Feature selection is a crucial preprocessing step in data analytics and machine learning. Classical feature selection algorithms select features based on the correlations between predictive features and the class variable and do not attempt to capture causal relationships between them. It has been shown that the knowledge about the causal relationships between features and the class variable has potential benefits for building interpretable and robust prediction models, since causal relationships imply the underlying mechanism of a system. Consequently, causality-based feature selection has gradually attracted greater attentions and many algorithms have been proposed. In this paper, we present a comprehensive review of recent advances in causality-based feature selection. To facilitate the development of new algorithms in the research area and make it easy for the comparisons between new methods and existing ones, we develop the first open-source package, called CausalFS, which consists of most of the representative causality-based feature selection algorithms (available at https://github.com/kuiy/CausalFS). Using CausalFS, we conduct extensive experiments to compare the representative algorithms with both synthetic and real-world data sets. Finally, we discuss some challenging problems to be tackled in future causality-based feature selection research.

The de facto standard for causal inference is the randomized controlled trial, where one compares an manipulated group with a control group in order to determine the effect of an intervention. However, this research design is not always realistically possible due to pragmatic or ethical concerns. In these situations, quasi-experimental designs may provide a solution, as these allow for causal conclusions at the cost of additional design assumptions. In this paper, we provide a generic framework for quasi-experimental design using Bayesian model comparison, and we show how it can be used as an alternative to several common research designs. We provide a theoretical motivation for a Gaussian process based approach and demonstrate its convenient use in a number of simulations. Finally, we apply the framework to determine the effect of population-based thresholds for municipality funding in France, of the 2005 smoking ban in Sicily on the number of acute coronary events, and of the effect of an alleged historical phantom border in the Netherlands on Dutch voting behaviour.

In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective} prior distribution. Sampling from the objective prior corresponds to sampling different learning tasks from the environment. It is argued that for many common machine learning problems, although we don't know the true (objective) prior for the problem, we do have some idea of a set of possible priors to which the true prior belongs. It is shown that under these circumstances a learner can use Bayesian inference to learn the true prior by sampling from the objective prior. Bounds are given on the amount of information required to learn a task when it is simultaneously learnt with several other tasks. The bounds show that if the learner has little knowledge of the true prior, and the dimensionality of the true prior is small, then sampling multiple tasks is highly advantageous.

Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces giving new momentum to the field. Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound change these developments may have on science.

The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Mat\'ern class possesses exponentially decaying tails, and thus may not be suitable for modeling long range dependence. This problem can be remedied using polynomial covariances; however one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. We construct a new family of covariance functions using a scale mixture representation of the Mat\'ern class where one obtains the benefits of both Mat\'ern and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. Using a spectral representation, we derive theoretical properties of this new covariance including equivalence measures and asymptotic behavior of the maximum likelihood estimators under infill asymptotics. The improved theoretical properties in predictive performance of this new covariance class are verified via extensive simulations. Application using NASA's Orbiting Carbon Observatory-2 satellite data confirms the advantage of this new covariance class over the Mat\'ern class, especially in extrapolative settings.

We consider black-box global optimization of time-consuming-to-evaluate functions on behalf of a decision-maker whose preferences must be learned. Each feasible design is associated with a time-consuming-to-evaluate vector of attributes, each vector of attributes is assigned a utility by the decision-maker's utility function, and this utility function may be learned approximately using preferences expressed by the decision-maker over pairs of attribute vectors. Past work has used this estimated utility function as if it were error-free within single-objective optimization. However, errors in utility estimation may yield a poor suggested decision. Furthermore, this approach produces a single suggested "best" design, whereas decision-makers often prefer to choose among a menu of designs. We propose a novel Bayesian optimization algorithm that acknowledges the uncertainty in preference estimation and implicitly chooses designs to evaluate using the time-consuming function that are good not just for a single estimated utility function but a range of likely utility functions. Our algorithm then shows a menu of designs and evaluated attributes to the decision-maker who makes a final selection. We demonstrate the value of our algorithm in a variety of numerical experiments.

A key challenge in crowdsourcing is inferring the ground truth from noisy and unreliable data. To do so, existing approaches rely on collecting redundant information from the crowd, and aggregating it with some probabilistic method. However, oftentimes such methods are computationally inefficient, are restricted to some specific settings, or lack theoretical guarantees. In this paper, we revisit the problem of binary classification from crowdsourced data. Specifically we propose Streaming Bayesian Inference for Crowdsourcing (SBIC), a new algorithm that does not suffer from any of these limitations. First, SBIC has low complexity and can be used in a real-time online setting. Second, SBIC has the same accuracy as the best state-of-the-art algorithms in all settings. Third, SBIC has provable asymptotic guarantees both in the online and offline settings.

We develop a real-time anomaly detection algorithm for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent factors in addition to sender- and receiver-specific popularity scores; deviations from this underlying model constitute potential anomalies. Latent nodal attributes are estimated via a variational Bayesian approach and may change over time, representing natural shifts in network activity. Estimation is augmented with a case-control approximation to take advantage of the sparsity of the network and reduces computational complexity from $O(N^2)$ to $O(E)$, where $N$ is the number of nodes and $E$ is the number of observed edges. We run our algorithm on network event records collected from an enterprise network of over 25,000 computers and are able to identify a red team attack with half the detection rate required of the model without latent interaction terms.

The darknet markets are notorious black markets in cyberspace, which involve selling or brokering drugs, weapons, stolen credit cards, and other illicit goods. To combat illicit transactions in the cyberspace, it is important to analyze the behaviors of participants in darknet markets. Currently, many studies focus on studying the behavior of vendors. However, there is no much work on analyzing buyers. The key challenge is that the buyers are anonymized in darknet markets. For most of the darknet markets, We only observe the first and last digits of a buyer's ID, such as ``a**b''. To tackle this challenge, we propose a hidden buyer identification model, called UNMIX, which can group the transactions from one hidden buyer into one cluster given a transaction sequence from an anonymized ID. UNMIX is able to model the temporal dynamics information as well as the product, comment, and vendor information associated with each transaction. As a result, the transactions with similar patterns in terms of time and content group together as the subsequence from one hidden buyer. Experiments on the data collected from three real-world darknet markets demonstrate the effectiveness of our approach measured by various clustering metrics. Case studies on real transaction sequences explicitly show that our approach can group transactions with similar patterns into the same clusters.

In this article, we propose a novel probabilistic framework to improve the accuracy of a weighted majority voting algorithm. In order to assign higher weights to the classifiers which can correctly classify hard-to-classify instances, we introduce the Item Response Theory (IRT) framework to evaluate the samples' difficulty and classifiers' ability simultaneously. Three models are created with different assumptions suitable for different cases. When making an inference, we keep a balance between the accuracy and complexity. In our experiment, all the base models are constructed by single trees via bootstrap. To explain the models, we illustrate how the IRT ensemble model constructs the classifying boundary. We also compare their performance with other widely used methods and show that our model performs well on 19 datasets.