NeurIPS 2020 论文列表

We revisit the problem of counting the number of distinct elements $\dist$ in a data stream $D$, over a domain $[u]$. We propose an $(\epsilon,\delta)$-differentially private algorithm that approximates $\dist$ within a factor of $(1\pm\gamma)$, and with additive error of $O(\sqrt{\ln(1/\delta)}/\epsilon)$, using space $O(\ln(\ln(u)/\gamma)/\gamma^2)$. We improve on the prior work at least quadratically and up to exponentially, in terms of both space and additive error. Our additive error guarantee is optimal up to a factor of $O(\sqrt{\ln(1/\delta)})$, and the space bound is optimal up to a factor of $O\left(\min\left\{\ln\left(\frac{\ln(u)}{\gamma}\right), \frac{1}{\gamma^2}\right\}\right)$. We assume the existence of an ideal uniform random hash function, and ignore the space required to store it. We later relax this requirement by assuming pseudorandom functions and appealing to a computational variant of differential privacy, SIM-CDP. Our algorithm is built on top of the celebrated Flajolet-Martin (FM) sketch. We show that FM-sketch is differentially private as is, as long as there are $\approx \sqrt{\ln(1/\delta)}/(\epsilon\gamma)$ distinct elements in the data set. Along the way, we prove a structural result showing that the maximum of $k$ i.i.d. random variables is statistically close (in the sense of $\epsilon$-differential privacy) to the maximum of $(k+1)$ i.i.d. samples from the same distribution, as long as $k=\Omega\left(\frac{1}{\epsilon}\right)$. Finally, experiments show that our algorithms introduces error within an order of magnitude of the non-private analogues for streams with thousands of distinct elements, even while providing strong privacy guarantee ($\eps\leq 1$).

Ensemble is a general way of improving the accuracy and stability of learning models, especially for the generalization ability on small datasets. Compared with tree-based methods, relatively less works have been devoted to an in-depth study on effective ensemble design for neural networks. In this paper, we propose a principled ensemble technique by constructing the so-called diversified ensemble layer to combine multiple networks as individual modules. We theoretically show that each individual model in our ensemble layer corresponds to weights in the ensemble layer optimized in different directions. Meanwhile, the devised ensemble layer can be readily integrated into popular neural architectures, including CNNs, RNNs, and GCNs. Extensive experiments are conducted on public tabular datasets, images, and texts. By adopting weight sharing approach, the results show our method can notably improve the accuracy and stability of the original neural networks with ignorable extra time and space overhead.

A key tool for building differentially private systems is adding Gaussian noise to the output of a function evaluated on a sensitive dataset. Unfortunately, using a continuous distribution presents several practical challenges. First and foremost, finite computers cannot exactly represent samples from continuous distributions, and previous work has demonstrated that seemingly innocuous numerical errors can entirely destroy privacy. Moreover, when the underlying data is itself discrete (e.g., population counts), adding continuous noise makes the result less interpretable.

Triplet loss with batch hard mining (TriHard loss) is an important variation of triplet loss inspired by the idea that hard triplets improve the performance of metric leaning networks. However, there is a dilemma in the training process. The hard negative samples contain various quite similar characteristics compared with anchors and positive samples in a batch. Features of these characteristics should be clustered between anchors and positive samples while are also utilized to repel between anchors and hard negative samples. It is harmful for learning mutual features within classes. Several methods to alleviate the dilemma are designed and tested. In the meanwhile, an element-weighted TriHard loss is emphatically proposed to enlarge the distance between partial elements of feature vectors selectively which represent the different characteristics between anchors and hard negative samples. Extensive evaluations are conducted on Market1501 and MSMT17 datasets and the results achieve state-of-the-art on public baselines.

