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In predictive modelling for high‐stake decision‐making, predictors must be not only accurate but also reliable. Conformal prediction (CP) is a promising approach for obtaining the coverage of prediction results with fewer theoretical assumptions. To obtain the prediction set by so‐called full‐CP, we need to refit the predictor for all possible values of prediction results, which is only possible for simple predictors. For complex predictors such as random forests (RFs) or neural networks (NNs), split‐CP is often employed where the data is split into two parts: one part for fitting and another for computing the prediction set. Unfortunately, because of the reduced sample size, split‐CP is inferior to full‐CP both in fitting as well as prediction set computation. In this paper, we develop a full‐CP of sparse high‐order interaction model (SHIM), which is sufficiently flexible as it can take into account high‐order interactions among variables. We resolve the computational challenge for full‐CP of SHIM by introducing a novel approach called homotopy mining. Through numerical experiments, we demonstrate that SHIM is as accurate as complex predictors such as RF and NN and enjoys the superior statistical power of full‐CP. [ABSTRACT FROM AUTHOR]

Image registration is a widely used tool for matching two images of the same scene with one another. In the literature, several image registration techniques are available to register rigid‐body and non‐rigid‐body transformations. One such important transformation is zooming. There are very few feature‐based methods that address this particular problem. These methods fail miserably when there are only a limited number of point features available in the image. This paper proposes a feature‐based approach that works with a feature that is readily available in almost all images, for registering two images of the same image object where one is a zoomed‐in version of the other. In the proposed method, we first detect the possible edge points which we consider as features in both the reference and the zoomed image. Then, we map these features of the reference and the zoomed image with one another and find the relationship between them using a mathematical model. Finally, we use the relationship to register the zoomed‐in image. This method outperforms some of the state‐of‐the‐art methods in many occasions. Several numerical examples and some statistical properties justify that this method works well in many applications. [ABSTRACT FROM AUTHOR]

Modelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones. [ABSTRACT FROM AUTHOR]

Data science consulting and collaboration units (DSUs) are core infrastructure for research at universities. Activities span data management, study design, data analysis, data visualization, predictive modelling, preparing reports, manuscript writing and advising on statistical methods and may include an experiential or teaching component. Partnerships are needed for a thriving DSU as an active part of the larger university network. Guidance for identifying, developing and managing successful partnerships for DSUs can be summarized in six rules: (1) align with institutional strategic plans, (2) cultivate partnerships that fit your mission, (3) ensure sustainability and prepare for growth, (4) define clear expectations in a partnership agreement, (5) communicate and (6) expect the unexpected. While these rules are not exhaustive, they are derived from experiences in a diverse set of DSUs, which vary by administrative home, mission, staffing and funding model. As examples in this paper illustrate, these rules can be adapted to different organizational models for DSUs. Clear expectations in partnership agreements are essential for high quality and consistent collaborations and address core activities, duration, staffing, cost and evaluation. A DSU is an organizational asset that should involve thoughtful investment if the institution is to gain real value. [ABSTRACT FROM AUTHOR]

The COVID‐19 pandemic led to unprecedented changes in all levels of society, including the statistical consulting field. This paper focuses on the experiences of graduate student consultants and clients at our statistical consulting center (SCC) that operates all year independent of semesters. During the lockdown period, work continued without interruption and was conducted remotely, but there was a temporary reduction in utilization. Advice on statistical methods, help with data analysis and educational offerings are the main appeals to utilize SCC services. We describe our mentoring approach for graduate student research assistants (RAs) and how pandemic changes affected RAs and clients. Based on experiences during the pandemic, we offer practical suggestions for SCCs' approaches to research support, work characteristics and collaborations to improve the experiences of graduate students, both as consultants and clients. Most collaboration meetings are now virtual by request from clients. Telecommuting supports flexible personal schedules and needs. Online educational offerings provide easier access for participants and more opportunities for a wider range of topics and presenters. However, mentoring sessions for RAs are best conducted in‐person, and every effort should be made to encourage in‐person interactions and collaborations between staff members to advance the effectiveness of post‐pandemic SCCs. [ABSTRACT FROM AUTHOR]

Deep learning has achieved unprecedented success in recent years. This approach essentially uses the composition of nonlinear functions to model the complex relationship between input features and output labels. However, a comprehensive theoretical understanding of why the hierarchical layered structure can exhibit superior expressive power is still lacking. In this paper, we provide an explanation for this phenomenon by measuring the approximation efficiency of neural networks with respect to discontinuous target functions. We focus on deep neural networks with rectified linear unit (ReLU) activation functions. We find that to achieve the same degree of approximation accuracy, the number of neurons required by a single‐hidden‐layer (SHL) network is exponentially greater than that required by a multi‐hidden‐layer (MHL) network. In practice, discontinuous points tend to contain highly valuable information (i.e., edges in image classification). We argue that this may be a very important reason accounting for the impressive performance of deep neural networks. We validate our theory in extensive experiments. [ABSTRACT FROM AUTHOR]

