The Latent Relation Mapping Engine: Algorithm and Experiments

Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure Mapping Engine (SME). A limitation of SME is the requirement for complex hand-coded representations. We introduce the Latent Relation Mapping Engine (LRME), which combines ideas from SME and Latent Relational Analysis (LRA) in order to remove the requirement for hand-coded representations. LRME builds analogical mappings between lists of words, using a large corpus of raw text to automatically discover the semantic relations among the words. We evaluate LRME on a set of twenty analogical mapping problems, ten based on scientific analogies and ten based on common metaphors. LRME achieves human-level performance on the twenty problems. We compare LRME with a variety of alternative approaches and find that they are not able to reach the same level of performance.Comment: related work available at http://purl.org/peter.turney

A theory of cross-validation error

This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of simplicity and accuracy. Furthermore, the theory indicates precisely how these conflicting demands must be balanced, in order to minimize cross-validation error. A general theory is presented, then it is developed in detail for linear regression and instance-based learning

Technical note: Bias and the quantification of stability

Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias

Cost-Sensitive Classification: Empirical Evaluation of a Hybrid Genetic Decision Tree Induction Algorithm

This paper introduces ICET, a new algorithm for cost-sensitive classification. ICET uses a genetic algorithm to evolve a population of biases for a decision tree induction algorithm. The fitness function of the genetic algorithm is the average cost of classification when using the decision tree, including both the costs of tests (features, measurements) and the costs of classification errors. ICET is compared here with three other algorithms for cost-sensitive classification - EG2, CS-ID3, and IDX - and also with C4.5, which classifies without regard to cost. The five algorithms are evaluated empirically on five real-world medical datasets. Three sets of experiments are performed. The first set examines the baseline performance of the five algorithms on the five datasets and establishes that ICET performs significantly better than its competitors. The second set tests the robustness of ICET under a variety of conditions and shows that ICET maintains its advantage. The third set looks at ICET's search in bias space and discovers a way to improve the search.Comment: See http://www.jair.org/ for any accompanying file

Human-Level Performance on Word Analogy Questions by Latent Relational Analysis

This paper introduces Latent Relational Analysis (LRA), a method for measuring relational similarity. LRA has potential applications in many areas, including information extraction, word sense disambiguation, machine translation, and information retrieval. Relational similarity is correspondence between relations, in contrast with attributional similarity, which is correspondence between attributes. When two words have a high degree of attributional similarity, we call them synonyms. When two pairs of words have a high degree of relational similarity, we say that their relations are analogous. For example, the word pair mason/stone is analogous to the pair carpenter/wood; the relations between mason and stone are highly similar to the relations between carpenter and wood. Past work on semantic similarity measures has mainly been concerned with attributional similarity. For instance, Latent Semantic Analysis (LSA) can measure the degree of similarity between two words, but not between two relations. Recently the Vector Space Model (VSM) of information retrieval has been adapted to the task of measuring relational similarity, achieving a score of 47% on a collection of 374 college-level multiple-choice word analogy questions. In the VSM approach, the relation between a pair of words is characterized by a vector of frequencies of predefined patterns in a large corpus. LRA extends the VSM approach in three ways: (1) the patterns are derived automatically from the corpus (they are not predefined), (2) the Singular Value Decomposition (SVD) is used to smooth the frequency data (it is also used this way in LSA), and (3) automatically generated synonyms are used to explore reformulations of the word pairs. LRA achieves 56% on the 374 analogy questions, statistically equivalent to the average human score of 57%. On the related problem of classifying noun-modifier relations, LRA achieves similar gains over the VSM, while using a smaller corpus

