Finite mixture models are a widely-used tool for modeling heterogeneous data, consisting of hidden subpopulations with distinct distributions. For applications exhibiting continuous data, location-scale Gaussian mixtures are arguably the most popular family of parametric mixture models. Beyond their broad applications as a modeling and clustering tool in the social, physical and life sciences (McLachlan & Peel 2004), Gaussian mixtures provide a flexible approach to density estimation (Genovese & Wasserman 2000, Ghosal & van der Vaart 2001). Estimating the parameters of a mixture model is crucial for quantifying the underlying heterogeneity of the data. One of the most widely-used approaches is the maximum likelihood estimator (MLE). A Gaussian mixture model with a known number of components K, all of which are well-separated, forms a regular parametric model for which the MLE achieves the standard parametric estimation rate (Ho & Nguyen 2016b, Chen 2017). Such rates are typically understood in terms of convergence of mixing measures, quantified using the Wasserstein distance as a means of avoiding label switching issues inherent in mixture modeling (Nguyen 2013).

Simulators often require calibration inputs estimated from real world data and the quality of the estimate can significantly affect simulation output. Particularly when performing simulation optimisation to find an optimal solution, the uncertainty in the inputs significantly affects the quality of the found solution. One remedy is to search for the solution that has the best performance on average over the uncertain range of inputs yielding an optimal compromise solution. We consider the more general setting where a user may choose between either running simulations or instead collecting real world data. A user may choose an input and a solution and observe the simulation output, or instead query an external data source improving the input estimate enabling the search for a more focused, less compromised solution. We explicitly examine the trade-off between simulation and real data collection in order to find the optimal solution of the simulator with the true inputs. Using a value of information procedure, we propose a novel unified simulation optimisation procedure called Bayesian Information Collection and Optimisation (BICO) that, in each iteration, automatically determines which of the two actions (running simulations or data collection) is more beneficial. Numerical experiments demonstrate that the proposed algorithm is able to automatically determine an appropriate balance between optimisation and data collection.

This paper proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a generalization error bound of the proposed classifier based on the strength of the individual hyperbox-based classifiers as well as the correlation among them. The effectiveness of the proposed classifier is analyzed using a carefully selected illustrative example and compared empirically with other popular single and ensemble classifiers via 20 datasets using statistical testing methods. The experimental results confirmed that our proposed method outperformed other fuzzy min-max neural networks, popular learning algorithms, and is competitive with other ensemble methods. Finally, we identify the existing issues related to the generalization error bounds of the real datasets and inform the potential research directions.

This paper provides the foundations of a unified cognitive decision-making framework (QulBIT) which is derived from quantum theory. The main advantage of this framework is that it can cater for paradoxical and irrational human decision making. Although quantum approaches for cognition have demonstrated advantages over classical probabilistic approaches and bounded rationality models, they still lack explanatory power. To address this, we introduce a novel explanatory analysis of the decision-maker's belief space. This is achieved by exploiting quantum interference effects as a way of both quantifying and explaining the decision-maker's uncertainty. We detail the main modules of the unified framework, the explanatory analysis method, and illustrate their application in situations violating the Sure Thing Principle.

This paper provides a graphical characterization of Markov blankets in chain graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithm for Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationally tractable and more reliable because they exploit locality.

Framed in positive terms, this report examines how technical AI research might be steered in a manner that is more attentive to humanity's long-term prospects for survival as a species. In negative terms, we ask what existential risks humanity might face from AI development in the next century, and by what principles contemporary technical research might be directed to address those risks. A key property of hypothetical AI technologies is introduced, called \emph{prepotence}, which is useful for delineating a variety of potential existential risks from artificial intelligence, even as AI paradigms might shift. A set of \auxref{dirtot} contemporary research \directions are then examined for their potential benefit to existential safety. Each research direction is explained with a scenario-driven motivation, and examples of existing work from which to build. The research directions present their own risks and benefits to society that could occur at various scales of impact, and in particular are not guaranteed to benefit existential safety if major developments in them are deployed without adequate forethought and oversight. As such, each direction is accompanied by a consideration of potentially negative side effects.

We propose an adaptation of the Random Forest algorithm to estimate the conditional distribution of a possibly multivariate response. We suggest a new splitting criterion based on the MMD two-sample test, which is suitable for detecting heterogeneity in multivariate distributions. The weights provided by the forest can be conveniently used as an input to other methods in order to locally solve various learning problems. The code is available as \texttt{R}-package \texttt{drf}.

Deep neural networks have revolutionized medical image analysis and disease diagnosis. Despite their impressive performance, it is difficult to generate well-calibrated probabilistic outputs for such networks, which makes them uninterpretable black boxes. Bayesian neural networks provide a principled approach for modelling uncertainty and increasing patient safety, but they have a large computational overhead and provide limited improvement in calibration. In this work, by taking skin lesion classification as an example task, we show that by shifting Bayesian inference to the functional space we can craft meaningful priors that give better calibrated uncertainty estimates at a much lower computational cost.

We report a triangular neural network implementation of neural autoregressive flow (NAF). Unlike many universal autoregressive density models, our design is highly modular, parameter economy, computationally efficient, and applicable to density estimation of data with high dimensions. It achieves state-of-the-art bits-per-dimension indices on MNIST and CIFAR-10 (about 1.1 and 3.7, respectively) in the category of general-purpose density estimators.

Recommendation system or also known as a recommender system is a tool to help the user in providing a suggestion of a specific dilemma. Thus, recently, the interest in developing a recommendation system in many fields has increased. Fuzzy Logic system (FLSs) is one of the approaches that can be used to model the recommendation systems as it can deal with uncertainty and imprecise information. However, one of the fundamental issues in FLS is the problem of the curse of dimensionality. That is, the number of rules in FLSs is increasing exponentially with the number of input variables. One effective way to overcome this problem is by using Hierarchical Fuzzy System (HFSs). This paper aims to explore the use of HFSs for Recommendation system. Specifically, we are interested in exploring and comparing the HFS and FLS for the Career path recommendation system (CPRS) based on four key criteria, namely topology, the number of rules, the rules structures and interpretability. The findings suggested that the HFS has advantages over FLS towards improving the interpretability models, in the context of a recommendation system example. This study contributes to providing an insight into the development of interpretable HFSs in the Recommendation systems.