Estimating processes in adapted Wasserstein distance

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods, designed to directly construct the optimal feedback representation of hedging or investment decisions, are analyzed in this framework demonstrating their effectiveness as well as their susceptibility to generalization error. Use of classical techniques shows that over‐training renders trained investment decisions to become anticipative, and proves overlearning for large hypothesis spaces. On the other hand, nonasymptotic estimates based on Rademacher complexity show the convergence for sufficiently large training sets. These results emphasize the importance of synthetic data generation and the appropriate calibration of complex models to market data. A numerically studied stylized example illustrates these possibilities, including the importance of problem dimension in the degree of overlearning, and the effectiveness of this approach.

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“…Proposition 1 in Pflug and Pichler (2016). A similar observation is also made in Example 7.1 in Backhoff et al (2022).…”

Section: Examplessupporting

confidence: 79%

Deep empirical risk minimization in finance: Looking into the future

Reppen

Soner

2022

Mathematical Finance

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“…This entails an important practical implication: When approximating an AOT problem with marginals µ and ν by a sequence of discrete problems, the marginals have to be approximated with respect to an adapted distance, and not just the Wasserstein distance. Such approximations are studied for instance in [3,8,9]. Our results show that AOT is surprisingly well behaved for an OT problem with additional constraints.…”

Section: Introductionmentioning

confidence: 85%

Computational methods for adapted optimal transport

Eckstein¹,

Pammer²

2022

Preprint

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Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT problems numerically. First, we show that AOT problems are stable with respect to perturbations in the marginals and thus arbitrary AOT problems can be approximated by sequences of linear programs. We further study entropic methods to solve AOT problems. We show that any entropically regularized AOT problem converges to the corresponding unregularized problem if the regularization parameter goes to zero. The proof is based on a novel method -even in the non-adapted case -to easily obtain smooth approximations of a given coupling with fixed marginals. Finally, we show tractability of the adapted version of Sinkhorn's algorithm. We give explicit solutions for the occurring projections and prove that the procedure converges to the optimizer of the entropic AOT problem.

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“…The application fields of MSDA approaches have been extended by recent research, which includes learning domain invariant features through adversarial learning [19] and integrating moment matching components into deep neural networks [20]. In addition, there are many methods to improve the generalization capability of the model, including using k-domain discriminators [21], merging decision boundaries for sliced Wasserstein distance processing tasks [22], and a new framework for adjusting domain-specific distributions [23]. However, the abovementioned methods often do not fully utilize the pseudo-labels generated from multiple source domains, which may lead to mutual suppression of classification accuracy among different source domains.…”

Section: Msdamentioning

confidence: 99%

Dual-weight attention-based multi-source multi-stage alignment domain adaptation for industrial fault diagnosis

Wang,

Chen,

Chen

et al. 2024

Meas. Sci. Technol.

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Cross-domain fault diagnosis is crucial for industrial applications with various and unknown operating conditions. However, due to the significant differences in the distribution of features in multiple source domains, it may lead to mutual interference of features between different domains and reduce the accuracy of diagnosis, which is a problem not considered by most current researches. In addition, most of the existing methods focus only on the extraction of low-frequency global information and cannot adequately deal with high-frequency local information. Consequently, this paper provides a multi-stage processing integrated dual-weight attention-based multi-source multi-stage aligned domain adaptation (DAMMADA) method. Global fault features that are shared by various subdomains are extracted by three domain-specific feature extractors from various domains. In a local feature extractor, the dual-weight attention module not only uses shared weights to aggregate local information, but it also uses contextual weights to improve local features. In terms of loss handling, multiple pseudo-labels are used to reduce the loss of the local maximum mean discrepancy (LMMD) in order to learn the domain-invariant characteristics after improving the high-frequency and low-frequency information extraction. To modify the classification boundaries, the pseudo-labels' mean square errors (MSE) are combined. Comprehensive experiments were carried out on two platforms for fault diagnosis of SCARA robots and bearings respectively, and the results demonstrated that DAMMADA is superior to other methods in terms of accuracy and its ability to suppress negative migration for cross-domain tasks.

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Estimating processes in adapted Wasserstein distance

Cited by 12 publications

References 33 publications

Deep empirical risk minimization in finance: Looking into the future

Deep empirical risk minimization in finance: Looking into the future

Computational methods for adapted optimal transport

Dual-weight attention-based multi-source multi-stage alignment domain adaptation for industrial fault diagnosis

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