Distributionally Robust Selection of the Best

In this paper, we introduce the semi-stochastic model for dealing with input uncertainty in optimization problems. This model is a hybrid between the overly pessimistic online model and the highly optimistic stochastic (or Bayesian) model. In this model, the algorithm can obtain only limited stochastic information about the future (i.e. about the input distribution)---as the amount of stochastic information we make available to the algorithm grows from no information to full information, we interpolate between the online and stochastic models. The central question in this framework is the trade-off between the performance of an algorithm, and the stochastic information that it can access. As a first step towards understanding this trade-off, we consider the ski-rental problem in the semi-stochastic setting. More precisely, given a desired competitive ratio, we give upper and lower bounds on the amount of stochastic information required by a deterministic algorithm for the ski-rental problem to achieve that competitive ratio.

Outpatient workload in China

A widely acknowledged challenge in ranking and selection is how to allocate the simulation budget such that the probability of correction selection (PCS) is maximized. However, there is yet another challenge: when the input distributions are estimated using finite real-world data, simulation output is subject to input uncertainty and we may fail to identify the best system even using infinite simulation budget. We propose a new formulation that captures the tradeoff between collecting input data and running simulations. To solve the formulation, we develop an algorithm for two-stage allocation of finite budget. We use numerical experiment to demonstrate the performance of our algorithm.

To use simulation models to study the behaviors of stochastic systems, one needs to specify the distribution of the input random variables. However, specifying this distribution precisely is typically difficult and even impossible in practice. The issue is known as input uncertainty in the simulation literature, and it has been considered and studied extensively in recent years. In this paper, we model the uncertainty by an ambiguity set that is defined based on the likelihood ratio between the true (unknown) distribution and the nominal distribution (i.e., the best estimate), and develop a robust simulation (RS) approach that estimates the worst-case values of performance measures of the random simulation output when the true distribution varies in the ambiguity set. We show that the RS approach is computationally tractable, and the corresponding results reveal important information of the stochastic systems and help decision makers make better decisions.

Simulation is often used to study stochastic systems. A key step of this approach is to specify a distribution for the random input. This is called input modeling, which is important and even critical for simulation study. However, specifying a distribution precisely is usually difficult and even impossible in practice. This issue is called input uncertainty in simulation study. In this paper we study input uncertainty when using simulation to estimate important performance measures: expectation, probability, and value-at-risk. We propose a robust simulation (RS) approach, which assumes the real distribution is contained in a certain ambiguity set constructed using statistical divergences, and simulates the maximum and the minimum of the performance measures when the distribution varies in the ambiguity set. We show that the RS approach is computationally tractable and the corresponding results can disclose important information about the systems, which may help decision makers better understand the systems.

In this paper we examine methods for the selection of measurement subsets using information theory. These methods are applied to an overdetermined inverse problem typical to high‐resolution spectrometry. The optimal selection of spectral channels becomes especially important with the recent introduction of high spectral resolution satellite instruments for monitoring the atmosphere. The vast amount of data these instruments provide in a continuous fashion makes it necessary to carefully consider which channels are really needed in the retrieval of geophysical quantities. Two optimization problems in channel selection, both taking the information content of the measurements as a criterion, are defined and discussed. The concept of the information content of each individual measurement is introduced, and basic analytical relations are derived. A sequential deselecting procedure is developed, and a fast algorithm for channel selection is proposed. These provide approximations to solutions of the optimization problem. The efficiencies of these selection procedures and a sequential selection procedure [Rodgers, 1996] are compared by means of a Monte Carlo generation of the forward model in a low‐dimensional case. As a real application, the selection of the most informative spectral channels for GOMOS measurements is considered.

