While neural networks have shown remarkable success on classification tasks in terms of average-case performance, they often fail to perform well on certain groups of the data. Such group information may be expensive to obtain; thus, recent works in robustness and fairness have proposed ways to improve worst-group performance even when group labels are unavailable for the training data. However, these methods generally underperform methods that utilize group information at training time. In this work, we assume access to a small number of group labels alongside a larger dataset without group labels. We propose BARACK, a simple two-step framework to utilize this partial group information to improve worst-group performance: train a model to predict the missing group labels for the training data, and then use these predicted group labels in a robust optimization objective. Theoretically, we provide generalization bounds for our approach in terms of the worst-group performance, showing how the generalization error scales with respect to both the total number of training points and the number of training points with group labels. Empirically, our method outperforms the baselines that do not use group information, even when only 1-33% of points have group labels. We provide ablation studies to support the robustness and extensibility of our framework.
A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizing a linear-Gaussian SEM. Developing a full Bayesian posterior over DAGs is challenging due to the the discrete and combinatorial nature of graphs. We analyse key design choices for scalable VI over DAGs, such as 1) the parametrization of DAGs via an expressive variational family, 2) a continuous relaxation that enables low-variance stochastic optimization, and 3) suitable priors over the latent variables. We provide a series of experiments on real and synthetic data showing that BCD Nets outperform maximum-likelihood methods on standard causal discovery metrics such as structural Hamming distance in low data regimes.
Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond $2$-WL graph separation, and $n$-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.
We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific geometries and typically suffer from high computational costs. We introduce Moser Flow (MF), a new class of generative models within the family of continuous normalizing flows (CNF). MF also produces a CNF via a solution to the change-of-variable formula, however differently from other CNF methods, its model (learned) density is parameterized as the source (prior) density minus the divergence of a neural network (NN). The divergence is a local, linear differential operator, easy to approximate and calculate on manifolds. Therefore, unlike other CNFs, MF does not require invoking or backpropagating through an ODE solver during training. Furthermore, representing the model density explicitly as the divergence of a NN rather than as a solution of an ODE facilitates learning high fidelity densities. Theoretically, we prove that MF constitutes a universal density approximator under suitable assumptions. Empirically, we demonstrate for the first time the use of flow models for sampling from general curved surfaces and achieve significant improvements in density estimation, sample quality, and training complexity over existing CNFs on challenging synthetic geometries and real-world benchmarks from the earth and climate sciences.
We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, our paradigm leverages the demonstrator's behavior en route to optimality, and in particular, the exploration phase, to obtain consistent reward estimates. We develop simple and efficient reward estimation procedures for demonstrations within a class of upper-confidence-based algorithms, showing that reward estimation gets progressively easier as the regret of the algorithm increases. We match these upper bounds with information-theoretic lower bounds that apply to any demonstrator algorithm, thereby characterizing the optimal tradeoff between exploration and reward estimation. Extensive empirical evaluations on both synthetic data and simulated experimental design data from the natural sciences corroborate our theoretical results.
We introduce a framework that abstracts Reinforcement Learning (RL) as a sequence modeling problem. This allows us to draw upon the simplicity and scalability of the Transformer architecture, and associated advances in language modeling such as GPT-x and BERT. In particular, we present Decision Transformer, an architecture that casts the problem of RL as conditional sequence modeling. Unlike prior approaches to RL that fit value functions or compute policy gradients, Decision Transformer simply outputs the optimal actions by leveraging a causally masked Transformer. By conditioning an autoregressive model on the desired return (reward), past states, and actions, our Decision Transformer model can generate future actions that achieve the desired return. Despite its simplicity, Decision Transformer matches or exceeds the performance of state-of-the-art model-free offline RL baselines on Atari, OpenAI Gym, and Key-to-Door tasks.
Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional Theory (DFT), are limited in their practical use due to their high computational expense. Machine learning approaches have the potential to approximate DFT in a computationally efficient manner, which could dramatically increase the impact of computational simulations on real-world problems. Approximating DFT poses several challenges. These include accurately modeling the subtle changes in the relative positions and angles between atoms, and enforcing constraints such as rotation invariance or energy conservation. We introduce a novel approach to modeling angular information between sets of neighboring atoms in a graph neural network. Rotation invariance is achieved for the network's edge messages through the use of a per-edge local coordinate frame and a novel spin convolution over the remaining degree of freedom. Two model variants are proposed for the applications of structure relaxation and molecular dynamics. State-of-the-art results are demonstrated on the large-scale Open Catalyst 2020 dataset. Comparisons are also performed on the MD17 and QM9 datasets.
The goal of Multi-task Bayesian Optimization (MBO) is to minimize the number of queries required to accurately optimize a target black-box function, given access to offline evaluations of other auxiliary functions. When offline datasets are large, the scalability of prior approaches comes at the expense of expressivity and inference quality. We propose JUMBO, an MBO algorithm that sidesteps these limitations by querying additional data based on a combination of acquisition signals derived from training two Gaussian Processes (GP): a cold-GP operating directly in the input domain and a warm-GP that operates in the feature space of a deep neural network pretrained using the offline data. Such a decomposition can dynamically control the reliability of information derived from the online and offline data and the use of pretrained neural networks permits scalability to large offline datasets. Theoretically, we derive regret bounds for JUMBO and show that it achieves no-regret under conditions analogous to GP-UCB (Srinivas et. al. 2010). Empirically, we demonstrate significant performance improvements over existing approaches on two real-world optimization problems: hyper-parameter optimization and automated circuit design.
We investigate the capability of a transformer pretrained on natural language to generalize to other modalities with minimal finetuning -- in particular, without finetuning of the self-attention and feedforward layers of the residual blocks. We consider such a model, which we call a Frozen Pretrained Transformer (FPT), and study finetuning it on a variety of sequence classification tasks spanning numerical computation, vision, and protein fold prediction. In contrast to prior works which investigate finetuning on the same modality as the pretraining dataset, we show that pretraining on natural language improves performance and compute efficiency on non-language downstream tasks. In particular, we find that such pretraining enables FPT to generalize in zero-shot to these modalities, matching the performance of a transformer fully trained on these tasks.