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike previous single-neuron relaxations which focus only on the univariate input space of the ReLU, our method considers the multivariate input space of the affine pre-activation function preceding the ReLU. Using results from submodularity and convex geometry, we derive an explicit description of the tightest possible convex relaxation when this multivariate input is over a box domain. We show that our convex relaxation is significantly stronger than the commonly used univariate-input relaxation which has been proposed as a natural convex relaxation barrier for verification. While our description of the relaxation may require an exponential number of inequalities, we show that they can be separated in linear time and hence can be efficiently incorporated into optimization algorithms on an as-needed basis. Based on this novel relaxation, we design two polynomial-time algorithms for neural network verification: a linear-programming-based algorithm that leverages the full power of our relaxation, and a fast propagation algorithm that generalizes existing approaches. In both cases, we show that for a modest increase in computational effort, our strengthened relaxation enables us to verify a significantly larger number of instances compared to similar algorithms.

We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and a nearly matching computational hardness result for this problem. An interesting implication of our findings is that the $L_{\infty}$ perturbations case is provably computationally harder than the case $2 \leq p < \infty$.

We study the statistical problem of estimating a rank-one sparse tensor corrupted by additive gaussian noise, a Gaussian additive model also known as sparse tensor PCA. We show that for Bernoulli and Bernoulli-Rademacher distributed signals and \emph{for all} sparsity levels which are sublinear in the dimension of the signal, the sparse tensor PCA model exhibits a phase transition called the \emph{all-or-nothing phenomenon}. This is the property that for some signal-to-noise ratio (SNR) $\mathrm{SNR_c}$ and any fixed $\epsilon>0$, if the SNR of the model is below $\left(1-\epsilon\right)\mathrm{SNR_c}$, then it is impossible to achieve any arbitrarily small constant correlation with the hidden signal, while if the SNR is above $\left(1+\epsilon \right)\mathrm{SNR_c}$, then it is possible to achieve almost perfect correlation with the hidden signal. The all-or-nothing phenomenon was initially established in the context of sparse linear regression, and over the last year also in the context of sparse 2-tensor (matrix) PCA and Bernoulli group testing. Our results follow from a more general result showing that for any Gaussian additive model with a discrete uniform prior, the all-or-nothing phenomenon follows as a direct outcome of an appropriately defined ``near-orthogonality" property of the support of the prior distribution.

Biased regularization and fine tuning are two recent meta-learning approaches. They have been shown to be effective to tackle distributions of tasks, in which the tasks’ target vectors are all close to a common meta-parameter vector. However, these methods may perform poorly on heterogeneous environments of tasks, where the complexity of the tasks’ distribution cannot be captured by a single meta- parameter vector. We address this limitation by conditional meta-learning, inferring a conditioning function mapping task’s side information into a meta-parameter vector that is appropriate for that task at hand. We characterize properties of the environment under which the conditional approach brings a substantial advantage over standard meta-learning and we highlight examples of environments, such as those with multiple clusters, satisfying these properties. We then propose a convex meta-algorithm providing a comparable advantage also in practice. Numerical experiments confirm our theoretical findings.

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees, based on solving large semidefinite programs which are impractical to run, or make strong assumptions such as requiring the factors to be nearly orthogonal. In this paper we introduce a new variant of alternating minimization, which in turn is inspired by understanding how the progress measures that guide convergence of alternating minimization in the matrix setting need to be adapted to the tensor setting. We show strong provable guarantees, including showing that our algorithm converges linearly to the true tensors even when the factors are highly correlated and can be implemented in nearly linear time. Moreover our algorithm is also highly practical and we show that we can complete third order tensors with a thousand dimensions from observing a tiny fraction of its entries. In contrast, and somewhat surprisingly, we show that the standard version of alternating minimization, without our new twist, can converge at a drastically slower rate in practice.

In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed light on this behavior carrying out a careful regret analysis. We prove a novel static regret bound that depends on the temporal variability of the sequence of loss functions, a quantity which is often encountered when considering dynamic competitors. We show, for example, that the regret can be constant if the temporal variability is constant and the learning rate is tuned appropriately, without the need of smooth losses. Moreover, we present an adaptive algorithm that achieves this regret bound without prior knowledge of the temporal variability and prove a matching lower bound. Finally, we validate our theoretical findings on classification and regression datasets.

