In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity between word embeddings. Using techniques from matrix perturbation theory, we reveal a fundamental bias-variance trade-off in dimensionality selection for word embeddings. This bias-variance trade-off sheds light on many empirical observations which were previously unexplained, for example the existence of an optimal dimensionality. Moreover, new insights and discoveries, like when and how word embeddings are robust to over-fitting, are revealed. By optimizing over the bias-variance trade-off of the PIP loss, we can explicitly answer the open question of dimensionality selection for word embedding.

Language is dynamic, constantly evolving and adapting with respect to time, domain or topic. The adaptability of language is an active research area, where researchers discover social, cultural and domain-specific changes in language using distributional tools such as word embeddings. In this paper, we introduce the global anchor method for detecting corpus-level language shifts. We show both theoretically and empirically that the global anchor method is equivalent to the alignment method, a widely-used method for comparing word embeddings, in terms of detecting corpus-level language shifts. Despite their equivalence in terms of detection abilities, we demonstrate that the global anchor method is superior in terms of applicability as it can compare embeddings of different dimensionalities. Furthermore, the global anchor method has implementation and parallelization advantages. We show that the global anchor method reveals fine structures in the evolution of language and domain adaptation. When combined with the graph Laplacian technique, the global anchor method recovers the evolution trajectory and domain clustering of disparate text corpora.

Information extraction and user intention identification is a central topic in modern query understanding and recommendation systems. In this paper, we propose DeepProbe, a generic information-directed interaction framework which is built around an attention-based sequence to sequence (seq2seq) recurrent neural network. DeepProbe can rephrase, evaluate, and even actively ask questions, leveraging the generative ability and likelihood estimation made possible by seq2seq models. DeepProbe makes decisions based on a derived uncertainty (entropy) measure conditioned on user inputs, possibly with multiple rounds of interactions. Three applications, namely a rewritter, a relevance scorer and a chatbot for ad recommendation, were built around DeepProbe, with the first two serving as precursory building blocks for the third. We first use the seq2seq model in DeepProbe to rewrite a user query into one of standard query form, which is submitted to an ordinary recommendation system. Secondly, we evaluate DeepProbe's seq2seq model-based relevance scoring. Finally, we build a chatbot prototype capable of making active user interactions, which can ask questions that maximize information gain, allowing for a more efficient user intention idenfication process. We evaluate first two applications by 1) comparing with baselines by BLEU and AUC, and 2) human judge evaluation. Both demonstrate significant improvements compared with current state-of-the-art systems, proving their values as useful tools on their own, and at the same time laying a good foundation for the ongoing chatbot application.