Hospital beds are one of the most critical medical resources. Large hospitals in China have caused bed utilization rates to exceed 100% due to long-term extra beds. To alleviate the contradiction between the supply of high-quality medical resources and the demand for hospitalization, in this paper, we address the decision of choosing a case mix for a respiratory medicine department. We aim to generate an optimal admission plan of elective patients with the stochastic length of stay and different resource consumption. We assume that we can classify elective patients according to their registration information before admission. We formulated a general integer programming model considering heterogeneous patients and introducing patient priority constraints. The mathematical model is used to generate a scientific and reasonable admission planning, determining the best admission mix for multitype patients in a period. Compared with model II that does not consider priority constraints, model I proposed in this paper is better in terms of admissions and revenue. The proposed model I can adjust the priority parameters to meet the optimal output under different goals and scenarios. The daily admission planning for each type of patient obtained by model I can be used to assist the patient admission management in large general hospitals.

This study investigates the inventory routing problem (IRP) under ambiguous demand distribution. Compared with existing research that assumes the demand distribution is either predefined or lies in an ambiguity set, we adopt a globalized distributionally robust approach. We construct both inner and outer ambiguity sets to describe distributional ambiguity, regardless of whether retailer demand follows a discrete distribution or an unspecified type. This approach ensures performance is maintained even when the demand distribution extends beyond the inner ambiguity set. Additionally, we introduce more flexible soft constraints, coupled with a budget violation metric, to manage the gaps between actual holding and penalty costs and the budgets at retailers, particularly when demand distribution lies outside the inner ambiguity set. Analysis of our model demonstrates its ability to generalize distributionally robust, robust, or stochastic IRP models through appropriate input settings, and thereby we establish the bounds for the objective values of these models. Numerical studies, based on a real-case scenario, show that the delivery solutions from our proposed models are more effective in mitigating the impact of retailer demand uncertainty and achieve superior out-of-sample performance compared to other benchmark models.

Input refers the effect of driving a simulation with input distributions that are based on real-world data. At WSC 2012, Ankenman and Nelson presented a quick-and-easy experiment to assess the overall effect of input uncertainty on simulation output. When their method reveals that input uncertainty is substantial, then the natural follow-up questions are which input distributions contribute the most to input uncertainty, and from which input processes would it be most beneficial to collect more data? To answer these questions Ankenman and Nelson proposed a sequence of additional experiments that are in no sense quick. In this paper we provide a follow-up analysis that requires no additional simulation experiments beyond the overall assessment, and yet provides more information than Ankenman and Nelson. Numerical illustrations are provided.

In recent years, Machine Learning (ML) models have led to a substantial improvement in hydrological predictions. It appears these models can distill information from catchment properties that is relevant for the relationship between meteorological drivers and streamflow, which has so far eluded hydrologists.In the first part of this talk, I shall demonstrate some of our attempts towards understanding these improvements. Utilising Autoencoders and intrinsic dimension estimators, we have shown that the wealth of available catchment properties can effectively be summarised into merely three features, insofar as they are relevant for streamflow prediction. Hybrid models, which combine the flexibility of ML models with mechanistic mass-balance models, are equally adept at predicting as pure ML models but come with only a few interpretable interior states. Combining these findings will, hopefully, bring us closer to understanding what these ML models seem to have 'grasped'.In the second part of the talk, I will address the issue of uncertainty quantification. I contend that error modelling should not be attempted on the residuals. Rather, we should model the errors where they originate, i.e., on the inputs, model states, and/or parameters. Such stochastic models are more adept at expressing the intricate distributions exhibited by real data. However, they come at the cost of a very large number of unobserved latent variables and thus pose a high-dimensional inference problem. This is particularly pertinent when our models include ML components. Fortunately, advances in inference algorithms and parallel computing infrastructure continue to extend the limits on the number of variables that can be inferred within a reasonable timeframe. I will present a straightforward example of a stochastic hydrological model with input uncertainty, where Hamiltonian Monte Carlo enables a comprehensive Bayesian inference of model parameters and the actual rain time-series simultaneously.

