Learning from multiple sources of information is an important problem in machine-learning research. The key challenges are learning representations and formulating inference methods that take into account the complementarity and redundancy of various information sources. In this paper we formulate a variational autoencoder based multi-source learning framework in which each encoder is conditioned on a different information source. This allows us to relate the sources via the shared latent variables by computing divergence measures between individual source's posterior approximations. We explore a variety of options to learn these encoders and to integrate the beliefs they compute into a consistent posterior approximation. We visualise learned beliefs on a toy dataset and evaluate our methods for learning shared representations and structured output prediction, showing trade-offs of learning separate encoders for each information source. Furthermore, we demonstrate how conflict detection and redundancy can increase robustness of inference in a multi-source setting.

Accurate and real-time traffic forecasting plays an important role in the Intelligent Traffic System (ITS), it is of great significance for urban traffic planning, traffic management, and traffic control. However, traffic forecasting has always been a concerned open scientific issue, owing to the constraint of urban road network topological structure and the law of dynamic change with time, namely spatial dependence and temporal dependence. In order to capture the spatial and temporal dependence simultaneously, we propose a novel neural network-based traffic forecasting method, temporal graph convolutional network (T-GCN) model, which is in combination with the graph convolutional network (GCN) and gated recurrent unit (GRU). Specifically, the graph convolutional network is used to learn the complex topological structure to capture the spatial dependence and the gated recurrent unit is used to learn the dynamic change of traffic flow to capture the temporal dependence. And then, the T-GCN model is employed to realize the traffic forecasting task based on urban road network. Experiments demonstrate that our T-GCN model can obtain the spatio temporal correlation from traffic data and the prediction effects outperform state-of-art baselines on real-world traffic datasets.

Most of the datasets normally contain either numeric or categorical features. Mixed data comprises of both numeric and categorical features, and they frequently occur in various domains, such as health, finance, marketing, etc. Clustering is often sought on mixed data to find structures and to group similar objects. However, clustering mixed data is challenging because it is difficult to directly apply mathematical operations, such as summation, average etc. on the feature values of these datasets. In this paper, we review various types of mixed data clustering techniques in detail. We present a taxonomy to identify ten types of different mixed data clustering techniques. We also compare the performance of several mixed data clustering methods on publicly available datasets. The paper further identifies challenges in developing different mixed data clustering algorithms and provides guidelines for future directions in this area.

Understanding procedural text requires tracking entities, actions and effects as the narrative unfolds (often implicitly). We focus on the challenging real-world problem of structured narrative extraction in the materials science domain, where language is highly specialized and suitable annotated data is not publicly available. We propose an approach, Text2Quest, where procedural text is interpreted as instructions for an interactive game. A reinforcement-learning agent completes the game by understanding and executing the procedure correctly, in a text-based simulated lab environment. The framework is intended to be more broadly applicable to other domain-specific and data-scarce settings. We conclude with a discussion of challenges and interesting potential extensions enabled by the agent-based perspective.

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal set of weights but also the ability to quantify uncertainty in decision making using the posterior distribution. Markov chain Monte Carlo (MCMC) techniques are typically used to obtain sample-based estimates of the posterior distribution. However, these techniques face challenges in convergence and scalability, particularly in settings with large datasets and network architectures. This paper address these challenges in two ways. First, parallel tempering is used used to explore multiple modes of the posterior distribution and implemented in multi-core computing architecture. Second, we make within-chain sampling schemes more efficient by using Langevin gradient information in forming Metropolis-Hastings proposal distributions. We demonstrate the techniques using time series prediction and pattern classification applications. The results show that the method not only improves the computational time, but provides better prediction or decision making capabilities when compared to related methods.

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial inference procedure for training them on data, while constraining their predictions to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep generative models as surrogates of physical systems in which the cost of data acquisition is high, and training data-sets are typically small. This provides a flexible framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations that entirely bypasses the need for repeatedly sampling expensive experiments or numerical simulators. We demonstrate the effectiveness of our approach through a series of examples involving uncertainty propagation in non-linear conservation laws, and the discovery of constitutive laws for flow through porous media directly from noisy data.

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models. In this paper, we propose \emph{block belief propagation learning} (BBPL), which uses block-coordinate updates of approximate marginals to compute approximate gradients, removing the need to compute inference on the entire graphical model. Thus, the iteration complexity of BBPL does not scale with the size of the graphs. We prove that the method converges to the same solution as that obtained by using full inference per iteration, despite these approximations, and we empirically demonstrate its scalability improvements over standard training methods.

The notion of \emph{policy regret} in online learning is a well defined? performance measure for the common scenario of adaptive adversaries, which more traditional quantities such as external regret do not take into account. We revisit the notion of policy regret and first show that there are online learning settings in which policy regret and external regret are incompatible: any sequence of play that achieves a favorable regret with respect to one definition must do poorly with respect to the other. We then focus on the game-theoretic setting where the adversary is a self-interested agent. In that setting, we show that external regret and policy regret are not in conflict and, in fact, that a wide class of algorithms can ensure a favorable regret with respect to both definitions, so long as the adversary is also using such an algorithm. We also show that the sequence of play of no-policy regret algorithms converges to a \emph{policy equilibrium}, a new notion of equilibrium that we introduce. Relating this back to external regret, we show that coarse correlated equilibria, which no-external regret players converge to, are a strict subset of policy equilibria. Thus, in game-theoretic settings, every sequence of play with no external regret also admits no policy regret, but the converse does not hold.

A colored graph is a directed graph in which either nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs are concerned with whether an agent observing the colors of edges or nodes traversed on a path in the graph can determine which node they are at currently or which nodes they have visited earlier in the path traversal. Previous research efforts have identified several different notions of observability as well as the associated properties of colored graphs for which those types of observability properties hold. This paper unifies the prior work into a common framework with several new analytic results about relationships between those notions and associated graph properties. The new framework provides an intuitive way to reason about the attainable path reconstruction accuracy as a function of lag and time spent observing, and identifies simple modifications that improve the observability properties of a given graph. This intuition is borne out in a series of numerical experiments. This work has implications for problems that can be described in terms of an agent traversing a colored graph, including the reconstruction of hidden states in a hidden Markov model (HMM).

Abstract--Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPNs (tSPNs). For the first time, through mapping an SPN onto a tSPN and employing novel optimization techniques, we demonstrate remarkable parameter compression with negligible loss in accuracy. INCE the inception of sum-product networks (SPNs) [1], a multitude of works have emerged with respect to their structure and weight learning, e.g., [2], [3], [4], as well as their application in image completion, speech modeling, semantic mapping and robotics, e.g., [5], just to name a few. An SPN exhibits a clear semantics of mixtures (sum nodes) and features (product nodes). Compared to other probabilistic graphical models like Bayesian and Markov networks with #P or NPhard computation, an SPN enjoys a tractable exact inference cost, and its learning is relatively simple and fast. On the other hand, there has been an exploding number of works on tensors (a multilinear operator rooted in physics) [6] including their connection and utilization in various engineering fields such as signal processing [7], and lately also in neural networks and machine learning [8], [9], [10].