NeurIPS 2019 论文列表

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly outperforms the oblivious sampling method, which is the common choice in the recent literature. The adaptive subspace can be efficiently generated by a correlated random matrix ensemble whose statistics mimic the input data. We prove that the improvement in the relative error of the solution can be tightly characterized in terms of the spectrum of the data matrix, and provide probabilistic upper-bounds. We then illustrate the consequences of our theory with data matrices of different spectral decay. Extensive experimental results show that the proposed approach offers significant speed ups in machine learning problems including logistic regression, kernel classification with random convolution layers and shallow neural networks with rectified linear units. Our analysis is based on convex analysis and Fenchel duality, and establishes connections to sketching and randomized matrix decompositions.

Predicting future video frames is extremely challenging, as there are many factors of variation that make up the dynamics of how frames change through time. Previously proposed solutions require complex inductive biases inside network architectures with highly specialized computation, including segmentation masks, optical flow, and foreground and background separation. In this work, we question if such handcrafted architectures are necessary and instead propose a different approach: finding minimal inductive bias for video prediction while maximizing network capacity. We investigate this question by performing the first large-scale empirical study and demonstrate state-of-the-art performance by learning large models on three different datasets: one for modeling object interactions, one for modeling human motion, and one for modeling car driving.

Hierarchical Reinforcement Learning (HRL) is a promising approach to solving long-horizon problems with sparse and delayed rewards. Many existing HRL algorithms either use pre-trained low-level skills that are unadaptable, or require domain-specific information to define low-level rewards. In this paper, we aim to adapt low-level skills to downstream tasks while maintaining the generality of reward design. We propose an HRL framework which sets auxiliary rewards for low-level skill training based on the advantage function of the high-level policy. This auxiliary reward enables efficient, simultaneous learning of the high-level policy and low-level skills without using task-specific knowledge. In addition, we also theoretically prove that optimizing low-level skills with this auxiliary reward will increase the task return for the joint policy. Experimental results show that our algorithm dramatically outperforms other state-of-the-art HRL methods in Mujoco domains. We also find both low-level and high-level policies trained by our algorithm transferable.

In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to transform a source dataset to match a target dataset using the Wasserstein distance as a divergence measure. We introduce a hierarchical formulation of OT which leverages clustered structure in data to improve alignment in noisy, ambiguous, or multimodal settings. To solve this numerically, we propose a distributed ADMM algorithm that also exploits the Sinkhorn distance, thus it has an efficient computational complexity that scales quadratically with the size of the largest cluster. When the transformation between two datasets is unitary, we provide performance guarantees that describe when and how well aligned cluster correspondences can be recovered with our formulation, as well as provide worst-case dataset geometry for such a strategy. We apply this method to synthetic datasets that model data as mixtures of low-rank Gaussians and study the impact that different geometric properties of the data have on alignment. Next, we applied our approach to a neural decoding application where the goal is to predict movement directions and instantaneous velocities from populations of neurons in the macaque primary motor cortex. Our results demonstrate that when clustered structure exists in datasets, and is consistent across trials or time points, a hierarchical alignment strategy that leverages such structure can provide significant improvements in cross-domain alignment.

The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word mover's distance. We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.

We explore using latent natural language instructions as an expressive and compositional representation of complex actions for hierarchical decision making. Rather than directly selecting micro-actions, our agent first generates a latent plan in natural language, which is then executed by a separate model. We introduce a challenging real-time strategy game environment in which the actions of a large number of units must be coordinated across long time scales. We gather a dataset of 76 thousand pairs of instructions and executions from human play, and train instructor and executor models. Experiments show that models using natural language as a latent variable significantly outperform models that directly imitate human actions. The compositional structure of language proves crucial to its effectiveness for action representation. We also release our code, models and data.

A limitation of Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regression coefficients. Additionally, in many applications, the data is obtained by averaging multiple measurements: this reduces the noise variance, but it dramatically reduces sample sizes and prevents refined noise modeling. In this work, we propose a concomitant estimator that can cope with complex noise structure by using non-averaged measurements, its data-fitting term arising as a smoothing of the nuclear norm. The resulting optimization problem is convex and amenable, thanks to smoothing theory, to state-of-the-art optimization techniques that leverage the sparsity of the solutions. Practical benefits are demonstrated on toy datasets, realistic simulated data and real neuroimaging data.

In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function, which is a quantity that describes the total energy of the system. In this paper we consider a convex optimization problem consisting of the sum of two convex functions, sometimes referred to as a composite objective, and we identify the duality gap to be the `energy' of the system. In the Hamiltonian formalism the energy is conserved, so we add a contractive term to the standard equations of motion so that this energy decreases linearly (ie, geometrically) with time. This yields a continuous-time ordinary differential equation (ODE) in the primal and dual variables which converges to zero duality gap, ie, optimality. This ODE has several useful properties: it induces a natural operator splitting; at convergence it yields both the primal and dual solutions; and it is invariant to affine transformation despite only using first order information. We provide several discretizations of this ODE, some of which are new algorithms and others correspond to known techniques, such as the alternating direction method of multipliers (ADMM). We conclude with some numerical examples that show the promise of our approach. We give an example where our technique can solve a convex quadratic minimization problem orders of magnitude faster than several commonly-used gradient methods, including conjugate gradient, when the conditioning of the problem is poor. Our framework provides new insights into previously known algorithms in the literature as well as providing a technique to generate new primal-dual algorithms.

