Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data.

Statistical Machine Learning (SML) refers to a body of algorithms and methods by which computers are allowed to discover important features of input data sets which are often very large in size. The very task of feature discovery from data is essentially the meaning of the keyword `learning' in SML. Theoretical justifications for the effectiveness of the SML algorithms are underpinned by sound principles from different disciplines, such as Computer Science and Statistics. The theoretical underpinnings particularly justified by statistical inference methods are together termed as statistical learning theory. This paper provides a review of SML from a Bayesian decision theoretic point of view -- where we argue that many SML techniques are closely connected to making inference by using the so called Bayesian paradigm. We discuss many important SML techniques such as supervised and unsupervised learning, deep learning, online learning and Gaussian processes especially in the context of very large data sets where these are often employed. We present a dictionary which maps the key concepts of SML from Computer Science and Statistics. We illustrate the SML techniques with three moderately large data sets where we also discuss many practical implementation issues. Thus the review is especially targeted at statisticians and computer scientists who are aspiring to understand and apply SML for moderately large to big data sets.

Learning from positive and unlabeled data or PU learning is the setting where a learner only has access to positive examples and unlabeled data. The assumption is that the unlabeled data can contain both positive and negative examples. This setting has attracted increasing interest within the machine learning literature as this type of data naturally arises in applications such as medical diagnosis and knowledge base completion. This article provides a survey of the current state of the art in PU learning. It proposes seven key research questions that commonly arise in this field and provides a broad overview of how the field has tried to address them.

We propose a generic framework to calibrate accuracy and confidence (score) of a prediction through stochastic inferences in deep neural networks. We first analyze relation between variation of multiple model parameters for a single example inference and variance of the corresponding prediction scores by Bayesian modeling of stochastic regularization. Our empirical observation shows that accuracy and score of a prediction are highly correlated with variance of multiple stochastic inferences given by stochastic depth or dropout. Motivated by these facts, we design a novel variance-weighted confidence-integrated loss function that is composed of two cross-entropy loss terms with respect to ground-truth and uniform distribution, which are balanced by variance of stochastic prediction scores. The proposed loss function enables us to learn deep neural networks that predict confidence calibrated scores using a single inference. Our algorithm presents outstanding confidence calibration performance and improves classification accuracy with two popular stochastic regularization techniques---stochastic depth and dropout---in multiple models and datasets; it alleviates overconfidence issue in deep neural networks significantly by training networks to achieve prediction accuracy proportional to confidence of prediction.

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known score-and-search approach. However, selecting a single model (i.e., the best scoring BN) can be misleading or may not achieve the best possible accuracy. An alternative to committing to a single model is to perform some form of Bayesian or frequentist model averaging, where the space of possible BNs is sampled or enumerated in some fashion. Unfortunately, existing approaches for model averaging either severely restrict the structure of the Bayesian network or have only been shown to scale to networks with fewer than 30 random variables. In this paper, we propose a novel approach to model averaging inspired by performance guarantees in approximation algorithms. Our approach has two primary advantages. First, our approach only considers credible models in that they are optimal or near-optimal in score. Second, our approach is more efficient and scales to significantly larger Bayesian networks than existing approaches.

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.

The benefits of automating design cycles for Bayesian inference-based algorithms are becoming increasingly recognized by the machine learning community. As a result, interest in probabilistic programming frameworks has much increased over the past few years. This paper explores a specific probabilistic programming paradigm, namely message passing in Forney-style factor graphs (FFGs), in the context of automated design of efficient Bayesian signal processing algorithms. To this end, we developed "ForneyLab" (https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message passing-based inference in FFGs. We show by example how ForneyLab enables automatic derivation of Bayesian signal processing algorithms, including algorithms for parameter estimation and model comparison. Crucially, due to the modular makeup of the FFG framework, both the model specification and inference methods are readily extensible in ForneyLab. In order to test this framework, we compared variational message passing as implemented by ForneyLab with automatic differentiation variational inference (ADVI) and Monte Carlo methods as implemented by state-of-the-art tools "Edward" and "Stan". In terms of performance, extensibility and stability issues, ForneyLab appears to enjoy an edge relative to its competitors for automated inference in state-space models.

We introduce a novel framework for the estimation of the posterior distribution of the weights of a neural network, based on a new probabilistic interpretation of adaptive subgradient algorithms such as AdaGrad and Adam. Having a confidence measure of the weights allows several shortcomings of neural networks to be addressed. In particular, the robustness of the network can be improved by performing weight pruning based on signal-to-noise ratios from the weight posterior distribution. Using the MNIST dataset, we demonstrate that the empirical performance of Badam, a particular instance of our framework based on Adam, is competitive in comparison to related Bayesian approaches such as Bayes By Backprop.

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multi-object posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.