We introduce Graph-Structured Sum-Product Networks (GraphSPNs), a probabilistic approach to structured prediction for problems where dependencies between latent variables are expressed in terms of arbitrary, dynamic graphs. While many approaches to structured prediction place strict constraints on the interactions between inferred variables, many real-world problems can be only characterized using complex graph structures of varying size, often contaminated with noise when obtained from real data. Here, we focus on one such problem in the domain of robotics. We demonstrate how GraphSPNs can be used to bolster inference about semantic, conceptual place descriptions using noisy topological relations discovered by a robot exploring large-scale office spaces. Through experiments, we show that GraphSPNs consistently outperform the traditional approach based on undirected graphical models, successfully disambiguating information in global semantic maps built from uncertain, noisy local evidence. We further exploit the probabilistic nature of the model to infer marginal distributions over semantic descriptions of as yet unexplored places and detect spatial environment configurations that are novel and incongruent with the known evidence.

We present a probabilistic model for learning from dynamic relational data, wherein the observed interactions among networked nodes are modeled via the Bernoulli Poisson link function, and the underlying network structure are characterized by nonnegative latent node-group memberships, which are assumed to be gamma distributed. The latent memberships evolve according to Markov processes.The optimal number of latent groups can be determined by data itself. The computational complexity of our method scales with the number of non-zero links, which makes it scalable to large sparse dynamic relational data. We present batch and online Gibbs sampling algorithms to perform model inference. Finally, we demonstrate the model's performance on both synthetic and real-world datasets compared to state-of-the-art methods.

Recently, crowdsourcing has emerged as an effective paradigm for human-powered large scale problem solving in various domains. However, task requester usually has a limited amount of budget, thus it is desirable to have a policy to wisely allocate the budget to achieve better quality. In this paper, we study the principle of information maximization for active sampling strategies in the framework of HodgeRank, an approach based on Hodge Decomposition of pairwise ranking data with multiple workers. The principle exhibits two scenarios of active sampling: Fisher information maximization that leads to unsupervised sampling based on a sequential maximization of graph algebraic connectivity without considering labels; and Bayesian information maximization that selects samples with the largest information gain from prior to posterior, which gives a supervised sampling involving the labels collected. Experiments show that the proposed methods boost the sampling efficiency as compared to traditional sampling schemes and are thus valuable to practical crowdsourcing experiments.

This paper proposes a cooperative learning algorithm to train both the undirected energy-based model and the directed latent variable model jointly. The learning algorithm interweaves the maximum likelihood algorithms for learning the two models, and each iteration consists of the following two steps: (1) Modified contrastive divergence for energy-based model: The learning of the energy-based model is based on the contrastive divergence, but the finite-step MCMC sampling of the model is initialized from the synthesized examples generated by the latent variable model instead of being initialized from the observed examples. (2) MCMC teaching of the latent variable model: The learning of the latent variable model is based on how the MCMC in (1) changes the initial synthesized examples generated by the latent variable model, where the latent variables that generate the initial synthesized examples are known so that the learning is essentially supervised. Our experiments show that the cooperative learning algorithm can learn realistic models of images.

Bayesian optimization (BayesOpt) is a derivative-free approach for sequentially optimizing stochastic black-box functions. Standard BayesOpt, which has shown many successes in machine learning applications, assumes a finite dimensional domain which often is a parametric space. The parameter space is defined by the features used in the function approximations which are often selected manually. Therefore, the performance of BayesOpt inevitably depends on the quality of chosen features. This paper proposes a new Bayesian optimization framework that is able to optimize directly on the domain of function spaces. The resulting framework, Bayesian Functional Optimization (BFO), not only extends the application domains of BayesOpt to functional optimization problems but also relaxes the performance dependency on the chosen parameter space. We model the domain of functions as a reproducing kernel Hilbert space (RKHS), and use the notion of Gaussian processes on a real separable Hilbert space. As a result, we are able to define traditional improvement-based (PI and EI) and optimistic acquisition functions (UCB) as functionals. We propose to optimize the acquisition functionals using analytic functional gradients that are also proved to be functions in a RKHS. We evaluate BFO in three typical functional optimization tasks: i) a synthetic functional optimization problem, ii) optimizing activation functions for a multi-layer perceptron neural network, and iii) a reinforcement learning task whose policies are modeled in RKHS.