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.

Machine Learning (ML) models trained on data from multiple demographic groups can inherit representation disparity (Hashimoto et al., 2018) that may exist in the data: the model may be less favorable to groups contributing less to the training process; this in turn can degrade population retention in these groups over time, and exacerbate representation disparity in the long run. In this study, we seek to understand the interplay between ML decisions and the underlying group representation, how they evolve in a sequential framework, and how the use of fairness criteria plays a role in this process. We show that the representation disparity can easily worsen over time under a natural user dynamics (arrival and departure) model when decisions are made based on a commonly used objective and fairness criteria, resulting in some groups diminishing entirely from the sample pool in the long run. It highlights the fact that fairness criteria have to be defined while taking into consideration the impact of decisions on user dynamics. Toward this end, we explain how a proper fairness criterion can be selected based on a general user dynamics model.

Recently, there has been a growing interest in developing saliency methods that provide visual explanations of network predictions. Still, the usability of existing methods is limited to image classification models. To overcome this limitation, we extend the existing approaches to generate grid saliencies, which provide spatially coherent visual explanations for (pixel-level) dense prediction networks. As the proposed grid saliency allows to spatially disentangle the object and its context, we specifically explore its potential to produce context explanations for semantic segmentation networks, discovering which context most influences the class predictions inside a target object area. We investigate the effectiveness of grid saliency on a synthetic dataset with an artificially induced bias between objects and their context as well as on the real-world Cityscapes dataset using state-of-the-art segmentation networks. Our results show that grid saliency can be successfully used to provide easily interpretable context explanations and, moreover, can be employed for detecting and localizing contextual biases present in the data.

Greedy algorithms such as adaptive sampling (k-means++) and furthest point traversal are popular choices for clustering problems. One the one hand, they possess good theoretical approximation guarantees, and on the other, they are fast and easy to implement. However, one main issue with these algorithms is the sensitivity to noise/outliers in the data. In this work we show that for k-means and k-center clustering, simple modifications to the well-studied greedy algorithms result in nearly identical guarantees, while additionally being robust to outliers. For instance, in the case of k-means++, we show that a simple thresholding operation on the distances suffices to obtain an O(\log k) approximation to the objective. We obtain similar results for the simpler k-center problem. Finally, we show experimentally that our algorithms are easy to implement and scale well. We also measure their ability to identify noisy points added to a dataset.

Graph-based semi-supervised learning is a very powerful tool in classification tasks, while in most existing literature the labelled nodes are assumed to be randomly sampled. When the labelling status depends on the unobserved node response, ignoring the missingness can lead to significant estimation bias and handicap the classifiers. This situation is called non-ignorable non-response. To solve the problem, we propose a Graph-based joint model with Non-ignorable Non-response (GNN), followed by a joint inverse weighting estimation procedure incorporated with sampling imputation approach. Our method is proved to outperform some state-of-art models in both regression and classification problems, by simulations and real analysis on the Cora dataset.

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-call meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two primary drawbacks: they either lack the ability to model high-order correlations among variables while maintaining computationally tractable inference, or they do not allow to explicitly model known correlations. To address this shortcoming, we introduce ‘Graph Structured Prediction Energy Networks,’ for which we develop inference techniques that allow to both model explicit local and implicit higher-order correlations while maintaining tractability of inference. We apply the proposed method to tasks from the natural language processing and computer vision domain and demonstrate its general utility.

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervised case, we combine graph normalizing flows with a novel graph auto-encoder to create a generative model of graph structures. Our model is permutation-invariant, generating entire graphs with a single feed-forward pass, and achieves competitive results with the state-of-the art auto-regressive models, while being better suited to parallel computing architectures.

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to \emph{infinitely wide} multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.

Graph-based algorithms are among the most successful paradigms for solving semi-supervised learning tasks. Recent work on graph convolutional networks and neural graph learning methods has successfully combined the expressiveness of neural networks with graph structures. We propose a technique that, when applied to these methods, achieves state-of-the-art results on semi-supervised learning datasets. Traditional graph-based algorithms, such as label propagation, were designed with the underlying assumption that the label of a node can be imputed from that of the neighboring nodes. However, real-world graphs are either noisy or have edges that do not correspond to label agreement. To address this, we propose Graph Agreement Models (GAM), which introduces an auxiliary model that predicts the probability of two nodes sharing the same label as a learned function of their features. The agreement model is used when training a node classification model by encouraging agreement only for the pairs of nodes it deems likely to have the same label, thus guiding its parameters to better local optima. The classification and agreement models are trained jointly in a co-training fashion. Moreover, GAM can also be applied to any semi-supervised classification problem, by inducing a graph whenever one is not provided. We demonstrate that our method achieves a relative improvement of up to 72% for various node classification models, and obtains state-of-the-art results on multiple established datasets.

We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes.