The threat status and criminal collaborations of potential terrorists are hidden but give rise to observable behaviours and communications. Terrorists, when acting in concert, need to communicate to organise their plots. The authorities utilise such observable behaviour and communication data to inform their investigations and policing. We present a dynamic latent network model that integrates real-time communications data with prior knowledge on individuals. This model estimates and predicts the latent strength of criminal collaboration between individuals to assist in the identification of potential cells and the measurement of their threat levels. We demonstrate how, by assuming certain plausible conditional independences across the measurements associated with this population, the network model can be combined with models of individual suspects to provide fast transparent algorithms to predict group attacks. The methods are illustrated using a simulated example involving the threat posed by a cell suspected of plotting an attack.

Determinantal point processes (DPPs) have become a significant tool for recommendation systems, feature selection, or summary extraction, harnessing the intrinsic ability of these probabilistic models to facilitate sample diversity. The ability to sample from DPPs is paramount to the empirical investigation of these models. Most exact samplers are variants of a spectral meta-algorithm due to Hough, Krishnapur, Peres and Vir\'ag (henceforth HKPV), which is in general time and resource intensive. For DPPs with symmetric kernels, scalable HKPV samplers have been proposed that either first downsample the ground set of items, or force the kernel to be low-rank, using e.g. Nystr\"om-type decompositions. In the present work, we contribute a radically different approach than HKPV. Exploiting the fact that many statistical and learning objectives can be effectively accomplished by only sampling certain key observables of a DPP (so-called linear statistics), we invoke an expression for the Laplace transform of such an observable as a single determinant, which holds in complete generality. Combining traditional low-rank approximation techniques with Laplace inversion algorithms from numerical analysis, we show how to directly approximate the distribution function of a linear statistic of a DPP. This distribution function can then be used in hypothesis testing or to actually sample the linear statistic, as per requirement. Our approach is scalable and applies to very general DPPs, beyond traditional symmetric kernels.

We propose a new model of Bayesian Neural Networks to not only detect the events of compact binary coalescence in the observational data of gravitational waves (GW) but also identify the time periods of the associated GW waveforms before the events. This is achieved by incorporating the Bayesian approach into the CLDNN classifier, which integrates together the Convolutional Neural Network (CNN) and the Long Short-Term Memory Recurrent Neural Network (LSTM). Our model successfully detect all seven BBH events in the LIGO Livingston O2 data, with the periods of their GW waveforms correctly labeled. The ability of a Bayesian approach for uncertainty estimation enables a newly defined `awareness' state for recognizing the possible presence of signals of unknown types, which is otherwise rejected in a non-Bayesian model. Such data chunks labeled with the awareness state can then be further investigated rather than overlooked. Performance tests show that our model recognizes 90% of the events when the optimal signal-to-noise ratio $\rho_\text{opt} >7$ (100% when $\rho_\text{opt} >8.5$) and successfully labels more than 95% of the waveform periods when $\rho_\text{opt} >8$. The latency between the arrival of peak signal and generating an alert with the associated waveform period labeled is only about 20 seconds for an unoptimized code on a moderate GPU-equipped personal computer. This makes our model possible for nearly real-time detection and for forecasting the coalescence events when assisted with deeper training on a larger dataset using the state-of-art HPCs.

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is typically NP-hard, and thus alternative approximate methods should be considered. In this paper, our choice for alternative method is sparse Bayesian learning, which, as empirical Bayesian approaches, uses a parameterized prior to encourage sparsity in solution, rather than the other methods with fixed priors such as LASSO. Screening test, however, aims at quickly identifying a subset of features whose coefficients are guaranteed to be zero in the optimal solution, and then can be safely removed from the complete dictionary to obtain a smaller, more easily solved problem. Next, we solve the smaller problem, after which the solution of the original problem can be recovered by padding the smaller solution with zeros. The performance of the proposed method will be examined on various data sets and applications.

Meta-learning has proven to be successful at few-shot learning across the regression, classification and reinforcement learning paradigms. Recent approaches have adopted Bayesian interpretations to improve gradient based meta-learners by quantifying the uncertainty of the post-adaptation estimates. Most of these works almost completely ignore the latent relationship between the covariate distribution (p(x)) of a task and the corresponding conditional distribution p(y|x). In this paper, we identify the need to explicitly model the meta-distribution over the task covariates in a hierarchical Bayesian framework. We begin by introducing a graphical model that explicitly leverages very few samples drawn from p(x) to better infer the posterior over the optimal parameters of the conditional distribution (p(y|x)) for each task. Based on this model we provide an inference strategy and a corresponding meta-algorithm that explicitly accounts for the meta-distribution over task covariates. Finally, we demonstrate the significant gains of our proposed algorithm on a synthetic regression dataset.

A Columbia University research team affiliated with the Data Science Institute (DSI) has received a Facebook Probability and Programming research award to develop static analysis methods that will enhance the usability and accuracy of probabilistic programming. The team includes Jeannette M. Wing, DSI's Avanessians Director and Professor of Computer Science; Andrew Gelman, Professor of Statistics and Political Science and DSI member; and Ryan Bernstein, a doctoral student in computer science who is co-advised by Wing and Gelman. The three will conduct a static analysis of Stan, an open-source probabilistic language program developed mainly at Columbia that describes statistical models. Their analysis will make it easier for users to reliably design statistical and machine learning models in high-level programming languages, according to Gelman, who is a co-principal investigator on the award. "Stan is used in applications ranging from drug development [for Novartis] to political polling and forecasting [for YouGov and The Economist]," Gelman said.

Propositional model counting or #SAT is the problem of computing the number of satisfying assignments of a Boolean formula and many discrete probabilistic inference problems can be translated into a model counting problem to be solved by #SAT solvers. Generic ``exact'' #SAT solvers, however, are often not scalable to industrial-level instances. In this paper, we present Neuro#, an approach for learning branching heuristics for exact #SAT solvers via evolution strategies (ES) to reduce the number of branching steps the solver takes to solve an instance. We experimentally show that our approach not only reduces the step count on similarly distributed held-out instances but it also generalizes to much larger instances from the same problem family. The gap between the learned and the vanilla solver on larger instances is sometimes so wide that the learned solver can even overcome the run time overhead of querying the model and beat the vanilla in wall-clock time by orders of magnitude.

Dynamic Bayesian networks have been well explored in the literature as discrete-time models; however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm for learning the structure of continuous-time Bayesian networks. We discuss the different statistical tests and the underlying hypotheses used by our proposal to establish conditional independence. Finally, we validate its performance using synthetic data, and discuss its strengths and limitations. We find that score-based is more accurate in learning networks with binary variables, while our constraint-based approach is more accurate with variables assuming more than two values. However, more experiments are needed for confirmation.

Precision farming is one way of many to meet a 70 percent increase in global demand for agricultural products on current agricultural land by 2050 at reduced need of fertilizers and efficient use of water resources. The catalyst for the emergence of precision farming has been satellite positioning and navigation followed by Internet-of-Things, generating vast information that can be used to optimize farming processes in real-time. Statistical tools from data mining, predictive modeling, and machine learning analyze pattern in historical data, to make predictions about future events as well as intelligent actions. This special issue presents the latest development in statistical inference, machine learning and optimum control for precision farming.

Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive with respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching (SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference (FD). Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations. Thus, it reduces the total computational cost while also improving numerical stability. We provide two instantiations by reformulating variants of SM objectives into the FD forms. Empirically, we demonstrate that our methods produce results comparable to the gradient-based counterparts while being much more computationally efficient.