Intensity Process for a Pure Jump L\'evy Structural Model with Incomplete Information

In this paper we discuss a credit risk model with a pure jump L\'evy process for the asset value and an unobservable random barrier. The default time is the first time when the asset value falls below the barrier. Using the indistinguishability of the intensity process and the likelihood process, we prove the existence of the intensity process of the default time and find its explicit representation in terms of the distance between the asset value and its running minimal value. We apply the result to find the instantaneous credit spread process and illustrate it with a numerical example.Comment: 15 pages, 2 figure

On Explicit Probability Densities Associated with Fuss-Catalan Numbers

In this note we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers. The densities appear naturally in random matrices, free probability and other contexts.Comment: 4 page

Transfer Learning for Speech and Language Processing

Transfer learning is a vital technique that generalizes models trained for one setting or task to other settings or tasks. For example in speech recognition, an acoustic model trained for one language can be used to recognize speech in another language, with little or no re-training data. Transfer learning is closely related to multi-task learning (cross-lingual vs. multilingual), and is traditionally studied in the name of `model adaptation'. Recent advance in deep learning shows that transfer learning becomes much easier and more effective with high-level abstract features learned by deep models, and the `transfer' can be conducted not only between data distributions and data types, but also between model structures (e.g., shallow nets and deep nets) or even model types (e.g., Bayesian models and neural models). This review paper summarizes some recent prominent research towards this direction, particularly for speech and language processing. We also report some results from our group and highlight the potential of this very interesting research field.Comment: 13 pages, APSIPA 201