Optimal Decision Rules Research Articles

Quickest Search and Learning Over Correlated Sequences: Theory and Application

Consider a set of information sources, each generating a sequence of independent and identically distributed random variables over time. Each information source generates its data according to one of the two possible distributions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . Due to potential physical couplings that govern the information sources, the underlying distribution of each sequence depends on those of the rest. Hence, the underlying distributions form a dependence kernel. Due to uncertainties in the physical models, however, the dependence kernel is not fully known. The objective is to design a sequential decision-making procedure that identifies a sequence generated according to F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> with the fewest number of measurements. Earlier analyses of such search problems have demonstrated that the optimal design of the sequential rules strongly hinges on knowing the dependence kernel precisely. Motivated by the premise that the dependence kernel is not known, this paper designs a sequential inference mechanism that forms two intertwined inferential decisions for identifying a sequence of interest and learning the parameters of the dependence kernel. This paper devises three strategies that place different levels of emphasis on each of these inference goals. Optimal decision rules are characterized, and their performance is evaluated analytically. Also, the application of the proposed framework to wideband spectrum sensing is discussed. Finally, numerical evaluations are provided to compare the performance of the framework to those of the relevant existing literature.

Optimal Data Center Scheduling for Quality of Service Management in Sensor-Cloud

The proposed work concentrates on the networking facets of sensor-cloud infrastructures—one of the first attempts of its kind. In a sensor-cloud, multiple sets of physical sensor nodes that are activated based on an application demand, in turn give rise to multiple distinct virtual sensors (VSs). The VSs are considered to span across multiple geographical regions; thereby, depositing the data (from each of the VS) to the closest cloud data center (DC). Quite obviously, multiple geospatial DCs get involve with an application. However, the principle of sensor-cloud is to store and conglomerate the data from various VSs, before they can be provisioned as Sensors-as-a-Service (Se-aaS). The assortation of data occurs within a single Virtual Machine (VM) (or in some cases multiple VMs) residing inside a particular DC. This work addresses the problem of scheduling a particular DC that congregates data from various VSs, and transmit the same to the end-user application. The work follows the general pairwise choice framework of the Optimal Decision Rule. The scheduling of the DC is performed under several network constraints, such as data migration cost, data delivery cost, and service delay of an application that ensures the preservation of the Quality-of-Service (QoS) and maintenance of the user satisfaction. The work quantifies the effective QoS of Se-aaS and determines an optimal decision rule for electing a particular DC. While arriving at a collective decision, the work incorporates the fallible decision making ability of a DC; thereby, excluding the loss of generality. Experimental results depict that the proposed algorithm for generating the optimal decision rule finds applicability in real-time cloud computing scenarios.

Decisions Under Persuasion

Many decisions are made based on persuasion. In the persuasion process, self-interested agents produce information to convince an evaluator to approve their proposals. Whether an evaluator will discount the agents’ suggestions and reject their proposal is neither clear nor obvious. We highlight that persuasion efforts do not necessarily invalidate the value of agents’ information production. Specifically, our study sheds light on why evaluators say “yes” to proposals even if self-interested agents have the intention to persuade the evaluator. The agents are reluctant to discover unfavorable information, which increases the probability of misidentifying bad projects as good ones. However, their efforts in producing favorable information allow the evaluator to identify more good projects out of a pool of unobservable good and bad projects. Following agents’ suggestions can be an optimal decision rule as it takes advantage of agents’ information to identify good projects.

An LP based approximate dynamic programming model to address airline overbooking under cancellation, refund and no-show

In this paper we simultaneously address four constraints relevant to airline revenue management problem: flight cancellation, customer no-shows, overbooking, and refunding. We develop a linear program closely related to the dynamic program formulation of the problem, which we later use to approximate the optimal decision rule for rejecting or accepting customers. First, we give a novel proof that the optimal objective function of this linear program is always an upper bound for the dynamic program. Secondly, we construct a decision rule based on this linear program and prove that it is asymptotically optimal under certain circumstances. Finally, using Monte Carlo simulation, we demonstrate that, numerically, the result of the linear programming policy presented in this paper has a short distance to the upper bound of the optimal answer, which makes it a fairly good approximate answer to the intractable dynamic program.