Empirical Evaluation of Four Tensor Decomposition Algorithms

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in information retrieval, collaborative filtering, computational linguistics, computational vision, and other fields. However, SVD is limited to two-dimensional arrays of data (two modes), and many potential applications have three or more modes, which require higher-order tensor decompositions. This paper evaluates four algorithms for higher-order tensor decomposition: Higher-Order Singular Value Decomposition (HO-SVD), Higher-Order Orthogonal Iteration (HOOI), Slice Projection (SP), and Multislice Projection (MP). We measure the time (elapsed run time), space (RAM and disk space requirements), and fit (tensor reconstruction accuracy) of the four algorithms, under a variety of conditions. We find that standard implementations of HO-SVD and HOOI do not scale up to larger tensors, due to increasing RAM requirements. We recommend HOOI for tensors that are small enough for the available RAM and MP for larger tensors

Distributional semantics beyond words: Supervised learning of analogy and paraphrase

There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to extend beyond words is to compare two tuples using a function that combines pairwise similarities between the component words in the tuples. A strength of this approach is that it works with both relational similarity (analogy) and compositional similarity (paraphrase). However, past work required hand-coding the combination function for different tasks. The main contribution of this paper is that combination functions are generated by supervised learning. We achieve state-of-the-art results in measuring relational similarity between word pairs (SAT analogies and SemEval~2012 Task 2) and measuring compositional similarity between noun-modifier phrases and unigrams (multiple-choice paraphrase questions)

Measuring Semantic Similarity by Latent Relational Analysis

This paper introduces Latent Relational Analysis (LRA), a method for measuring semantic similarity. LRA measures similarity in the semantic relations between two pairs of words. When two pairs have a high degree of relational similarity, they are analogous. For example, the pair cat:meow is analogous to the pair dog:bark. There is evidence from cognitive science that relational similarity is fundamental to many cognitive and linguistic tasks (e.g., analogical reasoning). In the Vector Space Model (VSM) approach to measuring relational similarity, the similarity between two pairs is calculated by the cosine of the angle between the vectors that represent the two pairs. The elements in the vectors are based on the frequencies of manually constructed patterns in a large corpus. LRA extends the VSM approach in three ways: (1) patterns are derived automatically from the corpus, (2) Singular Value Decomposition is used to smooth the frequency data, and (3) synonyms are used to reformulate word pairs. This paper describes the LRA algorithm and experimentally compares LRA to VSM on two tasks, answering college-level multiple-choice word analogy questions and classifying semantic relations in noun-modifier expressions. LRA achieves state-of-the-art results, reaching human-level performance on the analogy questions and significantly exceeding VSM performance on both tasks

Word Sense Disambiguation by Web Mining for Word Co-occurrence Probabilities

This paper describes the National Research Council (NRC) Word Sense Disambiguation (WSD) system, as applied to the English Lexical Sample (ELS) task in Senseval-3. The NRC system approaches WSD as a classical supervised machine learning problem, using familiar tools such as the Weka machine learning software and Brill's rule-based part-of-speech tagger. Head words are represented as feature vectors with several hundred features. Approximately half of the features are syntactic and the other half are semantic. The main novelty in the system is the method for generating the semantic features, based on word co-occurrence probabilities. The probabilities are estimated using the Waterloo MultiText System with a corpus of about one terabyte of unlabeled text, collected by a web crawler

A Uniform Approach to Analogies, Synonyms, Antonyms, and Associations

Recognizing analogies, synonyms, antonyms, and associations appear to be four\ud distinct tasks, requiring distinct NLP algorithms. In the past, the four\ud tasks have been treated independently, using a wide variety of algorithms.\ud These four semantic classes, however, are a tiny sample of the full\ud range of semantic phenomena, and we cannot afford to create ad hoc algorithms\ud for each semantic phenomenon; we need to seek a unified approach.\ud We propose to subsume a broad range of phenomena under analogies.\ud To limit the scope of this paper, we restrict our attention to the subsumption\ud of synonyms, antonyms, and associations. We introduce a supervised corpus-based\ud machine learning algorithm for classifying analogous word pairs, and we\ud show that it can solve multiple-choice SAT analogy questions, TOEFL\ud synonym questions, ESL synonym-antonym questions, and similar-associated-both\ud questions from cognitive psychology