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Pareto Invariant Risk Minimization [article]

Yongqiang Chen, Kaiwen Zhou, Yatao Bian, Binghui Xie, Kaili Ma, Yonggang Zhang, Han Yang, Bo Han, James Cheng
2022 arXiv   pre-print
To remedy the above issues, we reformulate IRM as a multi-objective optimization problem, and propose a new optimization scheme for IRM, called PAreto Invariant Risk Minimization (PAIR).  ...  Despite the success of invariant risk minimization (IRM) in tackling the Out-of-Distribution generalization problem, IRM can compromise the optimality when applied in practice.  ...  Introduction There are surging evidences showing that machine learning models using empirical risk minimization (ERM) (Vapnik, 1991) are prone to exploit shortcuts, or spurious features, and thus can  ... 
arXiv:2206.07766v1 fatcat:g3pjcyxn5ndn3lcywajhvs5joi

Sparse Invariant Risk Minimization

Xiao Zhou, Yong Lin, Weizhong Zhang, Tong Zhang
2022 International Conference on Machine Learning  
In this paper, we propose a simple yet effective paradigm named Sparse Invariant Risk Minimization (SparseIRM) to address this contradiction.  ...  Invariant Risk Minimization (IRM) is an emerging invariant feature extracting technique to help generalization with distributional shift.  ...  (Ahuja et al., 2020a; Jin et al., 2020) provides new perspectives by introducing game theory and regret minimization into invariant risk minimization.  ... 
dblp:conf/icml/ZhouLZZ22 fatcat:w5nbjcgqefe6tdeligy6buf6cm

Invariant Risk Minimization [article]

Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, David Lopez-Paz
2020 arXiv   pre-print
We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions.  ...  To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions.  ...  This is the ubiquitous Empirical Risk Minimization (ERM) principle [50] .  ... 
arXiv:1907.02893v3 fatcat:recyacztqzgqjf3ln3gprlwade

Empirical Risk Minimization [chapter]

Xinhua Zhang
2016 Encyclopedia of Machine Learning and Data Mining  
In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence, mixup trains a neural network on convex combinations of pairs of examples and their labels.  ...  (1) is known as the Empirical Risk Minimization (ERM) principle (Vapnik, 1998) .  ...  To learn using VRM, we sample the vicinal distribution to construct a dataset D ν : = {(x i ,ỹ i )} m i=1 , and minimize the empirical vicinal risk: R ν (f ) = 1 m m i=1 (f (x i ),ỹ i ).  ... 
doi:10.1007/978-1-4899-7502-7_79-1 fatcat:2sgqbsowcvcpxadlvudemmf7xu

Average Stability is Invariant to Data Preconditioning. Implications to Exp-concave Empirical Risk Minimization [article]

Alon Gonen, Shai Shalev-Shwartz
2017 arXiv   pre-print
Several important implications of our findings include: a) We demonstrate that the excess risk of empirical risk minimization (ERM) is controlled by the preconditioned stability rate.  ...  that includes a regularization for analyzing the sample complexity of generalized linear models.  ...  Acknowledgments We thank Iliya Tolstikhin for pointing out the alternative proof of Corollary 1 using local Rademacher complexities.  ... 
arXiv:1601.04011v4 fatcat:adut577725gilppaayglbrsbp4

Nonlinear Invariant Risk Minimization: A Causal Approach [article]

Chaochao Lu, Yuhuai Wu, Jośe Miguel Hernández-Lobato, Bernhard Schölkopf
2021 arXiv   pre-print
Prior work addressing this, either explicitly or implicitly, attempted to find a data representation that has an invariant relationship with the target.  ...  This is done by leveraging a diverse set of training environments to reduce the effect of spurious features and build an invariant predictor.  ...  Ahuja et al. (2020a) study the problem from the perspective of game theory, with an approach termed invariant risk minimization games (IRMG).  ... 
arXiv:2102.12353v5 fatcat:jqixnfnfnrbv7mh4jpsfrx44pq

mixup: Beyond Empirical Risk Minimization [article]

Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, David Lopez-Paz
2018 arXiv   pre-print
In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence, mixup trains a neural network on convex combinations of pairs of examples and their labels.  ...  (1) is known as the Empirical Risk Minimization (ERM) principle (Vapnik, 1998) .  ...  To learn using VRM, we sample the vicinal distribution to construct a dataset D ν : = {(x i ,ỹ i )} m i=1 , and minimize the empirical vicinal risk: R ν (f ) = 1 m m i=1 (f (x i ),ỹ i ).  ... 
arXiv:1710.09412v2 fatcat:zpwavulzc5gbbea4g2xlgbutnu

Training genetic programming classifiers by vicinal-risk minimization

Ji Ni, Peter Rockett
2014 Genetic Programming and Evolvable Machines  
For some given size of training set, there is a trade-off between the empirical risk and the complexity of the discriminating function [4] .  ...  We demonstrate that VRM has a number of attractive properties and demonstrate that it has a better correlation with generalization error compared to empirical risk minimization so is more likely to lead  ...  error (either empirical or vicinal risk).  ... 
doi:10.1007/s10710-014-9222-4 fatcat:poubitheevfhxnbidae3h6q3z4