Optimal Decision Fusion Under Order Effects

Abstract This paper studies an optimal decision fusion problem with a group of human decision makers when an order effect is present. The order effect refers to situations wherein the process of decision making by a human is affected by the order of decisions. In our set-up, all human decision makers, called observers, receive the same data which is generated by a common but unknown hypothesis. Then, each observer independently generates a sequence of decisions which are modeled by employing non-commutative probabilistic models of the data and their relation to the unknown hypothesis. The use of non-commutative probability models is motivated by recent psychological studies which indicate that these non-commutative probability models are more suitable for capturing the order effect in human decision making, compared with the classical probability model. A central decision maker (CDM) receives (possibly a subset of) the observers’ decisions and decides on the true hypothesis. The considered problem becomes an optimal decision fusion problem with observations modeled using a non-commutative (Von Neumann) probability model. The structure of the optimal decision rule at the CDM is studied under two scenarios. In the first scenario, the CDM receives the entire history of the observers’ decisions whereas in the second scenario, the CDM receives only the last decision of each observer. The perfromance of the optimal fusion rule is numerically evaluated and compared with the optimal fusion rule derived when using a classical probability model.

Early Cancer Detection in Blood Vessels Using Mobile Nanosensors.

In this paper, we propose using mobile nanosensors (MNSs) for early stage anomaly detection. For concreteness, we focus on the detection of cancer cells located in a particular region of a blood vessel. These cancer cells produce and emit special molecules, so-called biomarkers, which are symptomatic for the presence of anomaly, into the cardiovascular system. Detection of cancer biomarkers with conventional blood tests is difficult in the early stages of a cancer due to the very low concentration of the biomarkers in the samples taken. However, close to the cancer cells, the concentration of the cancer biomarkers is high. Hence, detection is possible if a sensor with the ability to detect these biomarkers is placed in the vicinity of the cancer cells. Therefore, in this paper, we study the use of MNSs that are injected at a suitable injection site and can move through the blood vessels of the cardiovascular system, which potentially contain cancer cells. These MNSs can be activated by the biomarkers close to the cancer cells, where the biomarker concentration is sufficiently high. Eventually, the MNSs are collected by a fusion center (FC), where their activation levels are read and exploited to declare the presence of anomaly. We analytically derive the biomarker concentration in a network of interconnected blood vessels as well as the probability mass function of the MNSs' activation levels and validate the obtained results via particle-based simulations. Then, we derive the optimal decision rule for the FC regarding the presence of anomaly assuming that the entire network is known at the FC. Finally, for the FC, we propose a simple sum detector that does not require knowledge of the network topology. Our simulations reveal that while the optimal detector achieves a higher performance than the sum detector, both proposed detectors significantly outperform a benchmark scheme that uses fixed nanosensors at the FC.

On the Optimality of Likelihood Ratio Test for Prospect Theory-Based Binary Hypothesis Testing

In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to cognitively distort probabilities and costs based on some weight and value functions, respectively. It is proved that the LRT may or may not be an optimal decision rule for prospect theory based binary hypothesis testing and conditions are derived to specify different scenarios. In addition, it is shown that when the LRT is an optimal decision rule, it corresponds to a randomized decision rule in some cases; i.e., nonrandomized LRTs may not be optimal. This is unlike Bayesian binary hypothesis testing in which the optimal decision rule can always be expressed in the form of a nonrandomized LRT. Finally, it is proved that the optimal decision rule for prospect theory based binary hypothesis testing can always be represented by a decision rule that randomizes at most two LRTs. Two examples are presented to corroborate the theoretical results.

