# Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learning

arXiv: https://arxiv.org/abs/2109.02150 · HTML: https://mlsanity.com/paper/2109.02150/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 5 Sep 2021.

## Builds on (most cited first, 11 of 11)

- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Coupled Generative Adversarial Networks](https://mlsanity.com/paper/1606.07536/) (2016)
- [Towards Robust Evaluations of Continual Learning](https://mlsanity.com/paper/1805.09733/) (2018)
- [A Unifying Bayesian View of Continual Learning](https://mlsanity.com/paper/1902.06494/) (2019)
- [Efficient Learning of Domain-invariant Image Representations](https://mlsanity.com/paper/1301.3224/) (2013)
- [Learning an Invariant Hilbert Space for Domain Adaptation](https://mlsanity.com/paper/1611.08350/) (2016)
- [Optimal Bayesian Transfer Learning](https://mlsanity.com/paper/1801.00857/) (2018)
- [Quantifying the multi-objective cost of uncertainty](https://mlsanity.com/paper/2010.04653/) (2020)
- [Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations](https://mlsanity.com/paper/2007.06117/) (2020)
- [Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning](https://mlsanity.com/paper/2106.00332/) (2021)

## Built on by (most cited first, 1 of 1)

- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)

## Abstract (arXiv)

Classification has been a major task for building intelligent systems as it enables decision-making under uncertainty. Classifier design aims at building models from training data for representing feature-label distributions--either explicitly or implicitly. In many scientific or clinical settings, training data are typically limited, which makes designing accurate classifiers and evaluating their classification error extremely challenging. While transfer learning (TL) can alleviate this issue by incorporating data from relevant source domains to improve learning in a different target domain, it has received little attention for performance assessment, notably in error estimation. In this paper, we fill this gap by investigating knowledge transferability in the context of classification error estimation within a Bayesian paradigm. We introduce a novel class of Bayesian minimum mean-square error (MMSE) estimators for optimal Bayesian transfer learning (OBTL), which enables rigorous evaluation of classification error under uncertainty in a small-sample setting. Using Monte Carlo importance sampling, we employ the proposed estimator to evaluate the classification accuracy of a broad family of classifiers that span diverse learning capabilities. Experimental results based on both synthetic data as well as real-world RNA sequencing (RNA-seq) data show that our proposed OBTL error estimation scheme clearly outperforms standard error estimators, especially in a small-sample setting, by tapping into the data from other relevant domains.