Robust 1-Bit Compressed Sensing via Hinge Loss Minimization [article]

Martin Genzel, Alexander Stollenwerk
2018 arXiv   pre-print
While such a risk minimization strategy is very natural to learn binary output models, such as in classification, its capacity to estimate a specific signal vector is largely unexplored.  ...  ., the square or logistic loss, which are at least locally strongly convex.  ...  m, it is very convenient to work with a scaling invariant complexity parameter.  ... 
arXiv:1804.04846v2 fatcat:jgy74pfvebcopcmw7dd6g3qzce

Direct Gibbs posterior inference on risk minimizers: construction, concentration, and calibration [article]

Ryan Martin, Nicholas Syring
2022 arXiv   pre-print
Loss functions provide an alternative link, where the quantity of interest is defined, or at least could be defined, as a minimizer of the corresponding risk, or expected loss.  ...  In this case, one can obtain what is commonly referred to as a Gibbs posterior distribution by using the empirical risk function directly.  ...  The authors also thank the editors of this Handbook, Alastair Young in particular, for the invitation to make a contribution.  ... 
arXiv:2203.09381v2 fatcat:3p5v5weszjfkpcodivyacfydwi

Optimal Sketching Bounds for Exp-concave Stochastic Minimization [article]

Naman Agarwal, Alon Gonen
2019 arXiv   pre-print
Our main computational result is a fast implementation of a sketch-to-precondition approach in the context of exp-concave empirical risk minimization.  ...  In particular, our statistical analysis highlights a novel and natural relationship between algorithmic stability of empirical risk minimization and ridge leverage scores, which play significant role in  ...  Furthermore, does achieving such bounds require incorporating sketching methodologies directly into the learning algorithm itself or can such bounds be proved for generic regularized empirical risk minimization  ... 
arXiv:1805.08268v7 fatcat:p4upor3ezbbvzgnccs2nlv6ciu

Minimizing Convex Functions with Integral Minimizers [article]

Haotian Jiang
2020 arXiv   pre-print
Given a separation oracle 𝖲𝖮 for a convex function f that has an integral minimizer inside a box with radius R, we show how to find an exact minimizer of f using at most (a) O(n (n + log(R))) calls to  ...  𝖲𝖮 and 𝗉𝗈𝗅𝗒(n, log(R)) arithmetic operations, or (b) O(n log(nR)) calls to 𝖲𝖮 and (n) ·𝗉𝗈𝗅𝗒(log(R)) arithmetic operations.  ...  A special thanks to Daniel Dadush for pointing out the implication of the Grötschel-Lovász-Schrijver approach to our problem and many other insightful comments, and to Thomas Rothvoss for many helpful  ... 
arXiv:2007.01445v4 fatcat:3wcqykchlnfg5ikcgt6ujwfwu4

Domain Adaptation via Bregman divergence minimization

Mozhdeh Zandifar, Shiva Noori Saray, Jafar Tahmoresnezhad
2021 Scientia Iranica. International Journal of Science and Technology  
via domain invariant representation.  ...  However, when the learning data (source domain) have a different distribution compared with the testing data (target domain), the FLDA-based models may not work well, and the performance degrades, dramatically  ...  Marginal distribution adaptation The existing dimensionality reduction methods obtain a linear combination of features that characterize or seperate two or more classes of objects or events.  ... 
doi:10.24200/sci.2021.51486.2210 fatcat:xlwuk7kikffirkr5t6yesn7ylq

Reparameterized Variational Divergence Minimization for Stable Imitation [article]

Dilip Arumugam, Debadeepta Dey, Alekh Agarwal, Asli Celikyilmaz, Elnaz Nouri, Bill Dolan
2020 arXiv   pre-print
We contribute a reparameterization trick for adversarial imitation learning to alleviate the optimization challenges of the promising f-divergence minimization framework.  ...  We unfortunately find that f-divergence minimization through reinforcement learning is susceptible to numerical instabilities.  ...  id=rkHywl-A-. Ghasemipour, S. K. S., Zemel, R., and Gu, S. A divergence minimization perspective on imitation learning methods. arXiv preprint arXiv:1911.02256, 2019.  ... 
arXiv:2006.10810v1 fatcat:zobyenu2rbfqfbjlk22yhus74u

Statistical Inference for Bayesian Risk Minimization via Exponentially Tilted Empirical Likelihood [article]

Rong Tang, Yun Yang
2021 arXiv   pre-print
We show that the Bayesian posterior obtained by combining this surrogate empirical likelihood and the prior is asymptotically close to a normal distribution centering at the empirical risk minimizer with  ...  Our surrogate empirical likelihood is carefully constructed by using the first order optimality condition of the empirical risk minimization as the moment condition.  ...  risks (i.e., R n (θ S , 0) wherê θ S is the constrained empirical risk minimizer on model S) while in the meantime do not have large complexities.  ... 
arXiv:2109.07792v1 fatcat:tfl47krurvg5znsncy6ksoxg6u
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