Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling

This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network using stochastic gradient descent. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method of Rolland et al. [2022], assuming a sufficiently good estimation of the score function. Finally, we analyze the upper bound of score-matching estimation within the score-based generative modeling, which has been applied for causal discovery but is also of independent interest within the domain of generative models.Comment: Accepted in NeurIPS 202

Learning Generative Models across Incomparable Spaces

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML

Learning Independent Causal Mechanisms

Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by physical mechanisms that give rise to dependences between observables. Mechanisms, however, can be meaningful autonomous modules of generative models that make sense beyond a particular entailed data distribution, lending themselves to transfer between problems. We develop an algorithm to recover a set of independent (inverse) mechanisms from a set of transformed data points. The approach is unsupervised and based on a set of experts that compete for data generated by the mechanisms, driving specialization. We analyze the proposed method in a series of experiments on image data. Each expert learns to map a subset of the transformed data back to a reference distribution. The learned mechanisms generalize to novel domains. We discuss implications for transfer learning and links to recent trends in generative modeling.Comment: ICML 201

Adversarial Discriminative Domain Adaptation

Adversarial learning methods are a promising approach to training robust deep networks, and can generate complex samples across diverse domains. They also can improve recognition despite the presence of domain shift or dataset bias: several adversarial approaches to unsupervised domain adaptation have recently been introduced, which reduce the difference between the training and test domain distributions and thus improve generalization performance. Prior generative approaches show compelling visualizations, but are not optimal on discriminative tasks and can be limited to smaller shifts. Prior discriminative approaches could handle larger domain shifts, but imposed tied weights on the model and did not exploit a GAN-based loss. We first outline a novel generalized framework for adversarial adaptation, which subsumes recent state-of-the-art approaches as special cases, and we use this generalized view to better relate the prior approaches. We propose a previously unexplored instance of our general framework which combines discriminative modeling, untied weight sharing, and a GAN loss, which we call Adversarial Discriminative Domain Adaptation (ADDA). We show that ADDA is more effective yet considerably simpler than competing domain-adversarial methods, and demonstrate the promise of our approach by exceeding state-of-the-art unsupervised adaptation results on standard cross-domain digit classification tasks and a new more difficult cross-modality object classification task