We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called ``adversarial losses'', which, besides classical L^p losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Multimodal sentiment analysis is a core research area that studies speaker sentiment expressed from the language, visual, and acoustic modalities. The central challenge in multimodal learning involves inferring joint representations that can process and relate information from these modalities. However, existing work learns joint representations by requiring all modalities as input and as a result, the learned representations may be sensitive to noisy or missing modalities at test time. With the recent success of sequence to sequence (Seq2Seq) models in machine translation, there is an opportunity to explore new ways of learning joint representations that may not require all input modalities at test time. In this paper, we propose a method to learn robust joint representations by translating between modalities. Our method is based on the key insight that translation from a source to a target modality provides a method of learning joint representations using only the source modality as input. We augment modality translations with a cycle consistency loss to ensure that our joint representations retain maximal information from all modalities. Once our translation model is trained with paired multimodal data, we only need data from the source modality at test time for final sentiment prediction. This ensures that our model remains robust from perturbations or missing information in the other modalities. We train our model with a coupled translation-prediction objective and it achieves new state-of-the-art results on multimodal sentiment analysis datasets: CMU-MOSI, ICT-MMMO, and YouTube. Additional experiments show that our model learns increasingly discriminative joint representations with more input modalities while maintaining robustness to missing or perturbed modalities.

Our team of artists and machine learning researchers designed a creative algorithm that can generate authentic sculptural artworks. These artworks do not mimic any given forms and cannot be easily categorized into the dataset categories. Our approach extends DeepDream from images to 3D point clouds. The proposed algorithm, Amalgamated DeepDream (ADD), leverages the properties of point clouds to create objects with better quality than the naive extension. ADD presents promise for the creativity of machines, the kind of creativity that pushes artists to explore novel methods or materials and to create new genres instead of creating variations of existing forms or styles within one genre. For example, from Realism to Abstract Expressionism, or to Minimalism. Lastly, we present the sculptures that are 3D printed based on the point clouds created by ADD.

Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show a straightforward extension of existing GAN algorithm is not applicable to point clouds, because the constraint required for discriminators is undefined for set data. We propose a two fold modification to GAN algorithm for learning to generate point clouds (PC-GAN). First, we combine ideas from hierarchical Bayesian modeling and implicit generative models by learning a hierarchical and interpretable sampling process. A key component of our method is that we train a posterior inference network for the hidden variables. Second, instead of using only state-of-the-art Wasserstein GAN objective, we propose a sandwiching objective, which results in a tighter Wasserstein distance estimate than the commonly used dual form. Thereby, PC-GAN defines a generic framework that can incorporate many existing GAN algorithms. We validate our claims on ModelNet40 benchmark dataset. Using the distance between generated point clouds and true meshes as metric, we find that PC-GAN trained by the sandwiching objective achieves better results on test data than the existing methods. Moreover, as a byproduct, PC- GAN learns versatile latent representations of point clouds, which can achieve competitive performance with other unsupervised learning algorithms on object recognition task. Lastly, we also provide studies on generating unseen classes of objects and transforming image to point cloud, which demonstrates the compelling generalization capability and potentials of PC-GAN.

One of the mystery in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies this surprising phenomenon for two-layer fully connected ReLU activated neural networks. For an $m$ hidden node shallow neural network with ReLU activation and $n$ training data, we show as long as $m$ is large enough and the data is non-degenerate, randomly initialized gradient descent converges a globally optimal solution with a linear convergence rate for the quadratic loss function. Our analysis is based on the following observation: over-parameterization and random initialization jointly restrict every weight vector to be close to its initialization for all iterations, which allows us to exploit a strong convexity-like property to show that gradient descent converges at a global linear rate to the global optimum. We believe these insights are also useful in analyzing deep models and other first order methods.

Multimodal machine learning is a core research area spanning the language, visual and acoustic modalities. The central challenge in multimodal learning involves learning representations that can process and relate information from multiple modalities. In this paper, we propose two methods for unsupervised learning of joint multimodal representations using sequence to sequence (Seq2Seq) methods: a \textit{Seq2Seq Modality Translation Model} and a \textit{Hierarchical Seq2Seq Modality Translation Model}. We also explore multiple different variations on the multimodal inputs and outputs of these seq2seq models. Our experiments on multimodal sentiment analysis using the CMU-MOSI dataset indicate that our methods learn informative multimodal representations that outperform the baselines and achieve improved performance on multimodal sentiment analysis, specifically in the Bimodal case where our model is able to improve F1 Score by twelve points. We also discuss future directions for multimodal Seq2Seq methods.

We design a new myopic strategy for a wide class of sequential design of experiment (DOE) problems, where the goal is to collect data in order to to fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling (MPS), is inspired by the classical posterior (Thompson) sampling algorithm for multi-armed bandits and leverages the flexibility of probabilistic programming and approximate Bayesian inference to address a broad set of problems. Empirically, this general-purpose strategy is competitive with more specialised methods in a wide array of DOE tasks, and more importantly, enables addressing complex DOE goals where no existing method seems applicable. On the theoretical side, we leverage ideas from adaptive submodularity and reinforcement learning to derive conditions under which MPS achieves sublinear regret against natural benchmark policies.

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers --- between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We provide a general analysis of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network \emph{architectures}. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a $N \times N$ Gram matrix of pairwise kernel evaluations to work with a dataset of $N$ instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets, and makes kernel learning especially difficult. In this paper we introduce Bayesian nonparmetric kernel-learning (BaNK), a generic, data-driven framework for scalable learning of kernels. BaNK places a nonparametric prior on the spectral distribution of random frequencies allowing it to both learn kernels and scale to large datasets. We show that this framework can be used for large scale regression and classification tasks. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.