PLSI: The True Fisher Kernel and beyond IID Processes, Information Matrix and Model Identification in PLSI

The Probabilistic Latent Semantic indexing model, introduced by T. Hofmann (1999), has engendered applications ill numerous fields, notably document classification and information retrieval. In this context, the Fisher kernel was found to be an appropriate document similarity measure. However, the kernels published so far contain unjustified features, some of which hinder their performances. Furthermore, PLSI is not generative for unknown documents, a shortcoming usually remedied by "folding them in" the PLSI parameter space.

PLSI: the true Fisher Kernel and beyond

Jean-Cédric Chappelier, Emmanuel Eckard

The Probalistic Latent Semantic Indexing model, introduced by T. Hofmann (1999), has engendered applications in numerous fields, notably document classification and information retrieval. In this context, the Fisher kernel was found to be an appropriate document similarity measure. However, the kernels published so far contain unjustified features, some of which hinder their performances. Furthermore, PLSI is not generative for unknown documents, a shortcoming usually remedied by "folding them in" the PLSI parameter space. This paper contributes on both points by introducing: - a new, rigorous development of the Fisher kernel for PLSI, addressing the role of the Fisher Information Matrix; we show how it relates to the kernels proposed so far; - a novel and theoretically sound document similarity, which avoids the problem of "folding in" unknown documents through model identification. For both aspects, experimental results are provided on a large information retrieval evaluation set.

2009

Fisher Kernels and Probabilistic Latent Semantic Models

Emmanuel Eckard

Tasks that rely on semantic content of documents, notably Information Retrieval and Document Classification, can benefit from a good account of document context, i.e. the semantic association between documents. To this effect, the scheme of latent semantics blends individual words appearing throughout a document collection into latent topics, thus providing a way to handle documents that is less constrained than the conventional approach by the mere appearance of such or such word. Probabilistic latent semantic models take the matter further by providing assumptions on how the documents observed in the collection would have been generated. This allows derivation of inference algorithms that can fit the model parameters to the observed document collection; with their values set, these parameters can then be used to compute the similarities between documents. The Fisher kernels, similarity functions rooted in information geometry, constitute good candidates to measure the similarity between documents in the framework of probabilistic latent semantic models. In this context, we study the use of Fisher kernels for the Probabilistic Latent Semantic Indexing (PLSI) model. By thoroughly analysing the generative process of PLSI, we derive the proper Fisher kernel for PLSI and expose the hypotheses that relate former work to this kernel. In particular, we confirm that the Fisher information matrix (FIM) should not be approximated by the identity in the case of PLSI. We also study the impact on the performances of the Fisher kernel of the contribution of the latent topics and the one of the distribution of words among the topics; eventually, we provide empirical evidence, and theoretical arguments, showing that the Fisher kernel originally published by Hofmann, corrected to account for FIM, is the best of the PLSI Fisher kernels. It can compete with the strong BM25 baseline, and even significantly outperforms it when documents sharing few words must be matched. We further study of PLSI document similarities by applying the Language model approach. This approach shuns the usual IR paradigm that considers documents and queries to be of a similar nature. Instead, they consider documents as being representative of language models, and use probabilistic tools to determine which of these models would have generated the query with highest probability. Using this scheme in the framework of PLSI provides a way to bypass the issue of query representation, which constitutes one of the specific challenges of PLSI. We find the Language model approach to perform as well as the best of the Fisher kernels when enough latent categories are provided. Eventually, we propose a new probabilistic latent semantic model consisting in a mixture of Smoothed Dirichlet distributions which, by better modeling word burstiness, provides a more realistic model of empirical observations on real document collections than the usually used Multinomials.

EPFL2010

Machine learning for information retrieval

David Grangier

In this thesis, we explore the use of machine learning techniques for information retrieval. More specifically, we focus on ad-hoc retrieval, which is concerned with searching large corpora to identify the documents relevant to user queries. This identification is performed through a ranking task. Given a user query, an ad-hoc retrieval system ranks the corpus documents, so that the documents relevant to the query ideally appear above the others. In a machine learning framework, we are interested in proposing learning algorithms that can benefit from limited training data in order to identify a ranker likely to achieve high retrieval performance over unseen documents and queries. This problem presents novel challenges compared to traditional learning tasks, such as regression or classification. First, our task is a ranking problem, which means that the loss for a given query cannot be measured as a sum of an individual loss suffered for each corpus document. Second, most retrieval queries present a highly unbalanced setup, with a set of relevant documents accounting only for a very small fraction of the corpus. Third, ad-hoc retrieval corresponds to a kind of "double" generalization problem, since the learned model should not only generalize to new documents but also to new queries. Finally, our task also presents challenging efficiency constraints, since ad-hoc retrieval is typically applied to large corpora. The main objective of this thesis is to investigate the discriminative learning of ad-hoc retrieval models. For that purpose, we propose different models based on kernel machines or neural networks adapted to different retrieval contexts. The proposed approaches rely on different online learning algorithms that allow efficient learning over large corpora. The first part of the thesis focuses on text retrieval. In this case, we adopt a classical approach to the retrieval ranking problem, and order the text documents according to their estimated similarity to the text query. The assessment of semantic similarity between text items plays a key role in that setup and we propose a learning approach to identify an effective measure of text similarity. This identification is not performed relying on a set of queries with their corresponding relevant document sets, since such data are especially expensive to label and hence rare. Instead, we propose to rely on hyperlink data, since hyperlinks convey semantic proximity information that is relevant to similarity learning. This setup is hence a transfer learning setup, where we benefit from the proximity information encoded by hyperlinks to improve the performance over the ad-hoc retrieval task. We then investigate another retrieval problem, i.e. the retrieval of images from text queries. Our approach introduces a learning procedure optimizing a criterion related to the ranking performance. This criterion adapts our previous learning objective for learning textual similarity to the image retrieval problem. This yields an image ranking model that addresses the retrieval problem directly. This approach contrasts with previous research that relies on an intermediate image annotation task. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. In the last part of the thesis, we show that the objective function used in the previous retrieval problems can be applied to the task of keyword spotting, i.e. the detection of given keywords in speech utterances. For that purpose, we formalize this problem as a ranking task: given a keyword, the keyword spotter should order the utterances so that the utterances containing the keyword appear above the others. Interestingly, this formulation yields an objective directly maximizing the area under the receiver operating curve, the most common keyword spotter evaluation measure. This objective is then used to train a model adapted to this intrinsically sequential problem. This model is then learned with a procedure derived from the algorithm previously introduced for the image retrieval task. To conclude, this thesis introduces machine learning approaches for ad-hoc retrieval. We propose learning models for various multi-modal retrieval setups, i.e. the retrieval of text documents from text queries, the retrieval of images from text queries and the retrieval of speech recordings from written keywords. Our approaches rely on discriminative learning and enjoy efficient training procedures, which yields effective and scalable models. In all cases, links with prior approaches were investigated and experimental comparisons were conducted.