Benchmark datasets used for image classification tend to have very low levels of label noise. When Bayesian neural networks are trained on these datasets, they often underfit, misrepresenting the aleatoric uncertainty of the data. A common solution is to cool the posterior, which improves fit to the training data but is challenging to interpret from a Bayesian perspective. We explore whether posterior tempering can be replaced by a confidence-inducing prior distribution. First, we introduce a "DirClip" prior that is practical to sample and nearly matches the performance of a cold posterior. Second, we introduce a "confidence prior" that directly approximates a cold likelihood in the limit of decreasing temperature but cannot be easily sampled. Lastly, we provide several general insights into confidence-inducing priors, such as when they might diverge and how fine-tuning can mitigate numerical instability.
The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of sampling methods designed for effective sampling from distributions characterized by distant and disconnected modes. DiGS integrates recent developments in diffusion models, leveraging Gaussian convolution to create an auxiliary noisy distribution that bridges isolated modes in the original space and applying Gibbs sampling to alternately draw samples from both spaces. Our approach exhibits a better mixing property for sampling multi-modal distributions than state-of-the-art methods such as parallel tempering. We demonstrate that our sampler attains substantially improved results across various tasks, including mixtures of Gaussians, Bayesian neural networks and molecular dynamics.
In recent years, there has been considerable interest in developing machine learning models on graphs in order to account for topological inductive biases. In particular, recent attention was given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Mat\'ern kernel and one that additionally mixes information of different cell types.
Energy-Based Models (EBMs) offer a versatile framework for modeling complex data distributions. However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for scalable EBM training suffers from inconsistency issues, causing the energy model to learn a `noisy' data distribution. In this work, we propose an efficient sampling framework: (pseudo)-Gibbs sampling with moment matching, which enables effective sampling from the underlying clean model when given a `noisy' model that has been well-trained via DSM. We explore the benefits of our approach compared to related methods and demonstrate how to scale the method to high-dimensional datasets.
Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss the blindness problem and propose a new family of divergences that can mitigate the blindness problem. We illustrate our proposed divergence in the context of density estimation and report improved performance compared to traditional approaches.
Latent variable models like the Variational Auto-Encoder (VAE) are commonly used to learn representations of images. However, for downstream tasks like semantic classification, the representations learned by VAE are less competitive than other non-latent variable models. This has led to some speculations that latent variable models may be fundamentally unsuitable for representation learning. In this work, we study what properties are required for good representations and how different VAE structure choices could affect the learned properties. We show that by using a decoder that prefers to learn local features, the remaining global features can be well captured by the latent, which significantly improves performance of a downstream classification task. We further apply the proposed model to semi-supervised learning tasks and demonstrate improvements in data efficiency.
The original "Seven Motifs" set forth a roadmap of essential methods for the field of scientific computing, where a motif is an algorithmic method that captures a pattern of computation and data movement. We present the "Nine Motifs of Simulation Intelligence", a roadmap for the development and integration of the essential algorithms necessary for a merger of scientific computing, scientific simulation, and artificial intelligence. We call this merger simulation intelligence (SI), for short. We argue the motifs of simulation intelligence are interconnected and interdependent, much like the components within the layers of an operating system. Using this metaphor, we explore the nature of each layer of the simulation intelligence operating system stack (SI-stack) and the motifs therein: (1) Multi-physics and multi-scale modeling; (2) Surrogate modeling and emulation; (3) Simulation-based inference; (4) Causal modeling and inference; (5) Agent-based modeling; (6) Probabilistic programming; (7) Differentiable programming; (8) Open-ended optimization; (9) Machine programming. We believe coordinated efforts between motifs offers immense opportunity to accelerate scientific discovery, from solving inverse problems in synthetic biology and climate science, to directing nuclear energy experiments and predicting emergent behavior in socioeconomic settings. We elaborate on each layer of the SI-stack, detailing the state-of-art methods, presenting examples to highlight challenges and opportunities, and advocating for specific ways to advance the motifs and the synergies from their combinations. Advancing and integrating these technologies can enable a robust and efficient hypothesis-simulation-analysis type of scientific method, which we introduce with several use-cases for human-machine teaming and automated science.
Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of `automatic relevance determination' kernels, but in high-dimensional datasets this approach can be unreliable. A more probabilistically principled alternative is to use spike and slab priors and infer a posterior probability of variable inclusion. However, existing implementations in GPs are extremely costly to run in both high-dimensional and large-$n$ datasets, or are intractable for most kernels. As such, we develop a fast and scalable variational inference algorithm for the spike and slab GP that is tractable with arbitrary differentiable kernels. We improve our algorithm's ability to adapt to the sparsity of relevant variables by Bayesian model averaging over hyperparameters, and achieve substantial speed ups using zero temperature posterior restrictions, dropout pruning and nearest neighbour minibatching. In experiments our method consistently outperforms vanilla and sparse variational GPs whilst retaining similar runtimes (even when $n=10^6$) and performs competitively with a spike and slab GP using MCMC but runs up to $1000$ times faster.
In this work we introduce a new approach for identifiable non-linear ICA models. Recently there has been a renaissance in identifiability results in deep generative models, not least for non-linear ICA. These prior works, however, have assumed access to a sufficiently-informative auxiliary set of observations, denoted $\mathbf{u}$. We show here how identifiability can be obtained in the absence of this side-information, rendering possible fully-unsupervised identifiable non-linear ICA. While previous theoretical results have established the impossibility of identifiable non-linear ICA in the presence of infinitely-flexible universal function approximators, here we rely on the intrinsically-finite modelling capacity of any particular chosen parameterisation of a deep generative model. In particular, we focus on generative models which perform clustering in their latent space -- a model structure which matches previous identifiable models, but with the learnt clustering providing a synthetic form of auxiliary information. We evaluate our proposals using VAEs, on synthetic and image datasets, and find that the learned clusterings function effectively: deep generative models with latent clusterings are empirically identifiable, to the same degree as models which rely on side information.
When designing new molecules with particular properties, it is not only important what to make but crucially how to make it. These instructions form a synthesis directed acyclic graph (DAG), describing how a large vocabulary of simple building blocks can be recursively combined through chemical reactions to create more complicated molecules of interest. In contrast, many current deep generative models for molecules ignore synthesizability. We therefore propose a deep generative model that better represents the real world process, by directly outputting molecule synthesis DAGs. We argue that this provides sensible inductive biases, ensuring that our model searches over the same chemical space that chemists would also have access to, as well as interpretability. We show that our approach is able to model chemical space well, producing a wide range of diverse molecules, and allows for unconstrained optimization of an inherently constrained problem: maximize certain chemical properties such that discovered molecules are synthesizable.