The relevance between a query and a document in search can be represented as matching degree between the two objects. Latent space models have been proven to be effective for the task, which are often trained with click-through data. One technical challenge with the approach is that it is hard to train a model for tail queries and tail documents for which there are not enough clicks. In this paper, we propose to address the challenge by learning a latent matching model, using not only click-through data but also semantic knowledge. The semantic knowledge can be categories of queries and documents as well as synonyms of words, manually or automatically created. Specifically, we incorporate semantic knowledge into the objective function by including regularization terms. We develop two methods to solve the learning task on the basis of coordinate descent and gradient descent respectively, which can be employed in different settings. Experimental results on two datasets from an app search engine demonstrate that our model can make effective use of semantic knowledge, and thus can significantly enhance the accuracies of latent matching models, particularly for tail queries.
Topic modeling techniques aim to discover the topics as well as the topic representations of documents in the document collection, and can be used to deal with query document mismatch. Latent semantic indexing (LSI) @cite_20 is one typical non-probabilistic topic model, which decomposes the term-document matrix by Singular Value Composition (SVD) under the assumption that topic vectors are orthogonal. Regularized Latent Semantic Indexing (RLSI) @cite_8 formalizes topic modeling as matrix factorization with regularization of @math @math -norm on topic vectors and document representation vectors. Probabilistic Latent Semantic Indexing (PLSI) @cite_10 and Latent Dirichlet Allocation (LDA) @cite_9 are two widely used probabilistic topic models, in which each topic is defined as a probability distribution over terms and each document is defined as a probability distribution over topics. By employing one of the topic models, one can project queries and documents into the topic space and calculate their similarities in the space. However, topic modeling does not directly learn the query document matching relation, and thus its ability of dealing with query document mismatch is limited.
@cite_9 @cite_10 @cite_20 @cite_8
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Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5]. Topic modeling provides a powerful way to analyze the content of a collection of documents. It has become a popular tool in many research areas, such as text mining, information retrieval, natural language processing, and other related fields. In real-world applications, however, the usefulness of topic modeling is limited due to scalability issues. Scaling to larger document collections via parallelization is an active area of research, but most solutions require drastic steps, such as vastly reducing input vocabulary. In this article we introduce Regularized Latent Semantic Indexing (RLSI)---including a batch version and an online version, referred to as batch RLSI and online RLSI, respectively---to scale up topic modeling. Batch RLSI and online RLSI are as effective as existing topic modeling techniques and can scale to larger datasets without reducing input vocabulary. Moreover, online RLSI can be applied to stream data and can capture the dynamic evolution of topics. Both versions of RLSI formalize topic modeling as a problem of minimizing a quadratic loss function regularized by e1 and or e2 norm. This formulation allows the learning process to be decomposed into multiple suboptimization problems which can be optimized in parallel, for example, via MapReduce. We particularly propose adopting e1 norm on topics and e2 norm on document representations to create a model with compact and readable topics and which is useful for retrieval. In learning, batch RLSI processes all the documents in the collection as a whole, while online RLSI processes the documents in the collection one by one. We also prove the convergence of the learning of online RLSI. Relevance ranking experiments on three TREC datasets show that batch RLSI and online RLSI perform better than LSI, PLSI, LDA, and NMF, and the improvements are sometimes statistically significant. Experiments on a Web dataset containing about 1.6 million documents and 7 million terms, demonstrate a similar boost in performance. The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on @math matrices, where @math is the number of latent factors (e.g. the number of topics), rather than in the @math -dimensional observed space (typically @math ). Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both in machine learning and in theory have suggested a probabilistic model for documents, whereby documents arise as a convex combination of (i.e. distribution on) a small number of topic vectors, each topic vector being a distribution on words (i.e. a vector of word-frequencies). Similar models have since been used in a variety of application areas, the Latent Dirichlet Allocation or LDA model of is especially popular. Theoretical studies of topic modeling focus on learning the model's parameters assuming the data is actually generated from it. Existing approaches for the most part rely on Singular Value Decomposition (SVD), and consequently have one of two limitations: these works need to either assume that each document contains only one topic, or else can only recover the span of the topic vectors instead of the topic vectors themselves. This paper formally justifies Nonnegative Matrix Factorization (NMF) as a main tool in this context, which is an analog of SVD where all vectors are nonnegative. Using this tool we give the first polynomial-time algorithm for learning topic models without the above two limitations. The algorithm uses a fairly mild assumption about the underlying topic matrix called separability, which is usually found to hold in real-life data. Perhaps the most attractive feature of our algorithm is that it generalizes to yet more realistic models that incorporate topic-topic correlations, such as the Correlated Topic Model (CTM) and the Pachinko Allocation Model (PAM). We hope that this paper will motivate further theoretical results that use NMF as a replacement for SVD -- just as NMF has come to replace SVD in many applications.