** Accurately answering a question about a given image requires combining observations with general knowledge. While this is effortless for humans, reasoning with general knowledge remains an algorithmic challenge. To advance research in this direction a novel `fact-based' visual question answering (FVQA) task has been introduced recently along with a large set of curated facts which link two entities, i.e., two possible answers, via a relation. Given a question-image pair, deep network techniques have been employed to successively reduce the large set of facts until one of the two entities of the final remaining fact is predicted as the answer. We observe that a successive process which considers one fact at a time to form a local decision is sub-optimal. Instead, we develop an entity graph and use a graph convolutional network to `reason' about the correct answer by jointly considering all entities. We show on the challenging FVQA dataset that this leads to an improvement in accuracy of around 7% compared to the state of the art. **

** Predicting properties of nodes in a graph is an important problem with applications in a variety of domains. Graph-based Semi-Supervised Learning (SSL) methods aim to address this problem by labeling a small subset of the nodes as seeds and then utilizing the graph structure to predict label scores for the rest of the nodes in the graph. Recently, Graph Convolutional Networks (GCNs) have achieved impressive performance on the graph-based SSL task. In addition to label scores, it is also desirable to have confidence scores associated with them. Unfortunately, confidence estimation in the context of GCN has not been previously explored. We fill this important gap in this paper and propose ConfGCN, which estimates labels scores along with their confidences jointly in GCN-based setting. ConfGCN uses these estimated confidences to determine the influence of one node on another during neighborhood aggregation, thereby acquiring anisotropic capabilities. Through extensive analysis and experiments on standard benchmarks, we find that ConfGCN is able to outperform state-of-the-art baselines. We have made ConfGCN's source code available to encourage reproducible research. **

Multi-GCN: Graph Convolutional Networks for Multi-View Networks, with Applications to Global Poverty

** With the rapid expansion of mobile phone networks in developing countries, large-scale graph machine learning has gained sudden relevance in the study of global poverty. Recent applications range from humanitarian response and poverty estimation to urban planning and epidemic containment. Yet the vast majority of computational tools and algorithms used in these applications do not account for the multi-view nature of social networks: people are related in myriad ways, but most graph learning models treat relations as binary. In this paper, we develop a graph-based convolutional network for learning on multi-view networks. We show that this method outperforms state-of-the-art semi-supervised learning algorithms on three different prediction tasks using mobile phone datasets from three different developing countries. We also show that, while designed specifically for use in poverty research, the algorithm also outperforms existing benchmarks on a broader set of learning tasks on multi-view networks, including node labelling in citation networks. **

** We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper bounds and lower bounds for this problem. For mixtures of axis-aligned Gaussians, we show that $\tilde{O}(k d / \varepsilon^2)$ samples suffice, matching a known lower bound. Moreover, these results hold in the agnostic-learning/robust-estimation setting as well, where the target distribution is only approximately a mixture of Gaussians. The upper bound is shown using a novel technique for distribution learning based on a notion of `compression.' Any class of distributions that allows such a compression scheme can also be learned with few samples. Moreover, if a class of distributions has such a compression scheme, then so do the classes of products and mixtures of those distributions. The core of our main result is showing that the class of Gaussians in $\mathbb{R}^d$ admits a small-sized compression scheme. **

** Thoracic diseases are very serious health problems that plague a large number of people. Chest X-ray is currently one of the most popular methods to diagnose thoracic diseases, playing an important role in the healthcare workflow. However, reading the chest X-ray images and giving an accurate diagnosis remain challenging tasks for expert radiologists. With the success of deep learning in computer vision, a growing number of deep neural network architectures were applied to chest X-ray image classification. However, most of the previous deep neural network classifiers were based on deterministic architectures which are usually very noise-sensitive and are likely to aggravate the overfitting issue. In this paper, to make a deep architecture more robust to noise and to reduce overfitting, we propose using deep generative classifiers to automatically diagnose thorax diseases from the chest X-ray images. Unlike the traditional deterministic classifier, a deep generative classifier has a distribution middle layer in the deep neural network. A sampling layer then draws a random sample from the distribution layer and input it to the following layer for classification. The classifier is generative because the class label is generated from samples of a related distribution. Through training the model with a certain amount of randomness, the deep generative classifiers are expected to be robust to noise and can reduce overfitting and then achieve good performances. We implemented our deep generative classifiers based on a number of well-known deterministic neural network architectures, and tested our models on the chest X-ray14 dataset. The results demonstrated the superiority of deep generative classifiers compared with the corresponding deep deterministic classifiers. **

** We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models. **