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The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to carry out inference at controllable complexity using recursive computations over the factor graph representing the underlying distribution. An alternative model-agnostic approach utilizes machine learning (ML) methods. Here we propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. In the proposed approach, neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence, rather than the complete inference task. By exploiting stationary properties of this distribution, the resulting approach can be applied to sequences of varying temporal duration. Learned factor graph can be realized using compact neural networks that are trainable using small training sets, or alternatively, be used to improve upon existing deep inference systems. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data, and can be applied to sequences of different lengths. Our experimental results demonstrate the ability of the proposed learned factor graphs to learn to carry out accurate inference from small training sets for sleep stage detection using the Sleep-EDF dataset, as well as for symbol detection in digital communications with unknown channels.

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which can be very informative, especially in high-dimensional settings. To extract the information from the dependence structure for clustering, we propose a new latent variable model for the features arranged in matrix form, with some unknown membership matrices representing the clusters for the rows and columns. Under this model, we further propose a class of hierarchical clustering algorithms using the difference of a weighted covariance matrix as the dissimilarity measure. Theoretically, we show that under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. While this consistency result holds for our algorithm with a broad class of weighted covariance matrices, the conditions for this result depend on the choice of the weight. To investigate how the weight affects the theoretical performance of our algorithm, we establish the minimax lower bound for clustering under our latent variable model. Given these results, we identify the optimal weight in the sense that using this weight guarantees our algorithm to be minimax rate-optimal in terms of the magnitude of some cluster separation metric. The practical implementation of our algorithm with the optimal weight is also discussed. Finally, we conduct simulation studies to evaluate the finite sample performance of our algorithm and apply the method to a genomic dataset.

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This gives rise to a new definition of disentanglement, and to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.

There has recently been increasing interest in learning representations of temporal knowledge graphs (KGs), which record the dynamic relationships between entities over time. Temporal KGs often exhibit multiple simultaneous non-Euclidean structures, such as hierarchical and cyclic structures. However, existing embedding approaches for temporal KGs typically learn entity representations and their dynamic evolution in the Euclidean space, which might not capture such intrinsic structures very well. To this end, we propose Dy- ERNIE, a non-Euclidean embedding approach that learns evolving entity representations in a product of Riemannian manifolds, where the composed spaces are estimated from the sectional curvatures of underlying data. Product manifolds enable our approach to better reflect a wide variety of geometric structures on temporal KGs. Besides, to capture the evolutionary dynamics of temporal KGs, we let the entity representations evolve according to a velocity vector defined in the tangent space at each timestamp. We analyze in detail the contribution of geometric spaces to representation learning of temporal KGs and evaluate our model on temporal knowledge graph completion tasks. Extensive experiments on three real-world datasets demonstrate significantly improved performance, indicating that the dynamics of multi-relational graph data can be more properly modeled by the evolution of embeddings on Riemannian manifolds.

Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed D-VAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.

We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction.

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent work has shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al.~\cite{AroraGeLiMaZh17} suggests a dilemma about GANs' statistical properties: powerful discriminators cause overfitting, whereas weak discriminators cannot detect mode collapse. In contrast, we show in this paper that GANs can in principle learn distributions in Wasserstein distance (or KL-divergence in many cases) with polynomial sample complexity, if the discriminator class has strong distinguishing power against the particular generator class (instead of against all possible generators). For various generator classes such as mixture of Gaussians, exponential families, and invertible neural networks generators, we design corresponding discriminators (which are often neural nets of specific architectures) such that the Integral Probability Metric (IPM) induced by the discriminators can provably approximate the Wasserstein distance and/or KL-divergence. This implies that if the training is successful, then the learned distribution is close to the true distribution in Wasserstein distance or KL divergence, and thus cannot drop modes. Our preliminary experiments show that on synthetic datasets the test IPM is well correlated with KL divergence, indicating that the lack of diversity may be caused by the sub-optimality in optimization instead of statistical inefficiency.

Knowledge graphs contain rich relational structures of the world, and thus complement data-driven machine learning in heterogeneous data. One of the most effective methods in representing knowledge graphs is to embed symbolic relations and entities into continuous spaces, where relations are approximately linear translation between projected images of entities in the relation space. However, state-of-the-art relation projection methods such as TransR, TransD or TransSparse do not model the correlation between relations, and thus are not scalable to complex knowledge graphs with thousands of relations, both in computational demand and in statistical robustness. To this end we introduce TransF, a novel translation-based method which mitigates the burden of relation projection by explicitly modeling the basis subspaces of projection matrices. As a result, TransF is far more light weight than the existing projection methods, and is robust when facing a high number of relations. Experimental results on the canonical link prediction task show that our proposed model outperforms competing rivals by a large margin and achieves state-of-the-art performance. Especially, TransF improves by 9%/5% in the head/tail entity prediction task for N-to-1/1-to-N relations over the best performing translation-based method.

We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP layers to learn abstract representations of the state feature space, which is linked to the demonstrations through the Maximum Entropy learning framework. Incorporating the IRL engine into the nonlinear latent structure renders existing deep GP inference approaches intractable. To tackle this, we develop a non-standard variational approximation framework which extends previous inference schemes. This allows for approximate Bayesian treatment of the feature space and guards against overfitting. Carrying out representation and inverse reinforcement learning simultaneously within our model outperforms state-of-the-art approaches, as we demonstrate with experiments on standard benchmarks ("object world","highway driving") and a new benchmark ("binary world").