Suppose that one particular block in a stochastic block model is deemed "interesting," but block labels are only observed for a few of the vertices. Utilizing a graph realized from the model, the vertex nomination task is to order the vertices with unobserved block labels into a "nomination list" with the goal of having an abundance of interesting vertices near the top of the list. In this paper we extend and enhance two basic vertex nomination schemes; the canonical nomination scheme ${\mathcal L}^C$ and the spectral partitioning nomination scheme ${\mathcal L}^P$. The canonical nomination scheme ${\mathcal L}^C$ is provably optimal, but is computationally intractable, being impractical to implement even on modestly sized graphs. With this in mind, we introduce a scalable, Markov chain Monte Carlo-based nomination scheme, called the {\it canonical sampling nomination scheme} ${\mathcal L}^{CS}$, that converges to the canonical nomination scheme ${\mathcal L}^{C}$ as the amount of sampling goes to infinity. We also introduce a novel spectral partitioning nomination scheme called the {\it extended spectral partitioning nomination scheme} ${\mathcal L}^{EP}$. Real-data and simulation experiments are employed to illustrate the effectiveness of these vertex nomination schemes, as well as their empirical computational complexity.

We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood estimation, we explore the associated risk bound. Further, we consider the superposition of Hawkes processes within the model, and demonstrate that under certain conditions such an operation is beneficial for tightening the risk bound. Accordingly, we propose a stochastic optimization algorithm assisted with a diversity-driven superposition strategy, achieving better learning results with improved convergence properties. The effectiveness of the proposed method is verified on synthetic data, and its potential to solve the cold-start problem of sequential recommendation systems is demonstrated on real-world data.

The Tweedie Compound Poisson-Gamma model is routinely used for modelling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping hierarchy in the data. An important application of Tweedie mixed models is estimating the aggregated loss for insurance policies. However, the intractable likelihood function, the unknown variance function, and the hierarchical structure of mixed effects have presented considerable challenges for drawing inferences on Tweedie. In this study, we tackle the Bayesian Tweedie mixed-effects models via variational approaches. In particular, we empower the posterior approximation by implicit models trained in an adversarial setting. To reduce the variance of gradients, we reparameterize random effects, and integrate out one local latent variable of Tweedie. We also employ a flexible hyper prior to ensure the richness of the approximation. Our method is evaluated on both simulated and real-world data. Results show that the proposed method has smaller estimation bias on the random effects compared to traditional inference methods including MCMC; it also achieves a state-of-the-art predictive performance, meanwhile offering a richer estimation of the variance function.

Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due to its $O(N^3)$ running time for the model selection. We propose Scalable Kernel Composition (SKC), a scalable kernel search algorithm that extends the Automatic Statistician to bigger data sets. In doing so, we derive a cheap upper bound on the GP marginal likelihood that sandwiches the marginal likelihood with the variational lower bound . We show that the upper bound is significantly tighter than the lower bound and thus useful for model selection.

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter manifold. Thus it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there is sufficient data to tightly constrain any number of parameters, this reduces to Jeffreys prior. But we argue that this limit is pathological when applied to the hyper-ribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

We propose extreme stochastic variational inference (ESVI), an asynchronous and lock-free algorithm to perform variational inference on massive real world datasets. Stochastic variational inference (SVI), the state-of-the-art algorithm for scaling variational inference to large-datasets, is inherently serial. Moreover, it requires the parameters to fit in the memory of a single processor; this is problematic when the number of parameters is in billions. ESVI overcomes these limitations by requiring that each processor only access a subset of the data and a subset of the parameters, thus providing data and model parallelism simultaneously. We demonstrate the effectiveness of ESVI by running Latent Dirichlet Allocation (LDA) on UMBC-3B, a dataset that has a vocabulary of 3 million and a token size of 3 billion. To best of our knowledge, this is an order of magnitude larger than the largest dataset on which results using variational inference have been reported in literature. In our experiments, we found that ESVI outperforms VI and SVI, and also achieves a better quality solution. In addition, we propose a strategy to speed up computation and save memory when fitting large number of topics.

Learning from expert demonstrations has received a lot of attention in artificial intelligence and machine learning. The goal is to infer the underlying reward function that an agent is optimizing given a set of observations of the agent's behavior over time in a variety of circumstances, the system state trajectories, and a plant model specifying the evolution of the system state for different agent's actions. The system is often modeled as a Markov decision process, that is, the next state depends only on the current state and agent's action, and the the agent's choice of action depends only on the current state. While the former is a Markovian assumption on the evolution of system state, the later assumes that the target reward function is itself Markovian. In this work, we explore learning a class of non-Markovian reward functions, known in the formal methods literature as specifications. These specifications offer better composition, transferability, and interpretability. We then show that inferring the specification can be done efficiently without unrolling the transition system. We demonstrate on a 2-d grid world example.

During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still escapes current cognitive and linguistic theories. Recently, spectacular progress in the engineering science, notably, machine learning and wearable technology, offer the promise of revolutionizing the study of cognitive development. Machine learning offers powerful learning algorithms that can achieve human-like performance on many linguistic tasks. Wearable sensors can capture vast amounts of data, which enable the reconstruction of the sensory experience of infants in their natural environment. The project of 'reverse engineering' language development, i.e., of building an effective system that mimics infant's achievements appears therefore to be within reach. Here, we analyze the conditions under which such a project can contribute to our scientific understanding of early language development. We argue that instead of defining a sub-problem or simplifying the data, computational models should address the full complexity of the learning situation, and take as input the raw sensory signals available to infants. This implies that (1) accessible but privacy-preserving repositories of home data be setup and widely shared, and (2) models be evaluated at different linguistic levels through a benchmark of psycholinguist tests that can be passed by machines and humans alike, (3) linguistically and psychologically plausible learning architectures be scaled up to real data using probabilistic/optimization principles from machine learning. We discuss the feasibility of this approach and present preliminary results.

Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and generative adversarial networks (GANs), are often developed independently. In this paper, we propose the concept of {\em continuous-time flows} (CTFs), a family of diffusion-based methods that are able to asymptotically approach a target distribution. Distinct from normalizing flows and GANs, CTFs can be adopted to achieve the above two goals in one framework, with theoretical guarantees. Our framework includes distilling knowledge from a CTF for efficient inference, and learning an explicit energy-based distribution with CTFs for density estimation. Both tasks rely on a new technique for distribution matching within amortized learning. Experiments on various tasks demonstrate promising performance of the proposed CTF framework, compared to related techniques.

Inverse classification uses an induced classifier as a queryable oracle to guide test instances towards a preferred posterior class label. The result produced from the process is a set of instance-specific feature perturbations, or recommendations, that optimally improve the probability of the class label. In this work, we adopt a causal approach to inverse classification, eliciting treatment policies (i.e., feature perturbations) for models induced with causal properties. In so doing, we solve a long-standing problem of eliciting multiple, continuously valued treatment policies, using an updated framework and corresponding set of assumptions, which we term the inverse classification potential outcomes framework (ICPOF), along with a new measure, referred to as the individual future estimated effects ($i$FEE). We also develop the approximate propensity score (APS), based on Gaussian processes, to weight treatments, much like the inverse propensity score weighting used in past works. We demonstrate the viability of our methods on student performance.