Information Matrices in Estimating Function Approach: Tests for Model Misspecification and Model Selection

Estimating functions have been widely used for parameter estimation in various statistical problems. Regular estimating functions produce parameter estimators which have desirable properties, such as consistency and asymptotic normality. In quasi-likelihood inference, an important example of estimating functions, correct specification of the first two moments of the underlying distribution leads to the information unbiasedness, which states that two forms of the information matrix: the negative sensitivity matrix (negative expectation of the first order derivative of an estimating function) and the variability matrix (variance of an estimating function) are equal, or in other words, the analogue of the Fisher information is equivalent to the Godambe information. Consequently, the information unbiasedness indicates that the model-based covariance matrix estimator and sandwich covariance matrix estimator are equivalent. By comparing the model-based and sandwich variance estimators, we propose information ratio (IR) statistics for testing model misspecification of variance/covariance structure under correctly specified mean structure, in the context of linear regression models, generalized linear regression models and generalized estimating equations. Asymptotic properties of the IR statistics are discussed. In addition, through intensive simulation studies, we show that the IR statistics are powerful in various applications: test for heteroscedasticity in linear regression models, test for overdispersion in count data, and test for misspecified variance function and/or misspecified working correlation structure. Moreover, the IR statistics appear more powerful than the classical information matrix test proposed by White (1982). In the literature, model selection criteria have been intensively discussed, but almost all of them target choosing the optimal mean structure. In this thesis, two model selection procedures are proposed for selecting the optimal variance/covariance structure among a collection of candidate structures. One is based on a sequence of the IR tests for all the competing variance/covariance structures. The other is based on an ``information discrepancy criterion" (IDC), which provides a measurement of discrepancy between the negative sensitivity matrix and the variability matrix. In fact, this IDC characterizes the relative efficiency loss when using a certain candidate variance/covariance structure, compared with the true but unknown structure. Through simulation studies and analyses of two data sets, it is shown that the two proposed model selection methods both have a high rate of detecting the true/optimal variance/covariance structure. In particular, since the IDC magnifies the difference among the competing structures, it is highly sensitive to detect the most appropriate variance/covariance structure

Topic based language models for ad hoc information retrieval

We propose a topic based approach lo language modelling for ad-hoc Information Retrieval (IR). Many smoothed estimators used for the multinomial query model in IR rely upon the estimated background collection probabilities. In this paper, we propose a topic based language modelling approach, that uses a more informative prior based on the topical content of a document. In our experiments, the proposed model provides comparable IR performance to the standard models, but when combined in a two stage language model, it outperforms all other estimated models

Relevance-based Word Embedding

Learning a high-dimensional dense representation for vocabulary terms, also known as a word embedding, has recently attracted much attention in natural language processing and information retrieval tasks. The embedding vectors are typically learned based on term proximity in a large corpus. This means that the objective in well-known word embedding algorithms, e.g., word2vec, is to accurately predict adjacent word(s) for a given word or context. However, this objective is not necessarily equivalent to the goal of many information retrieval (IR) tasks. The primary objective in various IR tasks is to capture relevance instead of term proximity, syntactic, or even semantic similarity. This is the motivation for developing unsupervised relevance-based word embedding models that learn word representations based on query-document relevance information. In this paper, we propose two learning models with different objective functions; one learns a relevance distribution over the vocabulary set for each query, and the other classifies each term as belonging to the relevant or non-relevant class for each query. To train our models, we used over six million unique queries and the top ranked documents retrieved in response to each query, which are assumed to be relevant to the query. We extrinsically evaluate our learned word representation models using two IR tasks: query expansion and query classification. Both query expansion experiments on four TREC collections and query classification experiments on the KDD Cup 2005 dataset suggest that the relevance-based word embedding models significantly outperform state-of-the-art proximity-based embedding models, such as word2vec and GloVe.Comment: to appear in the proceedings of The 40th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR '17

Using the quantum probability ranking principle to rank interdependent documents

A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between documents through “quantum interference”. This paper explores whether this new ranking principle leads to improved performance for subtopic retrieval, where novelty and diversity is required. In a thorough empirical investigation, models based on the PRP, as well as other recently proposed ranking strategies for subtopic retrieval (i.e. Maximal Marginal Relevance (MMR) and Portfolio Theory(PT)), are compared against the QPRP. On the given task, it is shown that the QPRP outperforms these other ranking strategies. And unlike MMR and PT, one of the main advantages of the QPRP is that no parameter estimation/tuning is required; making the QPRP both simple and effective. This research demonstrates that the application of quantum theory to problems within information retrieval can lead to significant improvements

Transitive probabilistic CLIR models.

Transitive translation could be a useful technique to enlarge the number of supported language pairs for a cross-language information retrieval (CLIR) system in a cost-effective manner. The paper describes several setups for transitive translation based on probabilistic translation models. The transitive CLIR models were evaluated on the CLEF test collection and yielded a retrieval effectiveness\ud up to 83% of monolingual performance, which is significantly better than a baseline using the synonym operator

Rhetorical relations for information retrieval

Typically, every part in most coherent text has some plausible reason for its presence, some function that it performs to the overall semantics of the text. Rhetorical relations, e.g. contrast, cause, explanation, describe how the parts of a text are linked to each other. Knowledge about this socalled discourse structure has been applied successfully to several natural language processing tasks. This work studies the use of rhetorical relations for Information Retrieval (IR): Is there a correlation between certain rhetorical relations and retrieval performance? Can knowledge about a document's rhetorical relations be useful to IR? We present a language model modification that considers rhetorical relations when estimating the relevance of a document to a query. Empirical evaluation of different versions of our model on TREC settings shows that certain rhetorical relations can benefit retrieval effectiveness notably (> 10% in mean average precision over a state-of-the-art baseline)

Neural Vector Spaces for Unsupervised Information Retrieval

We propose the Neural Vector Space Model (NVSM), a method that learns representations of documents in an unsupervised manner for news article retrieval. In the NVSM paradigm, we learn low-dimensional representations of words and documents from scratch using gradient descent and rank documents according to their similarity with query representations that are composed from word representations. We show that NVSM performs better at document ranking than existing latent semantic vector space methods. The addition of NVSM to a mixture of lexical language models and a state-of-the-art baseline vector space model yields a statistically significant increase in retrieval effectiveness. Consequently, NVSM adds a complementary relevance signal. Next to semantic matching, we find that NVSM performs well in cases where lexical matching is needed. NVSM learns a notion of term specificity directly from the document collection without feature engineering. We also show that NVSM learns regularities related to Luhn significance. Finally, we give advice on how to deploy NVSM in situations where model selection (e.g., cross-validation) is infeasible. We find that an unsupervised ensemble of multiple models trained with different hyperparameter values performs better than a single cross-validated model. Therefore, NVSM can safely be used for ranking documents without supervised relevance judgments.Comment: TOIS 201

Investigating the relationship between language model perplexity and IR precision-recall measures

An empirical study has been conducted investigating the relationship between the performance of an aspect based language model in terms of perplexity and the corresponding information retrieval performance obtained. It is observed, on the corpora considered, that the perplexity of the language model has a systematic relationship with the achievable precision recall performance though it is not statistically significant