annotation by domain experts for tasks such as document relevance assessment. The crowdsourcing process traditionally relies on high degrees of label redundancy in order to mitigate the detrimental effects of individually noisy worker submissions. Such redundancy comes at the cost of increased label volume, and, subsequently, monetary requirements. In practice, especially as the size of datasets increases, this is undesirable.
In this paper, we focus on an alternate method that exploits document information instead, to infer relevance labels for unjudged documents. We present an active learning scheme for document selection that aims at maximising the overall relevance label prediction accuracy, for a given budget of available relevance judgements by exploiting system-wide estimates of label variance and mutual information. Our experiments are based on TREC 2011 Crowdsourcing Track data and show that our method is able to achieve state-of-the-art performance while requiring 17 – 25% less budget.
This paper has been accepted for presentation at the 25th ACM International Conference on Information and Knowledge Management (CIKM).
Maximizing Submodular Function over the Integer LatticeTasuku Soma
The document describes generalizations of submodular function maximization and submodular cover problems from sets to integer lattices. It presents polynomial-time approximation algorithms for maximizing monotone diminishing return (DR) submodular functions subject to constraints like cardinality, polymatroid and knapsack on the integer lattice. It also presents an algorithm for the DR-submodular cover problem of minimizing cost subject to achieving a quality threshold. The results provide useful extensions of submodular optimization to settings that cannot be modeled as set functions.
24. 提案 概要
1 各 t 対 s–t Ft 求
2 第 1 順番 ，各 線形変換 決定
線形変換 A : w → (Ft 対応 vi 部分 ) 正則
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25. 提案 概要
1 各 t 対 s–t Ft 求
2 第 1 順番 ，各 線形変換 決定
線形変換 A : w → (Ft 対応 vi 部分 ) 正則
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26. 提案 概要
vi+1 = MiXivi = MiXiPiw ,
Ft 対応 vi+1 部分 = Mi[Ft ]XiPiw
(Mi[Ft ]: Ft 対応 Mi 小行列)
Mi[Ft ]XiPi 正則 ⇐⇒ 混合行列
[
I O Pi
Xi I O
O Mi[Ft ] O
]
正則
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27. 提案 概要
全 t 対 混合行列
[
I O Pi
Xi I O
O Mi[Ft ] O
]
正則 Xi
同時混合行列補完 求 ．
定理 (S. ’14)
|F| > q LDRN 上 問題 O(dq(nr)3
log(nr)) 時間
解 ．
d: 受信者数, n: 最大 数, q: 数,
r: 容量
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