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.
In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online learning of the hyper-parameters have a constant (rather than cubic) time complexity and a constant (rather than squared) memory requirement in the number of observations, without resorting to approximations. Moreover, the proposed model is expressive in that the family of covariance functions of the implied latent process, namely the spectral Matern kernels, have …
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to capture the complex statistical structure. Finally, through the use of novel methods for additive non-separable kernels, we can scale the model to large datasets. We demonstrate the model on numerical and real world data, including a large spatio-temporal disease dataset where we…
Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. In addition, we propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practi…
Multi-View Oriented GPLVM: Expressiveness and Efficiency
School of Computing and Data Science University of Hong Kong（计算与数据科学学院 香港大学）；Department of Signal Theory and Communications Universidad Carlos III de Madrid（信号理论与通信系 马德里卡洛斯三世大学）
Carnegie Mellon University（卡内基梅隆大学）；Philips Research Hamburg（飞利浦汉堡研究院）
We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance kernel. SKI also provides a mechanism to create new scalable kernel methods, through choosing different kernel interpolation strategies. Using SKI, with local cubic ker…
Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models unfeasibly expensive in terms of parameters. We present an alternative parameterization scheme called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the …
Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such structure, we propose expressive closed-form kernel functions for Gaussian processes. The resulting model, GP-LSTM, fully encapsulates the inductive biases of long short-term memory (LSTM) recurrent networks, while retaining the non-parametric probabilistic advantages of Gaussian processes. We learn the properties of the proposed kernels by optimizing the G…
Stanford University（斯坦福大学）；Facebook AI Research（Facebook人工智能研究院）；University of California, Los Angeles（加州大学洛杉矶分校）
A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizi…
In this work, we propose a generalized product of experts (gPoE) framework for combining the predictions of multiple probabilistic models. We identify four desirable properties that are important for scalability, expressiveness and robustness, when learning and inferring with a combination of multiple models. Through analysis and experiments, we show that gPoE of Gaussian processes (GP) have these qualities, while no other existing combination schemes satisfy all of them at the same time. The resulting GP-gPoE is highly scalable as individual GP experts can be independently learned in parallel…
From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems
Department of Applied Mechanics（应用力学系）；Indian Institute of Technology Delhi（德里印度理工学院）；Yardi School of Artificial Intelligence (ScAI)（Yardi人工智能学院）；The Grainger College of Engineering University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格里纳尔工程学院）
Carnegie Mellon University（卡内基梅隆大学）；University of Toronto（多伦多大学）
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and structure exploiting (Kronecker and Toeplitz) algebra for a scalable kernel representation. These closed-form kernels can be used as drop-in replacements for standard kernels, with benefits in expressive power and scalability. We jointly learn the properties of these kernels through t…
U. Cambridge（剑桥大学）；WUSTL（圣路易斯华盛顿大学）；Columbia U.（哥伦比亚大学）
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large multidimensional datasets. GPatt unifies and extends highly expressive kernels and fast exact inference techniques. Without human intervention -- no hand crafting of kernel features, and no sophisticated initialisation procedures -- we show that GPatt can solve large scale pattern extrapolation, inpainting, and kernel discovery problems, including a problem with 383400 t…
Cranfield University（克兰菲尔德大学）；University of Warwick（华威大学）；Alan Turing Institute（艾伦·图灵研究所）
Achieving transparency in black-box deep learning algorithms is still an open challenge. High dimensional features and decisions given by deep neural networks (NN) require new algorithms and methods to expose its mechanisms. Current state-of-the-art NN interpretation methods (e.g. Saliency maps, DeepLIFT, LIME, etc.) focus more on the direct relationship between NN outputs and inputs rather than the NN structure and operations itself. In current deep NN operations, there is uncertainty over the exact role played by neurons with fixed activation functions. In this paper, we achieve partially ex…
Scalable Unsupervised Segmentation via Random Fourier Feature-based Gaussian Process
The University of Electro-Communications, Tokyo, Japan（电通大学）；Kyoto University, Kyoto, Japan（京都大学）；The Institute of Statistical Mathematics, Tokyo, Japan（统计数学研究所）；National Center of Neurology and Psychiatry, Tokyo, Japan（神经内科与精神科国立医院）
Given some observed data and a probabilistic generative model, Bayesian inference aims at obtaining the distribution of a model's latent parameters that could have yielded the data. This task is challenging for large population studies where thousands of measurements are performed over a cohort of hundreds of subjects, resulting in a massive latent parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that can efficiently tackle large population studies. To this end, our main idea is …