A robust loss function for classification with imbalanced datasets

Based on minimizing misclassification cost, a new robust loss function is designed in this paper to deal with the imbalanced classification problem under noise environment. It is nonconvex but maintains Fisher consistency. Applying the proposed loss function into support vector machine (SVM), a robust SVM framework is presented which results in a Bayes optimal classifier. However, nonconvexity makes the model difficult to optimize. We develop an alternative iterative algorithm to solve the proposed model. What’s more, we analyze the robustness of the proposed model theoretically from a re-weighted SVM viewpoint and the obtained optimal solution is consistent with Bayesian optimal decision rule. Furthermore, numerical experiments are carried out on databases that are drawn from UCI Machine Learning Repository and a practical application. With two different types of noise environments, one with label noise and one with feature noise, experiment results show that on these two databases the proposed method achieves better generalization results compared to other SVM methods.

Bagging and deep learning in optimal individualized treatment rules.

An ENsemble Deep Learning Optimal Treatment (EndLot) approach is proposed for personalized medicine problems. The statistical framework of the proposed method is based on the outcome weighted learning (OWL) framework which transforms the optimal decision rule problem into a weighted classification problem. We further employ an ensemble of deep neural networks (DNNs) to learn the optimal decision rule. Utilizing the flexibility of DNNs and the stability of bootstrap aggregation, the proposed method achieves a considerable improvement over existing methods. An R package "ITRlearn" is developed to implement the proposed method. Numerical performance is demonstrated via simulation studies and a real data analysis of the Cancer Cell Line Encyclopedia data.

Adjustable Robust Optimization via Fourier–Motzkin Elimination

We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be cast as static robust optimization problems via Fourier–Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broad class of ARO problems. A scheme based on a blending of classical FME and a simple linear programming technique that can efficiently remove redundant constraints is developed to reformulate ARO problems. This generic reformulation technique enhances the classical approximation scheme via decision rules, and it enables us to solve adjustable optimization problems to optimality. We show via numerical experiments that, for small-sized ARO problems, our novel approach finds the optimal solution. For moderate- or large-sized instances, we eliminate a subset of the adjustable variables, which improves the solutions obtained from linear decision rules.

A Bayesian Machine Learning Approach for Optimizing Dynamic Treatment Regimes

ABSTRACTMedical therapy often consists of multiple stages, with a treatment chosen by the physician at each stage based on the patient’s history of treatments and clinical outcomes. These decisions can be formalized as a dynamic treatment regime. This article describes a new approach for optimizing dynamic treatment regimes, which bridges the gap between Bayesian inference and existing approaches, like Q-learning. The proposed approach fits a series of Bayesian regression models, one for each stage, in reverse sequential order. Each model uses as a response variable the remaining payoff assuming optimal actions are taken at subsequent stages, and as covariates the current history and relevant actions at that stage. The key difficulty is that the optimal decision rules at subsequent stages are unknown, and even if these decision rules were known the relevant response variables may be counterfactual. However, posterior distributions can be derived from the previously fitted regression models for the optimal decision rules and the counterfactual response variables under a particular set of rules. The proposed approach averages over these posterior distributions when fitting each regression model. An efficient sampling algorithm for estimation is presented, along with simulation studies that compare the proposed approach with Q-learning. Supplementary materials for this article are available online.

Flexible capacity planning for engineering systems based on decision rules and differential evolution

Abstract This paper proposes a novel approach to managing capacity planning flexibility in engineering systems based on decision rules and differential evolution (DE) algorithm. A multi-stage capacity expansion problem is formalized based on a decision rule representation. The formalized model can analyze multiple sources of uncertainty simultaneously (e.g., changes in demand and material price) and explicitly consider design principles like economies of scale and learning effect. An evolutionary decision rule optimization framework based on the DE algorithm is proposed to automatically optimize the decision rule for capacity planning. Compared to traditional capacity planning models (e.g., stochastic programming), this work is able to offer a flexible capacity plan under uncertainty assumptions at the system design stage. The output of our approach is a decision rule that provides thresholds/conditions for decision-makers to adaptively adjust decisions at the system deployment stage. In the application of capacity planning for a waste-to-energy system, experimental results show that the decision rules generated by our approach offer a 20% improvement in terms of expected net present value, compared to a fixed capacity plan generated by stochastic programming.

