Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution with polynomial time and sample complexity.

Meta-Learning is a subarea of Machine Learning that aims to take advantage of prior knowledge to learn faster and with fewer data [1]. There are different scenarios where meta-learning can be applied, and one of the most common is algorithm recommendation, where previous experience on applying machine learning algorithms for several datasets can be used to learn which algorithm, from a set of options, would be more suitable for a new dataset [2]. Perhaps the most popular form of meta-learning is transfer learning, which consists of transferring knowledge acquired by a machine learning algorithm in a previous learning task to increase its performance faster in another and similar task [3]. Transfer Learning has been widely applied in a variety of complex tasks such as image classification, machine translation and, speech recognition, achieving remarkable results [4,5,6,7,8]. Although transfer learning is very used in traditional or base-learning, it is still unknown if it is useful in a meta-learning setup. For that purpose, in this paper, we investigate the effects of transferring knowledge in the meta-level instead of base-level. Thus, we train a neural network on meta-datasets related to algorithm recommendation, and then using transfer learning, we reuse the knowledge learned by the neural network in other similar datasets from the same domain, to verify how transferable is the acquired meta-knowledge.

Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training a deep network configuration may fail with an out-of-memory error when the model is too large. In this work, we focus on a general formulation of Gaussian process-based BO with continuous or binary constraints. We propose constrained Max-value Entropy Search (cMES), a novel information theoretic-based acquisition function implementing this formulation. We also revisit the validity of the factorized approximation adopted for rapid computation of the MES acquisition function, showing empirically that this leads to inaccurate results. On an extensive set of real-world constrained hyperparameter optimization problems we show that cMES compares favourably to prior work, while being simpler to implement and faster than other constrained extensions of Entropy Search.

Contextual bandits serve as a fundamental model for many sequential decision making tasks. The most popular theoretically justified approaches are based on the optimism principle. While these algorithms can be practical, they are known to be suboptimal asymptotically (Lattimore and Szepesvari, 2017). On the other hand, existing asymptotically optimal algorithms for this problem do not exploit the linear structure in an optimal way and suffer from lower-order terms that dominate the regret in all practically interesting regimes. We start to bridge the gap by designing an algorithm that is asymptotically optimal and has good finite-time empirical performance. At the same time, we make connections to the recent literature on when exploration-free methods are effective. Indeed, if the distribution of contexts is well behaved, then our algorithm acts mostly greedily and enjoys sub-logarithmic regret. Furthermore, our approach is adaptive in the sense that it automatically detects the nice case. Numerical results demonstrate significant regret reductions by our method relative to several baselines.

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems. The cornerstone of the proposed method is the maximum volume algorithm. We demonstrate efficiency on VGG and ResNet architectures pre-trained on different datasets. We show that in many practical cases it is possible to replace convolutional layers with much smaller fully-connected layers with a relatively small drop in accuracy.

We begin by congratulating Yixin Wang and David Blei for their thought-provoking article that opens up a new research frontier in the field of causal inference. The authors directly tackle the challenging question of how to infer causal effects of many treatments in the presence of unmeasured confounding. We expect their article to have a major impact by further advancing our understanding of this important methodological problem. This commentary has two goals. We then briefly consider three possible ways to address some of the limitations of the deconfounder method. We first discuss several advantages offered by the deconfounder method. We then examine the assumptions required by the method and discuss its limitations.

This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof scheme provides another perspective on how the NTK regime arises from rescaling: redundancy in the weights due to resampling allows individual weights to be scaled down. Regarding the second contribution, the most notable transport mapping asserts that roughly $1 / \delta^{10d}$ nodes are sufficient to approximate continuous functions, where $\delta$ depends on the continuity properties of the target function. By contrast, nearly the same proof yields a bound of $1 / \delta^{2d}$ for shallow ReLU networks; this gap suggests a tantalizing direction for future work, separating shallow ReLU networks and their linearization.

Recurrent neural networks (RNNs) were designed for dealing with time-series data and have recently been used for creating predictive models from functional magnetic resonance imaging (fMRI) data. However, gathering large fMRI datasets for learning is a difficult task. Furthermore, network interpretability is unclear. To address these issues, we utilize multitask learning and design a novel RNN-based model that learns to discriminate between classes while simultaneously learning to generate the fMRI time-series data. Employing the long short-term memory (LSTM) structure, we develop a discriminative model based on the hidden state and a generative model based on the cell state. The addition of the generative model constrains the network to learn functional communities represented by the LSTM nodes that are both consistent with the data generation as well as useful for the classification task. We apply our approach to the classification of subjects with autism vs. healthy controls using several datasets from the Autism Brain Imaging Data Exchange. Experiments show that our jointly discriminative and generative model improves classification learning while also producing robust and meaningful functional communities for better model understanding.

This paper presents a phenomenon in neural networks that we refer to as \textit{local elasticity}. Roughly speaking, a classifier is said to be locally elastic if its prediction at a feature vector $\bx'$ is \textit{not} significantly perturbed, after the classifier is updated via stochastic gradient descent at a (labeled) feature vector $\bx$ that is \textit{dissimilar} to $\bx'$ in a certain sense. This phenomenon is shown to persist for neural networks with nonlinear activation functions through extensive simulations on real-life and synthetic datasets, whereas this is not observed in linear classifiers. In addition, we offer a geometric interpretation of local elasticity using the neural tangent kernel \citep{jacot2018neural}. Building on top of local elasticity, we obtain pairwise similarity measures between feature vectors, which can be used for clustering in conjunction with $K$-means. The effectiveness of the clustering algorithm on the MNIST and CIFAR-10 datasets in turn corroborates the hypothesis of local elasticity of neural networks on real-life data. Finally, we discuss some implications of local elasticity to shed light on several intriguing aspects of deep neural networks.

Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize highly predictive localized effects in favour of weakly predictive global patterns. This is a problem because localized effects are critical to developing individualized policies and treatment plans in applications ranging from precision medicine to advertising. To address this challenge, we propose to estimate sample-specific models that tailor inference and prediction at the individual level. In contrast to classical ML models that estimate a single, complex model (or only a few complex models), our approach produces a model personalized to each sample. These sample-specific models can be studied to understand subgroup dynamics that go beyond coarse-grained class labels. Crucially, our approach does not assume that relationships between samples (e.g. a similarity network) are known a priori. Instead, we use unmodeled covariates to learn a latent distance metric over the samples. We apply this approach to financial, biomedical, and electoral data as well as simulated data and show that sample-specific models provide fine-grained interpretations of complicated phenomena without sacrificing predictive accuracy compared to state-of-the-art models such as deep neural networks.