Many real-world reinforcement learning problems have a hierarchical nature, and often exhibit some degree of partial observability. While hierarchy and partial observability are usually tackled separately (for instance by combining recurrent neural networks and options), we show that addressing both problems simultaneously is simpler and more efficient in many cases. More specifically, we make the initiation set of options conditional on the previously-executed option, and show that options with such Option-Observation Initiation Sets (OOIs) are at least as expressive as Finite State Controllers (FSCs), a state-of-the-art approach for learning in POMDPs. OOIs are easy to design based on an intuitive description of the task, lead to explainable policies and keep the top-level and option policies memoryless. Our experiments show that OOIs allow agents to learn optimal policies in challenging POMDPs, while being much more sample-efficient than a recurrent neural network over options.

While all kinds of mixed data---from personal data, over panel and scientific data, to public and commercial data---are collected and stored, building probabilistic graphical models for these hybrid domains becomes more difficult. Users spend significant amounts of time in identifying the parametric form of the random variables (Gaussian, Poisson, Logit, etc.) involved and learning the mixed models. To make this difficult task easier, we propose the first trainable probabilistic deep architecture for hybrid domains that features tractable queries. It is based on Sum-Product Networks (SPNs) with piecewise polynomial leaf distributions together with novel nonparametric decomposition and conditioning steps using the Hirschfeld-Gebelein-Renyi Maximum Correlation Coefficient. This relieves the user from deciding a-priori the parametric form of the random variables but is still expressive enough to effectively approximate any distribution and permits efficient learning and inference.Our experiments show that the architecture, called Mixed SPNs, can indeed capture complex distributions across a wide range of hybrid domains.

Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets---compressed data sets which can be used as proxy for the original data and have provably bounded worst case error---for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data.To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

Temporal point processes are a statistical framework for modelling the times at which events of interest occur. The Hawkes process is a well-studied instance of this framework that captures self-exciting behaviour, wherein the occurrence of one event increases the likelihood of future events. Such processes have been successfully applied to model phenomena ranging from earthquakes to behaviour in a social network. We propose a framework to design new loss functions to train linear and nonlinear Hawkes processes. This captures standard maximum likelihood as a special case, but allows for other losses that guarantee convex objective functions (for certain types of kernel), and admit simpler optimisation. We illustrate these points with three concrete examples: for linear Hawkes processes, we provide a least-squares style loss potentially admitting closed-form optimisation; for exponential Hawkes processes, we reduce training to a weighted logistic regression; and for sigmoidal Hawkes processes, we propose an asymmetric form of logistic regression.

Variations of human body skeletons may be considered as dynamic graphs, which are generic data representation for numerous real-world applications. In this paper, we propose a spatio-temporal graph convolution (STGC) approach for assembling the successes of local convolutional filtering and sequence learning ability of autoregressive moving average. To encode dynamic graphs, the constructed multi-scale local graph convolution filters, consisting of matrices of local receptive fields and signal mappings, are recursively performed on structured graph data of temporal and spatial domain. The proposed model is generic and principled as it can be generalized into other dynamic models. We theoretically prove the stability of STGC and provide an upper-bound of the signal transformation to be learnt. Further, the proposed recursive model can be stacked into a multi-layer architecture. To evaluate our model, we conduct extensive experiments on four benchmark skeleton-based action datasets, including the large-scale challenging NTU RGB+D. The experimental results demonstrate the effectiveness of our proposed model and the improvement over the state-of-the-art.