This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Applications include climate or crime measurements in a geographical area, or flow-cytometry experiments, where unsuitable recordings are discarded. A simple approach to modeling such data is through the use of mixture models, with each component following an appropriate truncated distribution. Problems arise when the truncation involves complicated constraints, leading to difficulties in specifying the component distributions, and in evaluating their normalization constants. Bayesian inference over the parameters of these models results in posterior distributions that are doubly-intractable. We address this problem via an algorithm based on rejection sampling and data augmentation. We view samples from a truncated distribution as outcomes of a rejection sampling scheme, where proposals are made from a simple mixture model, and are rejected if they violate the constraints. Our scheme proceeds by imputing the rejected samples given mixture parameters, and then resampling parameters given all samples. We study two modeling approaches: mixtures of truncated components and truncated mixtures of components. In both situations, we describe exact Markov chain Monte Carlo sampling algorithms, as well as approximations that bound the number of rejected samples, achieving computational efficiency and lower variance at the cost of asymptotic bias. Overall, our methodology only requires practitioners to provide an indicator function for the set of interest. We present results on simulated data and apply our algorithm to two problems, one involving flow-cytometry data, and the other, crime recorded in the city of Chicago.

The accurate measurement of security metrics is a critical research problem because an improper or inaccurate measurement process can ruin the usefulness of the metrics, no matter how well they are defined. This is a highly challenging problem particularly when the ground truth is unknown or noisy. In contrast to the well perceived importance of defining security metrics, the measurement of security metrics has been little understood in the literature. In this paper, we measure five malware detection metrics in the {\em absence} of ground truth, which is a realistic setting that imposes many technical challenges. The ultimate goal is to develop principled, automated methods for measuring these metrics at the maximum accuracy possible. The problem naturally calls for investigations into statistical estimators by casting the measurement problem as a {\em statistical estimation} problem. We propose statistical estimators for these five malware detection metrics. By investigating the statistical properties of these estimators, we are able to characterize when the estimators are accurate, and what adjustments can be made to improve them under what circumstances. We use synthetic data with known ground truth to validate these statistical estimators. Then, we employ these estimators to measure five metrics with respect to a large dataset collected from VirusTotal. We believe our study touches upon a vital problem that has not been paid due attention and will inspire many future investigations.

The topic or population polytope (Nguyen, 2015; Tang et al., 2014) is a fundamental geometric object that underlies the presence of latent topic variables in topic and admixture models (Blei et al., 2003; Pritchard et al., 2000). When data and the associated topics are indexed by time dimension, it is of interest to study the temporal dynamics of such latent geometric structures. In this paper, we will study the modeling and algorithms for learning the temporal dynamics of topic polytope that arises in the analysis of text corpora. The convex geometry of topic models provides the theoretical basis for posterior contraction analysis of latent topics (Nguyen, 2015; Tang et al., 2014). Furthermore, Yurochkin & Nguyen (2016); Yurochkin et al. (2017) exploited convex geometry to develop fast and quite accurate inference algorithms in a number of parametric and nonparametric settings.

Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex problems. While the Expectation-Maximization (EM) algorithm is the most popular approach for solving these non-convex problems, the behavior of this algorithm is not well understood. In this work, we focus on the case of mixture of Laplacian (or Gaussian) distribution. We start by analyzing a simple equally weighted mixture of two single dimensional Laplacian distributions and show that every local optimum of the population maximum likelihood estimation problem is globally optimal. Then, we prove that the EM algorithm converges to the ground truth parameters almost surely with random initialization. Our result extends the existing results for Gaussian distribution to Laplacian distribution. Then we numerically study the behavior of mixture models with more than two components. Motivated by our extensive numerical experiments, we propose a novel stochastic method for estimating the mean of components of a mixture model. Our numerical experiments show that our algorithm outperforms the Naive EM algorithm in almost all scenarios.

Developing automated methods to give advance warning of large gatherings of people, such as protests and social unrest events, are of interest to government agencies worldwide. With such events often being organised over online social media platforms, there exists the possibility to provide prior warning of large events solely through monitoring online data streams. Researchers have used open online data sources such as Twitter (Borge-Holthoefer et al., 2016; Agarwal and Sureka, 2016), Facebook, Tumblr (Xu et al., 2014), and Flickr (Alanyali et al., 2015) to characterise information propagation processes around protests, and have deployed machine learning methods on social media as well as blogs, news sources, and the dark web (Korkmaz et al., 2016) to predict civil unrest events. Twitter data in particular has been used broadly to monitor diverse largescale trends such as stock behaviour (Bollen et al., 2011), public opinion polling around 1 issues like climate change (Cody et al., 2015), and health characteristics (Alajajian et al., 2017). Recent studies have focussed on Twitter's role in particular in mobilisation and discourse around protest action in the United States (Theocharis et al., 2015; Gallagher et al., 2018).

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

Simulation plays an essential role in comprehending a target system in many fields of social and industrial sciences. A major task in simulation is the estimation of parameters, and optimal parameters to express the observed data need to directly elucidate the properties of the target system as the design of the simulator is based on the expert's domain knowledge. However, skilled human experts struggle to find the desired parameters.Data assimilation therefore becomes an unavoidable task in simulator design to reduce the cost of simulator optimization. Another necessary task is extrapolation; in many practical cases, the prediction based on simulation results will be often outside of the dominant range of the given data area, and this is referred to as the covariate shift. This paper focuses on the regression problem with the covariate shift. While the parameter estimation for the covariate shift has been studied thoroughly in parametric and nonparametric settings, conventional statistical methods of parameter searching are not applicable in the data assimilation of the simulation owing to the properties of the likelihood function: intractable or nondifferentiable. To address these problems, we propose a novel framework of Bayesian inference based on kernel mean embedding that comprises an extended kernel approximate Bayesian computation (ABC) of the importance weighted regression, kernel herding, and the kernel sum rule. This framework makes the prediction available in covariate shift situations, and its effectiveness is evaluated in both synthetic numerical experiments and a widely used production simulator.

Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy, establishes two orthogonal dimensions of question difficulty: obscurity (the rarity of the answer) and opacity (the indirectness of question cues, operationalized with word2vec). The importance of opacity, and the role of synergistic information in resolving it, suggests that accounts of difficulty in terms of prior expectations captures only a part of the question-asking process. A further regression analysis shows the presence of additional dimensions to question-asking: question complexity, the answer's local network density, cue intersection, and the presence of signal words. Our work shows how question-askers can help their interlocutors by using contextual cues, or, conversely, how a particular kind of unfamiliarity with the domain in question can make it harder for individuals to learn from others. Taken together, these results suggest how Bayesian models of question difficulty can be supplemented by process models and accounts of the heuristics individuals use to navigate conceptual spaces.

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called pseudo-marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.