Given partially observed pairwise comparison data generated by the Bradley-Terry-Luce (BTL) model, we study the problem of top-$k$ ranking. That is, to optimally identify the set of top-$k$ players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-$k$ ranking. We also derive the optimal signal to noise ratio condition for the exact recovery of the top-$k$ set. The maximum likelihood estimator (MLE) is shown to achieve both optimal partial recovery and optimal exact recovery. On the other hand, we show another popular algorithm, the spectral method, is in general sub-optimal. Our results complement the recent work by Chen et al. (2019) that shows both the MLE and the spectral method achieve the optimal sample complexity for exact recovery. It turns out the leading constants of the sample complexity are different for the two algorithms. Another contribution that may be of independent interest is the analysis of the MLE without any penalty or regularization for the BTL model. This closes an important gap between theory and practice in the literature of ranking.

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering nonlinear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multi-fidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.

Chain Event Graphs (CEGs) are a recent family of probabilistic graphical models - a generalisation of Bayesian Networks - providing an explicit representation of structural zeros and context-specific conditional independences within their graph topology. A CEG is constructed from an event tree through a sequence of transformations beginning with the colouring of the vertices of the event tree to identify one-step transition symmetries. This coloured event tree, also known as a staged tree, is the output of the learning algorithms used for this family. Surprisingly, no general algorithm has yet been devised that automatically transforms any staged tree into a CEG representation. In this paper we provide a simple iterative backward algorithm for this transformation. Additionally, we show that no information is lost from transforming a staged tree into a CEG. Finally, we demonstrate that with an optimal stopping time, our algorithm is more efficient than the generalisation of a special case presented in Silander and Leong (2013). We also provide Python code using this algorithm to obtain a CEG from any staged tree along with the functionality to add edges with sampling zeros.

These approaches, however, concept (for which there are many). Historically, most are based on general mixing patterns, which include community detection methods proposed have focused on assortativity only as a special case. In many ways this the detection of assortative communities, i.e. groups of is useful, and in fact arguably superior, since if assortativity nodes that tend to be more connected to themselves than happens to be the dominating pattern, then the to other nodes in the network. However, there are also general approach will capture it, otherwise it will reveal a community detection methods that are more general, and different structure. However, having only a more general attempt to cluster together nodes that have similar patterns method at our disposal also has its shortcomings. First, of connection, regardless if they are assortative or if it is true that assortativity is the main pattern for a not [3-5]. The widespread use of assortative community class of networks, then the more general representation detection methods has lead to the belief that the presence is needlessly wasteful for them, since it not only gives us of communities is a pervasive feature of many different more than we need, but in doing so it prevents us from kinds of real networks [6]. Although the concept of assortativity focusing on the more central features, at the cost of algorithmic is a central one in the study of social networks precision. Second, with a more general method (known as "homophily" in that context) [7], and is also an it can be difficult to quantify precisely how much has appealing construct in biology [8-10], it is to some extent been wasted in the representation, and what is indeed unclear if the perceived assortativity of many networks the simpler pattern hiding inside it.

The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to "burn in" and removed, whilst the remainder of the chain is "thinned" if compression is also required. In this paper we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in both Python and MATLAB.

Chain Event Graphs (CEGs) are a family of event-based graphical models that represent context-specific conditional independences typically exhibited by asymmetric state space problems. The class of continuous time dynamic CEGs (CT-DCEGs) provides a factored representation of longitudinally evolving trajectories of a process in continuous time. Temporal evidence in a CT-DCEG introduces dependence between its transition and holding time distributions. We present a tractable exact inferential scheme analogous to the scheme in Kj{\ae}rulff (1992) for discrete Dynamic Bayesian Networks (DBNs) which employs standard junction tree inference by "unrolling" the DBN. To enable this scheme, we present an extension of the standard CEG propagation algorithm (Thwaites et al., 2008). Interestingly, the CT-DCEG benefits from simplification of its graph on observing compatible evidence while preserving the still relevant symmetries within the asymmetric network. Our results indicate that the CT-DCEG is preferred to DBNs and continuous time BNs under contexts involving significant asymmetry and a natural total ordering of the process evolution.

Generative Adversarial Networks (GANs) software is software for producing forgeries and imitations of data (aka synthetic data, fake data). Human beings have been making fakes, with good or evil intent, of almost everything they possibly can, since the beginning of the human race. Thus, perhaps not too surprisingly, GAN software has been widely used since it was first proposed in this amazingly recent 2014 paper. To gauge how widely GAN software has been used so far, see, for example, this 2019 article entitled "18 Impressive Applications of Generative Adversarial Networks (GANs)" Sounds (voices, music,...), Images (realistic pictures, paintings, drawings, handwriting, ...), Text,etc. The forgeries can be tweaked so that they range from being very similar to the originals, to being whimsical exaggerations thereof.

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This paper formulates hypothesis verification as an RL problem. Specifically, we aim to build an agent that, given a hypothesis about the dynamics of the world, can take actions to generate observations which can help predict whether the hypothesis is true or false. Existing RL algorithms fail to solve this task, even for simple environments. In order to train the agents, we exploit the underlying structure of many hypotheses, factorizing them as {pre-condition, action sequence, post-condition} triplets. By leveraging this structure we show that RL agents are able to succeed at the task. Furthermore, subsequent fine-tuning of the policies allows the agent to correctly verify hypotheses not amenable to the above factorization.