Language Modeling with Power Low Rank Ensembles

We present power low rank ensembles (PLRE), a flexible framework for n-gram language modeling where ensembles of low rank matrices and tensors are used to obtain smoothed probability estimates of words in context. Our method can be understood as a generalization of n-gram modeling to non-integer n, and includes standard techniques such as absolute discounting and Kneser-Ney smoothing as special cases. PLRE training is efficient and our approach outperforms state-of-the-art modified Kneser Ney baselines in terms of perplexity on large corpora as well as on BLEU score in a downstream machine translation task

Statistical Machine Translation Features with Multitask Tensor Networks

We present a three-pronged approach to improving Statistical Machine Translation (SMT), building on recent success in the application of neural networks to SMT. First, we propose new features based on neural networks to model various non-local translation phenomena. Second, we augment the architecture of the neural network with tensor layers that capture important higher-order interaction among the network units. Third, we apply multitask learning to estimate the neural network parameters jointly. Each of our proposed methods results in significant improvements that are complementary. The overall improvement is +2.7 and +1.8 BLEU points for Arabic-English and Chinese-English translation over a state-of-the-art system that already includes neural network features.Comment: 11 pages (9 content + 2 references), 2 figures, accepted to ACL 2015 as a long pape

Bayesian learning of joint distributions of objects

There is increasing interest in broad application areas in defining flexible joint models for data having a variety of measurement scales, while also allowing data of complex types, such as functions, images and documents. We consider a general framework for nonparametric Bayes joint modeling through mixture models that incorporate dependence across data types through a joint mixing measure. The mixing measure is assigned a novel infinite tensor factorization (ITF) prior that allows flexible dependence in cluster allocation across data types. The ITF prior is formulated as a tensor product of stick-breaking processes. Focusing on a convenient special case corresponding to a Parafac factorization, we provide basic theory justifying the flexibility of the proposed prior and resulting asymptotic properties. Focusing on ITF mixtures of product kernels, we develop a new Gibbs sampling algorithm for routine implementation relying on slice sampling. The methods are compared with alternative joint mixture models based on Dirichlet processes and related approaches through simulations and real data applications.Comment: Appearing in Proceedings of the 16th International Conference on Artificial Intelligence and Statistics (AISTATS) 2013, Scottsdale, AZ, US

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System