782 research outputs found
Infinite Mixtures of Multivariate Gaussian Processes
This paper presents a new model called infinite mixtures of multivariate
Gaussian processes, which can be used to learn vector-valued functions and
applied to multitask learning. As an extension of the single multivariate
Gaussian process, the mixture model has the advantages of modeling multimodal
data and alleviating the computationally cubic complexity of the multivariate
Gaussian process. A Dirichlet process prior is adopted to allow the (possibly
infinite) number of mixture components to be automatically inferred from
training data, and Markov chain Monte Carlo sampling techniques are used for
parameter and latent variable inference. Preliminary experimental results on
multivariate regression show the feasibility of the proposed model.Comment: Proceedings of the International Conference on Machine Learning and
Cybernetics, 2013, pages 1011-101
The Discrete Infinite Logistic Normal Distribution
We present the discrete infinite logistic normal distribution (DILN), a
Bayesian nonparametric prior for mixed membership models. DILN is a
generalization of the hierarchical Dirichlet process (HDP) that models
correlation structure between the weights of the atoms at the group level. We
derive a representation of DILN as a normalized collection of gamma-distributed
random variables, and study its statistical properties. We consider
applications to topic modeling and derive a variational inference algorithm for
approximate posterior inference. We study the empirical performance of the DILN
topic model on four corpora, comparing performance with the HDP and the
correlated topic model (CTM). To deal with large-scale data sets, we also
develop an online inference algorithm for DILN and compare with online HDP and
online LDA on the Nature magazine, which contains approximately 350,000
articles.Comment: This paper will appear in Bayesian Analysis. A shorter version of
this paper appeared at AISTATS 2011, Fort Lauderdale, FL, US
Statistical metamodeling of dynamic network loading
Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications
Modulating Scalable Gaussian Processes for Expressive Statistical Learning
For a learning task, Gaussian process (GP) is interested in learning the
statistical relationship between inputs and outputs, since it offers not only
the prediction mean but also the associated variability. The vanilla GP however
struggles to learn complicated distribution with the property of, e.g.,
heteroscedastic noise, multi-modality and non-stationarity, from massive data
due to the Gaussian marginal and the cubic complexity. To this end, this
article studies new scalable GP paradigms including the non-stationary
heteroscedastic GP, the mixture of GPs and the latent GP, which introduce
additional latent variables to modulate the outputs or inputs in order to learn
richer, non-Gaussian statistical representation. We further resort to different
variational inference strategies to arrive at analytical or tighter evidence
lower bounds (ELBOs) of the marginal likelihood for efficient and effective
model training. Extensive numerical experiments against state-of-the-art GP and
neural network (NN) counterparts on various tasks verify the superiority of
these scalable modulated GPs, especially the scalable latent GP, for learning
diverse data distributions.Comment: 31 pages, 9 figures, 4 tables, preprint under revie
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