skip to main content

Explore Research Products in the NSF-PAR

Title: Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.  more » « less
Award ID(s):
2117429
NSF-PAR ID:
10301568
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Entropy
Volume:
23
Issue:
11
ISSN:
1099-4300
Page Range / eLocation ID:
1387
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ( , Geoscientific Model Development)
    null (Ed.)
    Abstract. Satellite remote sensing provides a global view to processes on Earth that has unique benefits compared to making measurements on the ground, such as global coverage and enormous data volume. The typical downsides are spatial and temporal gaps and potentially low data quality. Meaningful statistical inference from such data requires overcoming these problems and developing efficient and robust computational tools.We design and implement a computationally efficient multi-scale Gaussian process (GP) software package, satGP, geared towards remote sensing applications. The software is able to handle problems of enormous sizes and to compute marginals and sample from the random field conditioning on at least hundreds of millions of observations. This is achieved by optimizing the computation by, e.g., randomization and splitting the problem into parallel local subproblems which aggressively discard uninformative data. We describe the mean function of the Gaussian process by approximating marginals of a Markov random field (MRF). Variability around the mean is modeled with a multi-scale covariance kernel, which consists of Matérn, exponential, and periodic components. We also demonstrate how winds can be used to inform covariances locally.The covariance kernel parameters are learned by calculating an approximate marginal maximum likelihood estimate, and the validity of both the multi-scale approach and the method used to learn the kernel parameters is verified in synthetic experiments. We apply these techniques to a moderate size ozone data set produced by an atmospheric chemistry model and to the very large number of observations retrieved from the Orbiting Carbon Observatory 2 (OCO-2) satellite. The satGP software is released under an open-source license. 
    more » « less
  2. ; ( , Frontiers in Control Engineering)
    A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs leads to a large possible topology candidate space, which often cannot be exhaustively searched due to the limitation in computational resources. This paper develops a scalable and efficient topology inference for GRNs using Bayesian optimization and kernel-based methods. Rather than an exhaustive search over possible topologies, the proposed method constructs a Gaussian Process (GP) with a topology-inspired kernel function to account for correlation in the likelihood function. Then, using the posterior distribution of the GP model, the Bayesian optimization efficiently searches for the topology with the highest likelihood value by optimally balancing between exploration and exploitation. The performance of the proposed method is demonstrated through comprehensive numerical experiments using a well-known mammalian cell-cycle network. 
    more » « less
  3. ; ; ; ; ( , Stat)
    Abstract

    In electronic health records (EHRs) data analysis, nonparametric regression and classification using International Classification of Disease (ICD) codes as covariates remain understudied. Automated methods have been developed over the years for predicting biomedical responses using EHRs, but relatively less attention has been paid to developing patient similarity measures that use ICD codes and chronic conditions, where a chronic condition is defined as a set of ICD codes. We address this problem by first developing a string kernel function for measuring the similarity between a pair of primary chronic conditions, represented as subsets of ICD codes. Second, we extend this similarity measure to a family of covariance functions on subsets of chronic conditions. This family is used in developing Gaussian process (GP) priors for Bayesian nonparametric regression and classification using diagnoses and other demographic information as covariates. Markov chain Monte Carlo (MCMC) algorithms are used for posterior inference and predictions. The proposed methods are tuning free, so they are ideal for automated prediction of biomedical responses depending on chronic conditions. We evaluate the practical performance of our method on EHR data collected from 1660 patients at the University of Iowa Hospitals and Clinics (UIHC) with six different primary cancer sites. Our method provides better sensitivity and specificity than its competitors in classifying different primary cancer sites and estimates the marginal associations between chronic conditions and primary cancer sites.

     
    more » « less
  4. ; ; ; ; ; ; ( , Systematic Biology)
    Abstract

    The Lowest Radial Distance (LoRaD) method is a modification of the recently introduced Partition-Weighted Kernel method for estimating the marginal likelihood of a model, a quantity important for Bayesian model selection. For analyses involving a fixed tree topology, LoRaD improves upon the Steppingstone or Thermodynamic Integration (Path Sampling) approaches now in common use in phylogenetics because it requires sampling only from the posterior distribution, avoiding the need to sample from a series of ad hoc power posterior distributions, and yet is more accurate than other fast methods such as the Generalized Harmonic Mean (GHM) method. We show that the method performs well in comparison to the Generalized Steppingstone method on an empirical fixed-topology example from molecular phylogenetics involving 180 parameters. The LoRaD method can also be used to obtain the marginal likelihood in the variable-topology case if at least one tree topology occurs with sufficient frequency in the posterior sample to allow accurate estimation of the marginal likelihood conditional on that topology. [Bayesian; marginal likelihood; phylogenetics.]

     
    more » « less
  5. ; ; ; ( , Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021,)
    null (Ed.)
    Multiple Instance Learning (MIL) provides a promising solution to many real-world problems, where labels are only available at the bag level but missing for instances due to a high labeling cost. As a powerful Bayesian non-parametric model, Gaussian Processes (GP) have been extended from classical supervised learning to MIL settings, aiming to identify the most likely positive (or least negative) instance from a positive (or negative) bag using only the bag-level labels. However, solely focusing on a single instance in a bag makes the model less robust to outliers or multi-modal scenarios, where a single bag contains a diverse set of positive instances. We propose a general GP mixture framework that simultaneously considers multiple instances through a latent mixture model. By adding a top-k constraint, the framework is equivalent to choosing the top-k most positive instances, making it more robust to outliers and multimodal scenarios. We further introduce a Distributionally Robust Optimization (DRO) constraint that removes the limitation of specifying a fixed k value. To ensure the prediction power over high-dimensional data (e.g., videos and images) that are common in MIL, we augment the GP kernel with  fixed basis functions by using a deep neural network to learn adaptive basis functions so that the covariance structure of high-dimensional data can be accurately captured. Experiments are conducted on highly challenging real-world video anomaly detection tasks to demonstrate the effectiveness of the proposed model. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email