Understanding the relationships between biomedical terms like viruses, drugs, and symptoms is essential in the fight against diseases. Many attempts have been made to introduce the use of machine learning to the scientific process of hypothesis generation (HG), which refers to the discovery of meaningful implicit connections between biomedical terms. However, most existing methods fail to truly capture the temporal dynamics of scientific term relations and also assume unobserved connections to be irrelevant (i.e., in a positive-negative (PN) learning setting). To break these limits, we formulate this HG problem as future connectivity prediction task on a dynamic attributed graph via positive-unlabeled (PU) learning. Then, the key is to capture the temporal evolution of node pair (term pair) relations from just the positive and unlabeled data. We propose a variational inference model to estimate the positive prior, and incorporate it in the learning of node pair embeddings, which are then used for link prediction. Experiment results on real-world biomedical term relationship datasets and case study analyses on a COVID-19 dataset validate the effectiveness of the proposed model.

Generative adversarial networks (GANs) were originally envisioned as unsupervised generative models that learn to follow a target distribution. Variants such as conditional GANs, auxiliary-classifier GANs (ACGANs) project GANs on to supervised and semi-supervised learning frameworks by providing labelled data and using multi-class discriminators. In this paper, we approach the supervised GAN problem from a different perspective, one that is motivated by the philosophy of the famous Persian poet Rumi who said, "The art of knowing is knowing what to ignore." In the GAN framework, we not only provide the GAN positive data that it must learn to model, but also present it with so-called negative samples that it must learn to avoid — we call this "The Rumi Framework." This formulation allows the discriminator to represent the underlying target distribution better by learning to penalize generated samples that are undesirable — we show that this capability accelerates the learning process of the generator. We present a reformulation of the standard GAN (SGAN) and least-squares GAN (LSGAN) within the Rumi setting. The advantage of the reformulation is demonstrated by means of experiments conducted on MNIST, Fashion MNIST, CelebA, and CIFAR-10 datasets. Finally, we consider an application of the proposed formulation to address the important problem of learning an under-represented class in an unbalanced dataset. The Rumi approach results in substantially lower FID scores than the standard GAN frameworks while possessing better generalization capability.

Score function-based natural language generation (NLG) approaches such as REINFORCE, in general, suffer from low sample efficiency and training instability problems. This is mainly due to the non-differentiable nature of the discrete space sampling and thus these methods have to treat the discriminator as a black box and ignore the gradient information. To improve the sample efficiency and reduce the variance of REINFORCE, we propose a novel approach, TaylorGAN, which augments the gradient estimation by off-policy update and the first-order Taylor expansion. This approach enables us to train NLG models from scratch with smaller batch size --- without maximum likelihood pre-training, and outperforms existing GAN-based methods on multiple metrics of quality and diversity.

Efficient exploration is one of the main challenges in reinforcement learning (RL). Most existing sample-efficient algorithms assume the existence of a single reward function during exploration. In many practical scenarios, however, there is not a single underlying reward function to guide the exploration, for instance, when an agent needs to learn many skills simultaneously, or multiple conflicting objectives need to be balanced. To address these challenges, we propose the \textit{task-agnostic RL} framework: In the exploration phase, the agent first collects trajectories by exploring the MDP without the guidance of a reward function. After exploration, it aims at finding near-optimal policies for $N$ tasks, given the collected trajectories augmented with \textit{sampled rewards} for each task. We present an efficient task-agnostic RL algorithm, \textsc{UCBZero}, that finds $\epsilon$-optimal policies for $N$ arbitrary tasks after at most $\tilde O(\log(N)H^5SA/\epsilon^2)$ exploration episodes. We also provide an $\Omega(\log (N)H^2SA/\epsilon^2)$ lower bound, showing that the $\log$ dependency on $N$ is unavoidable. Furthermore, we provide an $N$-independent sample complexity bound of \textsc{UCBZero} in the statistically easier setting when the ground truth reward functions are known.

