Invariant Risk Minimization Is A Total Variation Model
- URL: http://arxiv.org/abs/2405.01389v5
- Date: Fri, 17 May 2024 04:14:34 GMT
- Title: Invariant Risk Minimization Is A Total Variation Model
- Authors: Zhao-Rong Lai, Weiwen Wang,
- Abstract summary: Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning.
We show that IRM is essentially a total variation based on $L2$ (TV-$ell$) of the learning risk.
We propose a novel IRM framework based on the TV-$ell$ model.
- Score: 3.000494957386027
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical essence of IRM remains to be properly explained. We verify that IRM is essentially a total variation based on $L^2$ norm (TV-$\ell_2$) of the learning risk with respect to the classifier variable. Moreover, we propose a novel IRM framework based on the TV-$\ell_1$ model. It not only expands the classes of functions that can be used as the learning risk and the feature extractor, but also has robust performance in denoising and invariant feature preservation based on the coarea formula. We also illustrate some requirements for IRM-TV-$\ell_1$ to achieve out-of-distribution generalization. Experimental results show that the proposed framework achieves competitive performance in several benchmark machine learning scenarios.
Related papers
- Inverse Reinforcement Learning with Unknown Reward Model based on
Structural Risk Minimization [9.44879308639364]
Inverse reinforcement learning (IRL) usually assumes the model of the reward function is pre-specified and estimates the parameter only.
A simplistic model is less likely to contain the real reward function, while a model with high complexity leads to substantial cost and risks overfitting.
This paper addresses this trade-off by introducing the structural risk minimization (SRM) method from statistical learning.
arXiv Detail & Related papers (2023-12-27T13:23:17Z) - Continual Invariant Risk Minimization [46.051656238770086]
Empirical risk minimization can lead to poor generalization behavior on unseen environments if the learned model does not capture invariant feature representations.
Invariant risk minimization (IRM) is a recent proposal for discovering environment-invariant representations.
arXiv Detail & Related papers (2023-10-21T11:44:47Z) - Learning Optimal Features via Partial Invariance [18.552839725370383]
Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments.
We show that IRM can over-constrain the predictor and to remedy this, we propose a relaxation via $textitpartial invariance$.
Several experiments, conducted both in linear settings as well as with deep neural networks on tasks over both language and image data, allow us to verify our conclusions.
arXiv Detail & Related papers (2023-01-28T02:48:14Z) - A Relational Intervention Approach for Unsupervised Dynamics
Generalization in Model-Based Reinforcement Learning [113.75991721607174]
We introduce an interventional prediction module to estimate the probability of two estimated $hatz_i, hatz_j$ belonging to the same environment.
We empirically show that $hatZ$ estimated by our method enjoy less redundant information than previous methods.
arXiv Detail & Related papers (2022-06-09T15:01:36Z) - The Missing Invariance Principle Found -- the Reciprocal Twin of
Invariant Risk Minimization [7.6146285961466]
In Risk Minimization (IRM) can fail to generalize poorly to out-of-distribution (OOD) data.
We show that MRI-v1 can guarantee invariant predictors given sufficient environments.
We also demonstrate that MRI strongly out-performs IRM and achieves a near-optimal OOD in image-based problems.
arXiv Detail & Related papers (2022-05-29T00:14:51Z) - Learning Augmentation Distributions using Transformed Risk Minimization [47.236227685707526]
We propose a new emphTransformed Risk Minimization (TRM) framework as an extension of classical risk minimization.
As a key application, we focus on learning augmentations to improve classification performance with a given class of predictors.
arXiv Detail & Related papers (2021-11-16T02:07:20Z) - Iterative Feature Matching: Toward Provable Domain Generalization with
Logarithmic Environments [55.24895403089543]
Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments.
We present a new algorithm based on performing iterative feature matching that is guaranteed with high probability to yield a predictor that generalizes after seeing only $O(logd_s)$ environments.
arXiv Detail & Related papers (2021-06-18T04:39:19Z) - On the Minimal Error of Empirical Risk Minimization [90.09093901700754]
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression.
Our sharp lower bounds shed light on the possibility (or impossibility) of adapting to simplicity of the model generating the data.
arXiv Detail & Related papers (2021-02-24T04:47:55Z) - The Risks of Invariant Risk Minimization [52.7137956951533]
Invariant Risk Minimization is an objective based on the idea for learning deep, invariant features of data.
We present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model.
We show that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve.
arXiv Detail & Related papers (2020-10-12T14:54:32Z) - An Empirical Study of Invariant Risk Minimization [5.412466703928342]
Invariant risk minimization is a proposed framework for learning predictors that are invariant to spurious correlations.
Despite its theoretical justifications, IRM has not been extensively tested across various settings.
We empirically investigate several research questions using IRMv1, which is the first practical algorithm proposed to approximately solve IRM.
arXiv Detail & Related papers (2020-04-10T12:23:29Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.