Predictive Complexity Priors

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and uninformative can have unintuitive and detrimental effects on a model's predictions. For this reason, we propose predictive complexity priors: a functional prior that is defined by comparing the model's predictions to those of a reference model. Although originally defined on the model outputs, we transfer the prior to the model parameters via a change of variables. The traditional Bayesian workflow can then proceed as usual. We apply our predictive complexity prior to high-dimensional regression, reasoning over neural network depth, and sharing of statistical strength for few-shot learning

Spectral Diffusion Processes

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To do so, we represent functional data in spectral space to dissociate the stochastic part of the processes from their space-time part. Using dimensionality reduction techniques we then sample from their stochastic component using finite dimensional SGM. We demonstrate our method's effectiveness for modelling various multimodal datasets.Comment: 17 pages, 11 figures, Score-based Method Workshop at 36th Conference on Neural Information Processing Systems (NeurIPS 2022

What Matters for Meta-Learning Vision Regression Tasks?

Meta-learning is widely used in few-shot classification and function regression due to its ability to quickly adapt to unseen tasks. However, it has not yet been well explored on regression tasks with high dimensional inputs such as images. This paper makes two main contributions that help understand this barely explored area. \emph{First}, we design two new types of cross-category level vision regression tasks, namely object discovery and pose estimation of unprecedented complexity in the meta-learning domain for computer vision. To this end, we (i) exhaustively evaluate common meta-learning techniques on these tasks, and (ii) quantitatively analyze the effect of various deep learning techniques commonly used in recent meta-learning algorithms in order to strengthen the generalization capability: data augmentation, domain randomization, task augmentation and meta-regularization. Finally, we (iii) provide some insights and practical recommendations for training meta-learning algorithms on vision regression tasks. \emph{Second}, we propose the addition of functional contrastive learning (FCL) over the task representations in Conditional Neural Processes (CNPs) and train in an end-to-end fashion. The experimental results show that the results of prior work are misleading as a consequence of a poor choice of the loss function as well as too small meta-training sets. Specifically, we find that CNPs outperform MAML on most tasks without fine-tuning. Furthermore, we observe that naive task augmentation without a tailored design results in underfitting.Comment: Accepted at CVPR 202