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# Learn to Solve Algebra Word Problems Using Quadratic Programming

Conference on Empirical Methods in Natural Language Processing, (2015)

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摘要

This paper presents a new algorithm to automatically solve algebra word problems. Our algorithm solves a word problem via analyzing a hypothesis space containing all possible equation systems generated by assigning the numbers in the word problem into a set of equation system templates extracted from the training data. To obtain a robust ...更多

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简介

- An algebra word problem describes a mathematical problem which can be typically modeled by an equation system, as demonstrated in Figure 1.
- Using machine learning techniques to construct the solver has become a new trend (Kushman et al, 2014; Hosseini et al, 2014; Amnueypornsakul and Bhat, 2014; Roy et al, 2015)
- This is based on the fact that word problems derived from the same mathematical problem share some common semantic and syntactic features due to the same underlying logic.

重点内容

- An algebra word problem describes a mathematical problem which can be typically modeled by an equation system, as demonstrated in Figure 1
- The experimental results show that our algorithm significantly outperforms the state-of-the-art baseline (Kushman et al, 2014)
- We present a new algorithm to learn to solve algebra word problems
- To reduce the possible derivations, we only consider filling the number slots of the equation system templates, and design effective features to describe the relationship between numbers and unknowns
- We use the max-margin objective to train the log-linear model. This results in a quadratic programming (QP) problem that can be efficiently solved via the constraint generation algorithm

方法

- Assume n1 and n2 are two numbers in a word Dataset: The dataset used in the experiment is problem.
- The version of the parser is the max same as (Kushman et al, 2014).
- The performance of the algorithm is evaluated by comparing each nouni1∈N P1, nounj2∈N P2 s.t. nouni1=nounj2 ord nouni1 + ord nounj2 number of the correct answer with the calculated one, regardless of the ordering.
- The authors report the average accuracy of 5-fold cross-validation

结果

- Experimental results show that the algorithm achieves 79.7% accuracy, about 10% higher than the state-of-the-art baseline (Kushman et al., 2014).
- Experimental results show that the algorithm significantly outperforms the state-of-the-art baseline (Kushman et al, 2014)

结论

- The authors present a new algorithm to learn to solve algebra word problems.
- The authors use the max-margin objective to train the log-linear model.
- This results in a QP problem that can be efficiently solved via the constraint generation algorithm.
- The authors would like to compare the algorithm with the algorithms designed for specific word problems, such as (Hosseini et al, 2014)

- Table1: Features used in our algorithm
- Table2: Learning statistics
- Table3: Algorithm comparison
- Table4: Ablation study for fully supervised data
- Table5: The problems of our algorithm

基金

- This work is supported by the National Basic Research Program of China (973 program No 2014CB340505)

引用论文

- Bussaba Amnueypornsakul and Suma Bhat. 2014. Machine-guided solution to mathematical word problems.
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