In recent years, multi‐response linear models have gained significant popularity in various statistical applications. However, the design aspects of multi‐response linear models with group‐wise considerations have received limited attention in the literature. This paper aims to thoroughly investigate D$$ D $$‐optimal designs for such models. Specifically, we focus on scenarios involving two groups, where the proportions of observations for each group can be arbitrarily selected or not. Two equivalence theorems are presented to elaborate the characterization of D$$ D $$‐optimal designs. Additionally, we delve into the admissibility of approximate designs and establish necessary conditions for a design to be deemed admissible. Several illustrative examples are addressed to demonstrate the application of the derived theoretical results. [ABSTRACT FROM AUTHOR]

Summary: Testing for equivalence, rather than testing for a difference, is an important component of some scientific studies. While the focus of the existing literature is on comparing two groups for equivalence, real‐world applications arise regularly that require testing across more than two groups. This paper reviews the existing approaches for testing across multiple groups and proposes a novel framework for multigroup equivalence testing under a Bayesian paradigm. This approach allows for a more scientifically meaningful definition of the equivalence margin and a more powerful test than the few existing alternatives. This approach also allows a new definition of equivalence based on future differences. [ABSTRACT FROM AUTHOR]

A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes, many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme has received wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships. However, the paper "Conditional extreme value models: fallacies and pitfalls" by Holger Drees and Anja Janßen provides a number of counterexamples to these results. This paper studies these counterexamples in a conditional extremes framework which involves marginal standardisation to a common exponentially decaying tailed marginal distribution. Our calculations show that some of the issues identified can be addressed in this way. [ABSTRACT FROM AUTHOR]

This paper introduces graph‐based mutually exciting processes (GB‐MEP) to model event times in network point processes, focusing on an application to docked bike‐sharing systems. GB‐MEP incorporates known relationships between nodes in a graph within the intensity function of a node‐based multivariate Hawkes process. This approach reduces the number of parameters to a quantity proportional to the number of nodes in the network, resulting in significant advantages for computational scalability when compared with traditional methods. The model is applied on event data observed on the Santander Cycles network in central London, demonstrating that exploiting network‐wide information related to geographical location of the stations is beneficial to improve the performance of node‐based models for applications in bike‐sharing systems. The proposed GB‐MEP framework is more generally applicable to any network point process where a distance function between nodes is available, demonstrating wider applicability. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach to reducing statistical errors in generative models, with a specific focus on generative adversarial networks (GANs). Inspired by the error analysis of GANs, we find that statistical errors mainly arise from random sampling, leading to significant uncertainties in GANs. To address this issue, we propose a selective sampling mechanism called space‐filling sampling. Our method aims to increase the sampling probability in areas with insufficient data, thereby improving the learning performance of the generator. Theoretical analysis confirms the effectiveness of our approach in reducing statistical errors and accelerating convergence in GANs. This research represents a pioneering effort in targeting the reduction of statistical errors in GANs, and it demonstrates the potential for enhancing the training of other generative models. [ABSTRACT FROM AUTHOR]

The deterministic non‐autonomous multispecies Holling type II model and its stochastic version with a simple type of noise have been proposed to infer multispecies community structure. However, these models fail to account for complex types of noises, which may render the model overly simplistic. In this paper, a non‐autonomous multispecies Holling type II model with a complex type of noise has been proposed. We establish sufficient conditions for various mathematical properties of the solutions, including existence and uniqueness, stochastic permanence and extinction. Additionally, numerical simulation studies are provided to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the universally optimal designs for estimating total effects under crossover models with partial interactions. We provide necessary and sufficient conditions for a symmetric design to be universally optimal, based on which algorithms can be used to derive optimal symmetric designs under any form of the within‐block covariance matrix. To cope with the computational complexity of algorithms when the experimental scale is too large, we provide the analytical form of optimal designs under the type‐H covariance matrix. We find that for a fixed number of treatments, say t$$ t $$, the number of distinct treatments appearing in the support sequences increases with the increase of the number of periods, k$$ k $$, until k≥t2$$ k\ge {t}^2 $$, in which case all t$$ t $$ treatments appear. The optimal design can be constructed from up to two representative sequences, within which each treatment appears in consecutive periods with equal or almost equal numbers of replications. [ABSTRACT FROM AUTHOR]

In this paper, we present a heuristic for the non‐unicost set covering problem using local branching. Local branching eliminates the need to define a problem specific search neighbourhood for any particular (zero‐one) optimisation problem. It does this by incorporating a generalised Hamming distance neighbourhood into the problem, and this leads naturally to an appropriate neighbourhood search procedure. We apply our approach to the non‐unicost set covering problem. Computational results are presented for 65 test problems that have been widely considered in the literature. Our results indicate that our heuristic is better than six of the eight other heuristics we examined, slightly worse than that of one heuristic, but that there is a single heuristic that outperforms all others. We believe that the work described here illustrates that the potential for using local branching, operating as a stand‐alone matheuristic, has not been fully exploited in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss discrete location problems where the objective is to locate a given number of facilities of different types in order to appropriately cover a given set of demand points. The coverage provided to each demand point is the result of the cooperation among the located facilities. The different types of facility refer to the coverage radius or quality of coverage that each type may provide. We present a non‐linear formulation of the problem where the objective is to maximize the percentage of demand points that are appropriately covered. We then show how the model can be linearized based on a representation of probabilities through a network structure. To address large instances of the problem, we introduce a genetic algorithm (GA) that is based on the representation of the solution by two chromosomes. Computational experiments over a wide range of randomly generated problems indicate the GA clearly outperforms CPLEX, especially in larger instances. [ABSTRACT FROM AUTHOR]

