Cheng Zhang

Divyat Mahajan, Jannes Gladrow, Agrin Hilmkil et al.

Structural Causal Models (SCMs) offer a principled framework to reason about interventions and support out-of-distribution generalization, which are key goals in scientific discovery. However, the task of learning SCMs from observed data poses formidable challenges, and often requires training a separate model for each dataset. In this work, we propose an amortized inference framework that trains a single model to predict the causal mechanisms of SCMs conditioned on their observational data and causal graph. We first use a transformer-based architecture for amortized learning of dataset embeddings, and then extend the Fixed-Point Approach (FiP) to infer the causal mechanisms conditionally on their dataset embeddings. As a byproduct, our method can generate observational and interventional data from novel SCMs at inference time, without updating parameters. Empirical results show that our amortized procedure performs on par with baselines trained specifically for each dataset on both in and out-of-distribution problems, and also outperforms them in scarce data regimes.

Shiyue Zhang, Ziheng Cheng, Cheng Zhang

Particle-based variational inference methods (ParVIs) use nonparametric variational families represented by particles to approximate the target distribution according to the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. Although functional gradient flows have been introduced to expand the kernel space for better flexibility, the deterministic updating mechanism may limit exploration and require expensive repetitive runs for new samples. In this paper, we propose Semi-Implicit Functional Gradient flow (SIFG), a functional gradient ParVI method that uses perturbed particles with Gaussian noise as the approximation family. We show that the corresponding functional gradient flow, which can be estimated via denoising score matching with neural networks, exhibits strong theoretical convergence guarantees due to a higher-order smoothness brought to the approximation family via Gaussian perturbation. In addition, we present an adaptive version of our method that automatically selects the appropriate noise magnitude during sampling, striking a good balance between exploration efficiency and approximation accuracy. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness and efficiency of the proposed framework.

Shiyue Zhang, Longlin Yu, Ziheng Cheng et al.

Recently, through a unified gradient flow perspective of Markov chain Monte Carlo (MCMC) and variational inference (VI), particle-based variational inference methods (ParVIs) have been proposed that tend to combine the best of both worlds. While typical ParVIs such as Stein Variational Gradient Descent (SVGD) approximate the gradient flow within a reproducing kernel Hilbert space (RKHS), many attempts have been made recently to replace RKHS with more expressive function spaces, such as neural networks. While successful, these methods are mainly designed for sampling from unconstrained domains. In this paper, we offer a general solution to constrained sampling by introducing a boundary condition for the gradient flow which would confine the particles within the specific domain. This allows us to propose a new functional gradient ParVI method for constrained sampling, called constrained functional gradient flow (CFG), with provable continuous-time convergence in total variation (TV). We also present novel numerical strategies to handle the boundary integral term arising from the domain constraints. Our theory and experiments demonstrate the effectiveness of the proposed framework.