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Bayesian optimal design of experiments is a well-established approach to planning experiments. Briefly, a probability distribution, known as a statistical model, for the responses is assumed which is dependent on a vector of unknown parameters. A utility function is then specified which gives the gain in information for estimating the true value of the parameters using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising the expectation of the utility with respect to the joint distribution given by the statistical model and prior distribution for the true parameter values. The approach takes account of the experimental aim via specification of the utility and of all assumed sources of uncertainty via the expected utility. However, it is predicated on the specification of the statistical model. Recently, a new type of statistical inference, known as Gibbs (or General Bayesian) inference, has been advanced. This is Bayesian-like, in that uncertainty on unknown quantities is represented by a posterior distribution, but does not necessarily rely on specification of a statistical model. Thus the resulting inference should be less sensitive to misspecification of the statistical model. The purpose of this paper is to propose Gibbs optimal design: a framework for optimal design of experiments for Gibbs inference. The concept behind the framework is introduced along with a computational approach to find Gibbs optimal designs in practice. The framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.

When multiple self-adaptive systems share the same environment and have common goals, they may coordinate their adaptations at runtime to avoid conflicts and to satisfy their goals. There are two approaches to coordination. (1) Logically centralized, where a supervisor has complete control over the individual self-adaptive systems. Such approach is infeasible when the systems have different owners or administrative domains. (2) Logically decentralized, where coordination is achieved through direct interactions. Because the individual systems have control over the information they share, decentralized coordination accommodates multiple administrative domains. However, existing techniques do not account simultaneously for both local concerns, e.g., preferences, and shared concerns, e.g., conflicts, which may lead to goals not being achieved as expected. Our idea to address this shortcoming is to express both types of concerns within the same constraint optimization problem. We propose CoADAPT, a decentralized coordination technique introducing two types of constraints: preference constraints, expressing local concerns, and consistency constraints, expressing shared concerns. At runtime, the problem is solved in a decentralized way using distributed constraint optimization algorithms implemented by each self-adaptive system. As a first step in realizing CoADAPT, we focus in this work on the coordination of adaptation planning strategies, traditionally addressed only with centralized techniques. We show the feasibility of CoADAPT in an exemplar from cloud computing and analyze experimentally its scalability.

The evaluation of clustering algorithms can involve running them on a variety of benchmark problems, and comparing their outputs to the reference, ground-truth groupings provided by experts. Unfortunately, many research papers and graduate theses consider only a small number of datasets. Also, the fact that there can be many equally valid ways to cluster a given problem set is rarely taken into account. In order to overcome these limitations, we have developed a framework whose aim is to introduce a consistent methodology for testing clustering algorithms. Furthermore, we have aggregated, polished, and standardised many clustering benchmark dataset collections referred to across the machine learning and data mining literature, and included new datasets of different dimensionalities, sizes, and cluster types. An interactive datasets explorer, the documentation of the Python API, a description of the ways to interact with the framework from other programming languages such as R or MATLAB, and other details are all provided at <//clustering-benchmarks.gagolewski.com>.

In the present era of sustainable innovation, the circular economy paradigm dictates the optimal use and exploitation of existing finite resources. At the same time, the transition to smart infrastructures requires considerable investment in capital, resources and people. In this work, we present a general machine learning approach for offering indoor location awareness without the need to invest in additional and specialised hardware. We explore use cases where visitors equipped with their smart phone would interact with the available WiFi infrastructure to estimate their location, since the indoor requirement poses a limitation to standard GPS solutions. Results have shown that the proposed approach achieves a less than 2m accuracy and the model is resilient even in the case where a substantial number of BSSIDs are dropped.

In contingency table analysis, one is interested in testing whether a model of interest (e.g., the independent or symmetry model) holds using goodness-of-fit tests. When the null hypothesis where the model is true is rejected, the interest turns to the degree to which the probability structure of the contingency table deviates from the model. Many indexes have been studied to measure the degree of the departure, such as the Yule coefficient and Cram\'er coefficient for the independence model, and Tomizawa's symmetry index for the symmetry model. The inference of these indexes is performed using sample proportions, which are estimates of cell probabilities, but it is well-known that the bias and mean square error (MSE) values become large without a sufficient number of samples. To address the problem, this study proposes a new estimator for indexes using Bayesian estimators of cell probabilities. Assuming the Dirichlet distribution for the prior of cell probabilities, we asymptotically evaluate the value of MSE when plugging the posterior means of cell probabilities into the index, and propose an estimator of the index using the Dirichlet hyperparameter that minimizes the value. Numerical experiments show that when the number of samples per cell is small, the proposed method has smaller values of bias and MSE than other methods of correcting estimation accuracy. We also show that the values of bias and MSE are smaller than those obtained by using the uniform and Jeffreys priors.

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element discretizations of the coupled Stokes-Darcy flow problem. We analyze the spectrum of the preconditioned matrix and we show how the new preconditioner can be efficiently applied. Numerical experiments are reported to illustrate the effectiveness of the preconditioner in conjunction with flexible GMRES for solving linear systems of equations arising from a 3D test problem.

We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the probabilistic stability regions and benchmark them against the absolute stability regions for deterministic Taylor schemes.

Knowledge graphs contain rich semantic relationships related to items and incorporating such semantic relationships into recommender systems helps to explore the latent connections of items, thus improving the accuracy of prediction and enhancing the explainability of recommendations. However, such explainability is not adapted to users' contexts, which can significantly influence their preferences. In this work, we propose CA-KGCN (Context-Aware Knowledge Graph Convolutional Network), an end-to-end framework that can model users' preferences adapted to their contexts and can incorporate rich semantic relationships in the knowledge graph related to items. This framework captures users' attention to different factors: contexts and features of items. More specifically, the framework can model users' preferences adapted to their contexts and provide explanations adapted to the given context. Experiments on three real-world datasets show the effectiveness of our framework: modeling users' preferences adapted to their contexts and explaining the recommendations generated.

Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional asymptotics regime, in which the ratio of the number of features to the number of observations converges to a constant. Specifically, we propose a general strategy to analyze the prediction risk under squared error loss of bagged predictors using classical results on simple random sampling. Specializing the strategy, we derive the exact asymptotic risk of the bagged ridge and ridgeless predictors with an arbitrary number of bags under a well-specified linear model with arbitrary feature covariance matrices and signal vectors. Furthermore, we prescribe a generic cross-validation procedure to select the optimal subsample size for bagging and discuss its utility to eliminate the non-monotonic behavior of the limiting risk in the sample size (i.e., double or multiple descents). In demonstrating the proposed procedure for bagged ridge and ridgeless predictors, we thoroughly investigate the oracle properties of the optimal subsample size and provide an in-depth comparison between different bagging variants.

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing {\it ad hoc} approach, such as the last value carried forward, is biased. We propose a kernel weighting approach to get an unbiased estimation of the non-parametric coefficient function and establish asymptotic normality for any fixed time point. Furthermore, we construct the simultaneous confidence band to examine the overall magnitude of the variation. Simulation studies support our theoretical predictions and show favorable performance of the proposed method. A data set from cerebral infarction is used to illustrate our methodology.