424 research outputs found
Streaming, Distributed Variational Inference for Bayesian Nonparametrics
This paper presents a methodology for creating streaming, distributed
inference algorithms for Bayesian nonparametric (BNP) models. In the proposed
framework, processing nodes receive a sequence of data minibatches, compute a
variational posterior for each, and make asynchronous streaming updates to a
central model. In contrast to previous algorithms, the proposed framework is
truly streaming, distributed, asynchronous, learning-rate-free, and
truncation-free. The key challenge in developing the framework, arising from
the fact that BNP models do not impose an inherent ordering on their
components, is finding the correspondence between minibatch and central BNP
posterior components before performing each update. To address this, the paper
develops a combinatorial optimization problem over component correspondences,
and provides an efficient solution technique. The paper concludes with an
application of the methodology to the DP mixture model, with experimental
results demonstrating its practical scalability and performance.Comment: This paper was presented at NIPS 2015. Please use the following
BibTeX citation: @inproceedings{Campbell15_NIPS, Author = {Trevor Campbell
and Julian Straub and John W. {Fisher III} and Jonathan P. How}, Title =
{Streaming, Distributed Variational Inference for Bayesian Nonparametrics},
Booktitle = {Advances in Neural Information Processing Systems (NIPS)}, Year
= {2015}
Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models
We develop a sequential low-complexity inference procedure for Dirichlet
process mixtures of Gaussians for online clustering and parameter estimation
when the number of clusters are unknown a-priori. We present an easily
computable, closed form parametric expression for the conditional likelihood,
in which hyperparameters are recursively updated as a function of the streaming
data assuming conjugate priors. Motivated by large-sample asymptotics, we
propose a novel adaptive low-complexity design for the Dirichlet process
concentration parameter and show that the number of classes grow at most at a
logarithmic rate. We further prove that in the large-sample limit, the
conditional likelihood and data predictive distribution become asymptotically
Gaussian. We demonstrate through experiments on synthetic and real data sets
that our approach is superior to other online state-of-the-art methods.Comment: 25 pages, To appear in Advances in Neural Information Processing
Systems (NIPS) 201
A trust-region method for stochastic variational inference with applications to streaming data
Stochastic variational inference allows for fast posterior inference in
complex Bayesian models. However, the algorithm is prone to local optima which
can make the quality of the posterior approximation sensitive to the choice of
hyperparameters and initialization. We address this problem by replacing the
natural gradient step of stochastic varitional inference with a trust-region
update. We show that this leads to generally better results and reduced
sensitivity to hyperparameters. We also describe a new strategy for variational
inference on streaming data and show that here our trust-region method is
crucial for getting good performance.Comment: in Proceedings of the 32nd International Conference on Machine
Learning, 201
Sequential Gaussian Processes for Online Learning of Nonstationary Functions
Many machine learning problems can be framed in the context of estimating
functions, and often these are time-dependent functions that are estimated in
real-time as observations arrive. Gaussian processes (GPs) are an attractive
choice for modeling real-valued nonlinear functions due to their flexibility
and uncertainty quantification. However, the typical GP regression model
suffers from several drawbacks: i) Conventional GP inference scales
with respect to the number of observations; ii) updating a GP model
sequentially is not trivial; and iii) covariance kernels often enforce
stationarity constraints on the function, while GPs with non-stationary
covariance kernels are often intractable to use in practice. To overcome these
issues, we propose an online sequential Monte Carlo algorithm to fit mixtures
of GPs that capture non-stationary behavior while allowing for fast,
distributed inference. By formulating hyperparameter optimization as a
multi-armed bandit problem, we accelerate mixing for real time inference. Our
approach empirically improves performance over state-of-the-art methods for
online GP estimation in the context of prediction for simulated non-stationary
data and hospital time series data
Dirichlet process mixture models for non-stationary data streams
In recent years, we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming inference under the concept drift phenomenon is still an open problem for these models. In this work, we propose a variational inference algorithm for Dirichlet process mixture models. Our proposal deals with the concept drift by including an exponential forgetting over the prior global parameters. Our algorithm allows adapting the learned model to the concept drifts automatically. We perform experiments in both synthetic and real data, showing that the proposed model outperforms state-of-the-art variational methods in density estimation, clustering and parameter tracking
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