ICML 2018 Papers

We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are often required for identification. The new algorithm is particularly suitable for cases where the available sample size is large enough to accurately estimate second-order output probabilities, but not higher-order ones. We show that if one is only able to obtain a reliable estimate of the pairwise co-occurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences learning in DAEs. By focusing on linear DAEs, we are able to derive analytic expressions that exactly describe their learning dynamics. We verify our theoretical predictions with simulations as well as experiments on MNIST and CIFAR-10. The theory illustrates how, when tuned correctly, noise allows DAEs to ignore low variance directions in the inputs while learning to reconstruct them. Furthermore, in a comparison of the learning dynamics of DAEs to standard regularised autoencoders, we show that noise has a similar regularisation effect to weight decay, but with faster training dynamics. We also show that our theoretical predictions approximate learning dynamics on real-world data and qualitatively match observed dynamics in nonlinear DAEs.

In this paper we advocate for a hyperparametric approach to learn diffusion in the independent cascade (IC) model. The sample complexity of this model is a function of the number of edges in the network and consequently learning becomes infeasible when the network is large. We study a natural restriction of the hypothesis class using additional information available in order to dramatically reduce the sample complexity of the learning process. In particular we assume that diffusion probabilities can be described as a function of a global hyperparameter and features of the individuals in the network. One of the main challenges with this approach is that training a model reduces to optimizing a non-convex objective. Despite this obstacle, we can shrink the best-known sample complexity bound for learning IC by a factor of |E|/d where |E| is the number of edges in the graph and d is the dimension of the hyperparameter. We show that under mild assumptions about the distribution generating the samples one can provably train a model with low generalization error. Finally, we use large-scale diffusion data from Facebook to show that a hyperparametric model using approximately 20 features per node achieves remarkably high accuracy.

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We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is substantially more efficient than in the Poincar{é}-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincar{é} embeddings, especially in low dimensions. Lastly, we apply our model to discover hierarchies in two real-world datasets: we show that an embedding in hyperbolic space can reveal important aspects of a company’s organizational structure as well as reveal historical relationships between language families.

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow neural networks. Our framework is general and covers weight-sharing (convolutional networks), sparsity (network pruning), and low-rank constraints among others. We first introduce covering dimension to quantify the complexity of the constraint set and provide insights on the generalization properties. Then, we show that proposed algorithms become well-behaved and local linear convergence occurs once the amount of data exceeds the covering dimension. Overall, our results demonstrate that near-optimal sample complexity is sufficient for efficient learning and illustrate how regularization can be beneficial to learn over-parameterized networks.

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and third order moment tensor of the observed data. We prove that under mild non-degeneracy conditions, our method consistently estimates the model parameters at the optimal parametric rate. Our tensor-based method generalizes previous orthogonal tensor decomposition approaches, where the hidden units were assumed to be either statistically independent or mutually exclusive. We illustrate the consistency of our method on simulated data and demonstrate its usefulness in learning a common model for population mixtures in genetics.

In this paper, we advocate for representation learning as the key to mitigating unfair prediction outcomes downstream. Motivated by a scenario where learned representations are used by third parties with unknown objectives, we propose and explore adversarial representation learning as a natural method of ensuring those parties act fairly. We connect group fairness (demographic parity, equalized odds, and equal opportunity) to different adversarial objectives. Through worst-case theoretical guarantees and experimental validation, we show that the choice of this objective is crucial to fair prediction. Furthermore, we present the first in-depth experimental demonstration of fair transfer learning and demonstrate empirically that our learned representations admit fair predictions on new tasks while maintaining utility, an essential goal of fair representation learning.

Many structured prediction problems (particularly in vision and language domains) are ambiguous, with multiple outputs being ‘correct’ for an input {–} e.g. there are many ways of describing an image, multiple ways of translating a sentence; however, exhaustively annotating the applicability of all possible outputs is intractable due to exponentially large output spaces (e.g. all English sentences). In practice, these problems are cast as multi-class prediction, with the likelihood of only a sparse set of annotations being maximized {–} unfortunately penalizing for placing beliefs on plausible but unannotated outputs. We make and test the following hypothesis {–} for a given input, the annotations of its neighbors may serve as an additional supervisory signal. Specifically, we propose an objective that transfers supervision from neighboring examples. We first study the properties of our developed method in a controlled toy setup before reporting results on multi-label classification and two image-grounded sequence modeling tasks {–} captioning and question generation. We evaluate using standard task-specific metrics and measures of output diversity, finding consistent improvements over standard maximum likelihood training and other baselines.

