Mingzhou Fan

Amir Hossein Rahmati, Mingzhou Fan, Ruida Zhou et al.

Instead of randomly acquiring training data points, Uncertainty-based Active Learning (UAL) operates by querying the label(s) of pivotal samples from an unlabeled pool selected based on the prediction uncertainty, thereby aiming at minimizing the labeling cost for model training. The efficacy of UAL critically depends on the model capacity as well as the adopted uncertainty-based acquisition function. Within the context of this study, our analytical focus is directed toward comprehending how the capacity of the machine learning model may affect UAL efficacy. Through theoretical analysis, comprehensive simulations, and empirical studies, we conclusively demonstrate that UAL can lead to worse performance in comparison with random sampling when the machine learning model class has low capacity and is unable to cover the underlying ground truth. In such situations, adopting acquisition functions that directly target estimating the prediction performance may be beneficial for improving the performance of UAL.

Mingzhou Fan, Ruida Zhou, Chao Tian et al.

Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling~(PGPS) method based on a novel Log-weighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.