Sensitivity and Uncertainty

Subject headings biopsy,needle/cytology; liver neoplasms/pathology Ultrasonography, CT and magnetic resonance have been widely used in the diagnosis of liver diseases in the past 20 years, but the final definite diagnosis of liver space occupying (LSO)lesions can not be made only by imaging methods. Ultrasonograp hy has been used in combination with fine-needle aspiration biopsy in the diagn osis of liver diseases since the 1970s. The accuracy of differential diagnosis of both benign and malignant lesions could reach 88.8%. Since then, this technique h as become popular in the diagnosis of LOS lesions in large hos pitals in China. Dr. Edoute reported 279 cases of LSO lesions in 1976-1988 diagnosed by non-ultrasonically-guided aspiration biopsy, which is of great importance in the diagnosis of LSO lesions by ultraso nically-guided fine-needle aspiration biopsy.

ABSTRACTThe distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust strategy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we study distributionally robust MDPs where ambiguity sets for the uncertain parameters are of a format that can easily incorporate in its description the generalized moment as well as statistical distance information of the uncertainty. In this way, we generalize existing works on distributionally robust MDPs with generalized-moment-based and statistical-distance-based ambiguity sets to incorporate information from the former class such as moments and dispersions to the latter class that critically depends on empirical observations of the uncertain parameters. We show that under this format of ambiguity sets, the resulting distributionally robust MDP remains tractable under mild technical conditions and a distributionally robust strategy can be constructed by solving a sequence of one-stage convex optimization subproblems through a Bellman type backward induction.

In many practical problems, simulation models are used to support complex decision-making processes comparing hundreds or thousands of solutions. These problems typically have a key objective but the final decision may be dependent on other factors, which cannot be incorporated into the simulation model. In such cases, decision-makers may request a short list of ‘good’ solutions, which work well for the main objective and satisfy one or more chance constraints. While fully sequential ranking and selection procedures can be effective at solving these problems, surveys of experimentation practice suggest that they are under-utilized, potentially due to difficulties automating commercial software. We develop an approach with just two stages of replications. The approach, which has been designed to cope with the use of common random numbers, draws on ideas from indifference zones and makes use of bootstrapping to find a subset of high quality solutions. A Python implementation is freely available.

BackgroundBacterial bloodstream infections (BSIs) cause high morbidity and mortality worldwide in humans, but the pathogenic spectrum varies from region to region. Long-term monitoring of the pathogenic spectrum and changes in bacterial antibiotic resistance is hugely important for effective clinical therapy and infection control. This study examined the data for BSIs in Tongji Hospital, one of the largest teaching hospitals in China, in an attempt to gain better understanding of bacterial antibiotic resistance in China, focusing on central China.MethodsData from Tongji Hospital for a 20-year period (1998–2017) were used for a retrospective analysis to understand the pathogenic spectrum of BSIs and the changes occurring in antimicrobial resistance in central China. The disk diffusion and E test methods were used for antimicrobial susceptibility testing according to Clinical & Laboratory Standards Institute methodologies, and the data were analyzed by WHONET 5.6 software.ResultsThe isolated pathogens mainly came from hospitalized patients not treated in intensive care units (ICUs), and accounted for 81.5% of the total (9130/11200). The most common Gram-negative and Gram-positive bacterial BSI-causing pathogens were Escherichia coli and Staphylococcus aureus, respectively. The detection rate for methicillin-resistant S. aureus (MRSA) in the hospitalized non-ICU patients increased from 8.4% in 1998–2002 to 63% in 2013–2017, while the detection rate for carbapenem-resistant (CR) Klebsiella pneumoniae was below 5% in 1998–2012 but increased to 34.9% in 2013–2017. In contrast, worryingly, the detection rate for CR K. pneumoniae in ICU patients increased from 0% in 2013 to 75% in 2016. E. coli displayed the highest sensitivity rates to imipenem, meropenem and amikacin, all of which were > 90%, followed by cefoxitin at > 80%, and cefoperazone/sulbactam at > 70%. K. pneumoniae isolates were most sensitive to imipenem, meropenem and amikacin antibiotics, with sensitivity rates exceeding 60%. S. aureus isolates were most sensitive to vancomycin, teicoplanin and trimethoprim/sulfamethoxazole, with sensitivity rates exceeding 90%.ConclusionsBSIs caused by CR K. pneumoniae clearly posed a severe challenge to infection control and treatment of ICU and non-ICU patients in this retrospective study, while MRSA was an issue for non-ICU patients.