We consider the problem of configuring general-purpose solvers to run efficiently on problem instances drawn from an unknown distribution. The goal of the configurator is to find a configuration that runs fast on average on most instances, and do so with the least amount of total work. It can run a chosen solver on a random instance until the solver finishes or a timeout is reached. We propose LeapsAndBounds, an algorithm that tests configurations on randomly selected problem instances for longer and longer time. We prove that the capped expected runtime of the configuration returned by LeapsAndBounds is close to the optimal expected runtime, while our algorithm’s running time is near-optimal. Our results show that LeapsAndBounds is more efficient than the recent algorithm of Kleinberg et al. (2017), which, to our knowledge, is the only other algorithm configuration method with non-trivial theoretical guarantees. Experimental results on configuring a public SAT solver on a new benchmark dataset also stand witness to the superiority of our method.

We address the problem of learning hierarchical deep neural network policies for reinforcement learning. In contrast to methods that explicitly restrict or cripple lower layers of a hierarchy to force them to use higher-level modulating signals, each layer in our framework is trained to directly solve the task, but acquires a range of diverse strategies via a maximum entropy reinforcement learning objective. Each layer is also augmented with latent random variables, which are sampled from a prior distribution during the training of that layer. The maximum entropy objective causes these latent variables to be incorporated into the layer’s policy, and the higher level layer can directly control the behavior of the lower layer through this latent space. Furthermore, by constraining the mapping from latent variables to actions to be invertible, higher layers retain full expressivity: neither the higher layers nor the lower layers are constrained in their behavior. Our experimental evaluation demonstrates that we can improve on the performance of single-layer policies on standard benchmark tasks simply by adding additional layers, and that our method can solve more complex sparse-reward tasks by learning higher-level policies on top of high-entropy skills optimized for simple low-level objectives.

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as “graphical lasso”, but its computational cost becomes prohibitive for large data sets. A recently line of results showed{–}under mild assumptions{–}that the graphical lasso estimator can be retrieved by soft-thresholding the sample covariance matrix and solving a maximum determinant matrix completion (MDMC) problem. This paper proves an extension of this result, and describes a Newton-CG algorithm to efficiently solve the MDMC problem. Assuming that the thresholded sample covariance matrix is sparse with a sparse Cholesky factorization, we prove that the algorithm converges to an $\epsilon$-accurate solution in $O(n\log(1/\epsilon))$ time and $O(n)$ memory. The algorithm is highly efficient in practice: we solve the associated MDMC problems with as many as 200,000 variables to 7-9 digits of accuracy in less than an hour on a standard laptop computer running MATLAB.

Gaussian process modulated Poisson processes provide a flexible framework for modeling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. In practice, we find that Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100 000 events with complex spatiotemporal patterns in three dimensions on a single GPU.

Most works on adversarial examples for deep-learning based image classifiers use noise that, while small, covers the entire image. We explore the case where the noise is allowed to be visible but confined to a small, localized patch of the image, without covering any of the main object(s) in the image. We show that it is possible to generate localized adversarial noises that cover only 2% of the pixels in the image, none of them over the main object, and that are transferable across images and locations, and successfully fool a state-of-the-art Inception v3 model with very high success rates.

Our work addresses two important issues with recurrent neural networks: (1) they are over-parametrized, and (2) the recurrent weight matrix is ill-conditioned. The former increases the sample complexity of learning and the training time. The latter causes the vanishing and exploding gradient problem. We present a flexible recurrent neural network model called Kronecker Recurrent Units (KRU). KRU achieves parameter efficiency in RNNs through a Kronecker factored recurrent matrix. It overcomes the ill-conditioning of the recurrent matrix by enforcing soft unitary constraints on the factors. Thanks to the small dimensionality of the factors, maintaining these constraints is computationally efficient. Our experimental results on seven standard data-sets reveal that KRU can reduce the number of parameters by three orders of magnitude in the recurrent weight matrix compared to the existing recurrent models, without trading the statistical performance. These results in particular show that while there are advantages in having a high dimensional recurrent space, the capacity of the recurrent part of the model can be dramatically reduced.

Classical distillation methods transfer representations from a “teacher” neural network to a “student” network by matching their output activations. Recent methods also match the Jacobians, or the gradient of output activations with the input. However, this involves making some ad hoc decisions, in particular, the choice of the loss function. In this paper, we first establish an equivalence between Jacobian matching and distillation with input noise, from which we derive appropriate loss functions for Jacobian matching. We then rely on this analysis to apply Jacobian matching to transfer learning by establishing equivalence of a recent transfer learning procedure to distillation. We then show experimentally on standard image datasets that Jacobian-based penalties improve distillation, robustness to noisy inputs, and transfer learning.

In this paper we introduce a novel neural network architecture, in which weight matrices are re-parametrized in terms of low-dimensional vectors, interacting through kernel functions. A layer of our network can be interpreted as introducing a (potentially infinitely wide) linear layer between input and output. We describe the theory underpinning this model and validate it with concrete examples, exploring how it can be used to impose structure on neural networks in diverse applications ranging from data visualization to recommender systems. We achieve state-of-the-art performance in a collaborative filtering task (MovieLens).

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.