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically equivalent across meta-training and meta-testing, rather than considering worst-case task performance. In this work we introduce the notion of ``task-robustness'' by reformulating the popular Model-Agnostic Meta-Learning (MAML) objective \citep{finn2017model} such that the goal is to minimize the maximum loss over the observed meta-training tasks. The solution to this novel formulation is task-robust in the sense that it places equal importance on even the most difficult and/or rare tasks. This also means that it performs well over all distributions of the observed tasks, making it robust to shifts in the task distribution between meta-training and meta-testing. We present an algorithm to solve the proposed min-max problem, and show that it converges to an $\epsilon$-accurate point at the optimal rate of $\mathcal{O}(1/\epsilon^2)$ in the convex setting and to an $(\epsilon, \delta)$-stationary point at the rate of $\mathcal{O}(\max\{1/\epsilon^5, 1/\delta^5\})$ in nonconvex settings. We also provide an upper bound on the new task generalization error that captures the advantage of minimizing the worst-case task loss, and demonstrate this advantage in sinusoid regression and image classification experiments.

Feature distillation, a primary method in knowledge distillation, always leads to significant accuracy improvements. Most existing methods distill features in the teacher network through a manually designed transformation. In this paper, we propose a novel distillation method named task-oriented feature distillation (TOFD) where the transformation is convolutional layers that are trained in a data-driven manner by task loss. As a result, the task-oriented information in the features can be captured and distilled to students. Moreover, an orthogonal loss is applied to the feature resizing layer in TOFD to improve the performance of knowledge distillation. Experiments show that TOFD outperforms other distillation methods by a large margin on both image classification and 3D classification tasks. Codes have been released in Github.

Continuously learning to solve unseen tasks with limited experience has been extensively pursued in meta-learning and continual learning, but with restricted assumptions such as accessible task distributions, independently and identically distributed tasks, and clear task delineations. However, real-world physical tasks frequently violate these assumptions, resulting in performance degradation. This paper proposes a continual online model-based reinforcement learning approach that does not require pre-training to solve task-agnostic problems with unknown task boundaries. We maintain a mixture of experts to handle nonstationarity, and represent each different type of dynamics with a Gaussian Process to efficiently leverage collected data and expressively model uncertainty. We propose a transition prior to account for the temporal dependencies in streaming data and update the mixture online via sequential variational inference. Our approach reliably handles the task distribution shift by generating new models for never-before-seen dynamics and reusing old models for previously seen dynamics. In experiments, our approach outperforms alternative methods in non-stationary tasks, including classic control with changing dynamics and decision making in different driving scenarios.

Gaussian processes (GPs) are flexible priors for modeling functions. However, their success depends on the kernel accurately reflecting the properties of the data. One of the appeals of the GP framework is that the marginal likelihood of the kernel hyperparameters is often available in closed form, enabling optimization and sampling procedures to fit these hyperparameters to data. Unfortunately, point-wise evaluation of the marginal likelihood is expensive due to the need to solve a linear system; searching or sampling the space of hyperparameters thus often dominates the practical cost of using GPs. We introduce an approach to the identification of kernel hyperparameters in GP regression and related problems that sidesteps the need for costly marginal likelihoods. Our strategy is to "amortize" inference over hyperparameters by training a single neural network, which consumes a set of regression data and produces an estimate of the kernel function, useful across different tasks. To accommodate the varying dimension and cardinality of different regression problems, we use a hierarchical self-attention-based neural network that produces estimates of the hyperparameters which are invariant to the order of the input data points and data dimensions. We show that a single neural model trained on synthetic data is able to generalize directly to several different unseen real-world GP use cases. Our experiments demonstrate that the estimated hyperparameters are comparable in quality to those from the conventional model selection procedures, while being much faster to obtain, significantly accelerating GP regression and its related applications such as Bayesian optimization and Bayesian quadrature. The code and pre-trained model are available at https://github.com/PrincetonLIPS/AHGP.