This paper introduces a new flow‐based mathematical formulation for the multivehicle covering tour problem. This problem determines a set of vehicle routes for the available fleet; therefore, the total distance traveled is minimal. In the proposed mathematical formulation, each vertex represents a location of interest, and these vertices belong to three sets: vertices that can be visited; vertices that must be visited; and vertices that must be covered, in the sense that each vertex must be close to a visited vertex in a route. The proposed formulation aims to find solutions with balanced routes (all the routes with an equal or similar number of visited nodes) and extends the previous formulations proposed in the literature by considering a two‐index vehicle flow formulation with a decision variable to find the balanced routes. It constitutes an NP‐hard integer programming problem based on a two‐commodity flow model, which is solved by applying the branch‐and‐cut and biased random‐key genetic algorithms. This paper reports computational results for some adapted instances from TSPLIB to evaluate the efficiency of the proposed model. The computational results validate the branch‐and‐cut and genetic algorithms, whereby the latter performs better in large‐size instances with reduced computational runtime. Finally, the used approaches obtained competitive solutions compared to the literature. [ABSTRACT FROM AUTHOR]

In this paper, we address the biobjective versions of the perfect matching problem (PMP) and the Chinese postman problem (CPP). Both problems are solved by means of integer formulations or separating blossom inequalities, exploiting the PMP relationship with the CPP. In both cases, we first find the set of supported nondominated solutions and then we use them to obtain the nonsupported ones. The set of supported nondominated solutions are obtained solving scalarized integer formulations. To obtain the sets of nonsupported solutions, we resort to solving lexicographic problems based on adding additional linear constraints to the original problems. For this reason, we also characterize the combinatorial structure of the PMP vertices with one or two additional constraints. We also investigate when it is possible to use the PMP to solve CPP in the biobjective case. We report computational experiments comparing the different approaches and formulations based on different types of graphs with up to 700 nodes. [ABSTRACT FROM AUTHOR]

About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo‐polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch‐and‐bound time thanks to the symmetries broken by the hybridisation. [ABSTRACT FROM AUTHOR]

The team orienteering problem (TOP) is an NP‐hard optimization problem with an increasing number of potential applications in smart cities, humanitarian logistics, wildfire surveillance, etc. In the TOP, a fixed fleet of vehicles is employed to obtain rewards by visiting nodes in a network. All vehicles share common origin and destination locations. Since each vehicle has a limitation in time or traveling distance, not all nodes in the network can be visited. Hence, the goal is focused on the maximization of the collected reward, taking into account the aforementioned constraints. Most of the existing literature on the TOP focuses on its deterministic version, where rewards and travel times are assumed to be predefined values. This paper focuses on a more realistic TOP version, where travel times are modeled as random variables, which introduces reliability issues in the solutions due to the route‐length constraint. In order to deal with these complexities, we propose a simheuristic algorithm that hybridizes biased‐randomized heuristics with a variable neighborhood search and MCS. To test the quality of the solutions generated by the proposed simheuristic approach, we employ the well‐known sample average approximation (SAA) method, as well as a combination model that hybridizes the metaheuristic used in the simheuristic approach with the SAA algorithm. The results show that our proposed simheuristic outperforms the SAA and the hybrid model both on the objective function values and computational time. [ABSTRACT FROM AUTHOR]

Innovation is one of the driving forces of economic development and social progress, and the crowdsourcing contest is a well‐established mechanism for encouraging innovation. This paper examines two incentive schemes in two‐stage innovation contests: feedback and elimination. Feedback enhances the efforts by revealing the competitive status, and elimination intensifies the competition by removing less‐qualified participants. We build a game theoretical model to investigate how the organizer should design the feedback and elimination schemes and then analyze the equilibrium efforts and optimal contest design in four‐solver contests. The results suggest that the optimal design depends on the combined effects of the reward, effort sensitivity, and cost coefficiency. Elimination and nonelimination contests can be optimal under different conditions. Furthermore, we extend the equilibrium analysis to competitions with n>4$n>4$ contestants and investigate the optimal design with numerical studies. The most interesting result is that the elimination contest with feedback from the organizer is an ideal option for a budget‐constrained enterprise that seeks an innovative solution from the public for a complex innovation project. Also, the optimal number of contestants in the second stage is not always two when feedback is combined with elimination. [ABSTRACT FROM AUTHOR]