Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralization Bounds for Vicinal Risk Minimization Principle
307
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The vicinal risk minimization (VRM) principle, first proposed by citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. Although there is strong numerical evidence showing that VRM outperforms ERM if appropriate vicinal functions are chosen, a comprehensive theoretical understanding of VRM is still lacking. In this paper, we study the generalization bounds for VRM. Our results support Vapniks original arguments and additionally provide deeper insights into VRM. First, we prove that the complexity of function classes convolving with vicinal functions can be controlled by that of the original function classes under the assumption that the function class is composed of Lipschitz-continuous functions. Then, the resulting generalization bounds for VRM suggest that the generalization performance of VRM is also effected by the choice of vicinity function and the quality of function classes. These findings can be used to examine whether the choice of vicinal function is appropriate for the VRM-based learning setting. Finally, we provide a theoretical explanation for existing VRM models, e.g., uniform distribution-based models, Gaussian distribution-based models, and mixup models.
rate research
Read More
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependence structure. Non-asymptotic bounds are explicitly written down in terms of the multivariate Rademacher complexities of the reservoir systems and the weak dependence structure of the signals that are being handled. This allows, in particular, to determine the minimal number of observations needed in order to guarantee a prescribed estimation accuracy with high probability for a given reservoir family. At the same time, the asymptotic behavior of the devised bounds guarantees the consistency of the empirical risk minimization procedure for various hypothesis classes of reservoir functionals.
Large deep neural networks are powerful, but exhibit undesirable behaviors such as memorization and sensitivity to adversarial examples. 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. By doing so, mixup regularizes the neural network to favor simple linear behavior in-between training examples. Our experiments on the ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI datasets show that mixup improves the generalization of state-of-the-art neural network architectures. We also find that mixup reduces the memorization of corrupt labels, increases the robustness to adversarial examples, and stabilizes the training of generative adversarial networks.
Inferring causal individual treatment effect (ITE) from observational data is a challenging problem whose difficulty is exacerbated by the presence of treatment assignment bias. In this work, we propose a new way to estimate the ITE using the domain generalization framework of invariant risk minimization (IRM). IRM uses data from multiple domains, learns predictors that do not exploit spurious domain-dependent factors, and generalizes better to unseen domains. We propose an IRM-based ITE estimator aimed at tackling treatment assignment bias when there is little support overlap between the control group and the treatment group. We accomplish this by creating diversity: given a single dataset, we split the data into multiple domains artificially. These diverse domains are then exploited by IRM to more effectively generalize regression-based models to data regions that lack support overlap. We show gains over classical regression approaches to ITE estimation in settings when support mismatch is more pronounced.
We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the generalization error that depend on local statistics of the stochastic gradients evaluated along the path of iterates calculated by SGD. The key factors our bounds depend on are the variance of the gradients (with respect to the data distribution) and the local smoothness of the objective function along the SGD path, and the sensitivity of the loss function to perturbations to the final output. Our key technical tool is combining the information-theoretic generalization bounds previously used for analyzing randomized variants of SGD with a perturbation analysis of the iterates.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
