Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support exact inference. While standard GP surrogates have been well-established in Bayesian optimization, Bayesian neural networks (BNNs) have recently become practical function approximators, with many benefits over standard GPs such as the ability to naturally handle non-stationarity and learn representations for high-dimensional data. In this paper, we study BNNs as alternatives to standard GP surrogates for optimization. We consider a variety of approximate inference procedures for finite-width BNNs, including high-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics such as deep ensembles. We also consider infinite-width BNNs and partially stochastic models such as deep kernel learning. We evaluate this collection of surrogate models on diverse problems with varying dimensionality, number of objectives, non-stationarity, and discrete and continuous inputs. We find: (i) the ranking of methods is highly problem dependent, suggesting the need for tailored inductive biases; (ii) HMC is the most successful approximate inference procedure for fully stochastic BNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is relatively competitive; (iv) infinite-width BNNs are particularly promising, especially in high dimensions.

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We also re-examine the connection between the marginal likelihood and PAC-Bayes bounds and use this connection to further elucidate the shortcomings of the marginal likelihood for model selection. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.

The ability to jointly learn from multiple modalities, such as text, audio, and visual data, is a defining feature of intelligent systems. While there have been promising advances in designing neural networks to harness multimodal data, the enormous success of data augmentation currently remains limited to single-modality tasks like image classification. Indeed, it is particularly difficult to augment each modality while preserving the overall semantic structure of the data; for example, a caption may no longer be a good description of an image after standard augmentations have been applied, such as translation. Moreover, it is challenging to specify reasonable transformations that are not tailored to a particular modality. In this paper, we introduce LeMDA, Learning Multimodal Data Augmentation, an easy-to-use method that automatically learns to jointly augment multimodal data in feature space, with no constraints on the identities of the modalities or the relationship between modalities. We show that LeMDA can (1) profoundly improve the performance of multimodal deep learning architectures, (2) apply to combinations of modalities that have not been previously considered, and (3) achieve state-of-the-art results on a wide range of applications comprised of image, text, and tabular data.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

Despite the clear performance benefits of data augmentations, little is known about why they are so effective. In this paper, we disentangle several key mechanisms through which data augmentations operate. Establishing an exchange rate between augmented and additional real data, we find that in out-of-distribution testing scenarios, augmentations which yield samples that are diverse, but inconsistent with the data distribution can be even more valuable than additional training data. Moreover, we find that data augmentations which encourage invariances can be more valuable than invariance alone, especially on small and medium sized training sets. Following this observation, we show that augmentations induce additional stochasticity during training, effectively flattening the loss landscape.

Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate reliable uncertainty estimates, and scalable Bayesian inference methods that can be applied to Flax-based deep neural networks trained from scratch for improved uncertainty quantification and accuracy. By providing a coherent framework for advanced uncertainty quantification methods, Fortuna simplifies the process of benchmarking and helps practitioners build robust AI systems.

Deep neural networks are susceptible to shortcut learning, using simple features to achieve low training loss without discovering essential semantic structure. Contrary to prior belief, we show that generative models alone are not sufficient to prevent shortcut learning, despite an incentive to recover a more comprehensive representation of the data than discriminative approaches. However, we observe that shortcuts are preferentially encoded with minimal information, a fact that generative models can exploit to mitigate shortcut learning. In particular, we propose Chroma-VAE, a two-pronged approach where a VAE classifier is initially trained to isolate the shortcut in a small latent subspace, allowing a secondary classifier to be trained on the complementary, shortcut-free latent subspace. In addition to demonstrating the efficacy of Chroma-VAE on benchmark and real-world shortcut learning tasks, our work highlights the potential for manipulating the latent space of generative classifiers to isolate or interpret specific correlations.

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on quantizing neural network parameters in a linear subspace, profoundly improving on previous results to provide state-of-the-art generalization bounds on a variety of tasks, including transfer learning. We use these tight bounds to better understand the role of model size, equivariance, and the implicit biases of optimization, for generalization in deep learning. Notably, we find large models can be compressed to a much greater extent than previously known, encapsulating Occam's razor. We also argue for data-independent bounds in explaining generalization.

Low-precision arithmetic has had a transformative effect on the training of neural networks, reducing computation, memory and energy requirements. However, despite its promise, low-precision arithmetic has received little attention for Gaussian processes (GPs), largely because GPs require sophisticated linear algebra routines that are unstable in low-precision. We study the different failure modes that can occur when training GPs in half precision. To circumvent these failure modes, we propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, and preconditioning. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low-precision over a wide range of settings, enabling GPs to train on $1.8$ million data points in $10$ hours on a single GPU, without any sparse approximations.

A broad class of stochastic volatility models are defined by systems of stochastic differential equations. While these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an ability to condition on historical data to produce a true posterior distribution. To address this fundamental limitation, we show how to re-cast a class of stochastic volatility models as a hierarchical Gaussian process (GP) model with specialized covariance functions. This GP model retains the inductive biases of the stochastic volatility model while providing the posterior predictive distribution given by GP inference. Within this framework, we take inspiration from well studied domains to introduce a new class of models, Volt and Magpie, that significantly outperform baselines in stock and wind speed forecasting, and naturally extend to the multitask setting.