[Paper Review] Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance

Neal Jean, Sang Michael Xie+1 more|arXiv (Cornell University)|May 26, 2018

Gaussian Processes and Bayesian Inference23 citations

TL;DR

This paper proposes Semi-supervised Deep Kernel Learning (SSDKL), a method that improves regression performance by minimizing predictive variance in a posterior regularization framework, combining deep neural networks with Gaussian processes to leverage unlabeled data. SSDKL achieves state-of-the-art results on real-world regression tasks, outperforming supervised deep kernel learning and semi-supervised baselines like VAT and Mean Teacher.

ABSTRACT

Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tasks over supervised deep kernel learning and semi-supervised methods such as VAT and mean teacher adapted for regression.

Motivation & Objective

• To address the challenge of limited labeled data in regression tasks by leveraging abundant unlabeled data.
• To develop a semi-supervised deep kernel learning framework that improves generalization without requiring extensive labeled data.
• To integrate hierarchical representation learning from deep neural networks with probabilistic modeling via Gaussian processes.
• To minimize predictive variance in the posterior distribution as a regularization mechanism for semi-supervised learning.
• To demonstrate consistent performance gains across diverse real-world regression benchmarks.

Proposed method

• SSDKL employs a posterior regularization framework that minimizes predictive variance across unlabeled data points to improve uncertainty estimation.
• It combines deep neural networks for hierarchical feature representation with Gaussian processes for probabilistic regression and uncertainty quantification.
• The model trains end-to-end using both labeled and unlabeled data, with the predictive variance of unlabeled samples serving as a regularizer.
• The method uses a variational inference approach to approximate the posterior distribution over functions, enabling uncertainty-aware predictions.
• It adapts semi-supervised techniques like VAT and Mean Teacher to regression by redefining their objectives in terms of predictive variance minimization.
• The framework supports both regression and uncertainty estimation, making it suitable for data-scarce applications.

Experimental results

Research questions

• RQ1 Can minimizing predictive variance in unlabeled data improve regression performance in deep kernel learning?
• RQ2 How does SSDKL compare to supervised deep kernel learning and existing semi-supervised methods in regression tasks?
• RQ3 To what extent can unlabeled data improve uncertainty estimation and generalization in regression models?
• RQ4 Does the integration of deep neural networks with Gaussian processes enhance performance when labeled data is limited?
• RQ5 Can the predictive variance regularization mechanism be effectively adapted to regression from classification-based semi-supervised methods?

Key findings

• SSDKL achieves consistent performance improvements over supervised deep kernel learning on diverse real-world regression datasets.
• The model outperforms semi-supervised baselines such as VAT and Mean Teacher when adapted for regression tasks.
• Minimizing predictive variance on unlabeled data leads to more robust and calibrated uncertainty estimates.
• The integration of deep neural networks with Gaussian processes enables effective use of unlabeled data for regression.
• SSDKL demonstrates strong generalization capabilities even with limited labeled data, highlighting the value of predictive variance regularization.
• The method achieves state-of-the-art results on benchmark regression tasks, validating its effectiveness in data-scarce settings.