Domain-Weighted Majority Voting for Crowdsourcing.

Crowdsourcing labeling systems provide an efficient way to generate multiple inaccurate labels for given observations. If the competence level or the "reputation," which can be explained as the probabilities of annotating the right label, for each crowdsourcing annotators is equal and biased to annotate the right label, majority voting (MV) is the optimal decision rule for merging the multiple labels into a single reliable one. However, in practice, the competence levels of annotators employed by the crowdsourcing labeling systems are often diverse very much. In these cases, weighted MV is more preferred. The weights should be determined by the competence levels. However, since the annotators are anonymous and the ground-truth labels are usually unknown, it is hard to compute the competence levels of the annotators directly. In this paper, we propose to learn the weights for weighted MV by exploiting the expertise of annotators. Specifically, we model the domain knowledge of different annotators with different distributions and treat the crowdsourcing problem as a domain adaptation problem. The annotators provide labels to the source domains and the target domain is assumed to be associated with the ground-truth labels. The weights are obtained by matching the source domains with the target domain. Although the target-domain labels are unknown, we prove that they could be estimated under mild conditions. Both theoretical and empirical analyses verify the effectiveness of the proposed method. Large performance gains are shown for specific data sets.

Switching from oil to gas production in a depleting field

We derive an optimal decision rule with regards to making an irreversible switch from oil to gas production. The approach can be used by petroleum field operators to maximize the value creation from a petroleum field with diminishing oil production and remaining gas reserves. Assuming that both the oil and gas prices follow a geometric Brownian motion we derive an analytical solution for the exercise threshold. We also propose an explicit solution for the option value that is new to the literature. Numerical examples are used to demonstrate the threshold and option value for a generic petroleum field. Both the threshold and option value solutions are relevant for application to other real options cases with similar features (e.g. other types of switching options or a perpetual spread option).

Method of Verification of Hypothesis about Mean Value on a Basis of Expansion in a Space with Generating Element

In this paper it is proposed an original method for verification of statistical hypotheses about mean values of random quantities. This method is based on Kunchenko stochastic polynomials tool and probabilistic description on a basis of higher order statistics (moments and/or cumulants). There are represented analytical expressions allowing to optimize decision rules using certain qualitive criterion and calculate decision-making error. It is shown polynomial decision rule in case of polynomial power S = 1 corresponds to classic linear decision rule which is used for comparative analysis. By means of multiple statistical experiments (Monte–Carlo method) obtained results of Neumann–Pierson criterion show proposed polynomial decision rules are characterized by increased accuracy (decrease of the 2nd genus errors probability) in compare to linear processing. The method efficiency increases with increase of stochastic polynomial order increase of degree of random quantities distribution difference from Gaussian probabilities distribution law.

Sparse learning for Intrapartum fetal heart rate analysis

Fetal Heart Rate (FHR) monitoring is used during delivery for fetal well-being assessment. Classically based on the visual evaluation of FIGO criteria, FHR characterization remains a challenging task that continuously receives intensive research efforts. Intrapartum FHR analysis is further complicated by the two different stages of labor (dilation and active pushing). Research works aimed at devising automated acidosis prediction procedures are either based on designing new advanced signal processing analyses or on efficiently combining a large number of features proposed in the literature. Such multi-feature procedures either rely on a prior feature selection step or end up with decision rules involving long lists of features. This many-feature outcome rule does not permit to easily interpret the decision and is hence not well suited for clinical practice. Machine-learning-based decision-rule assessment is often impaired by the use of different, proprietary and small databases, preventing meaningful comparisons of results reported in the literature. Here, sparse learning is promoted as a way to perform jointly feature selection and acidosis prediction, hence producing an optimal decision rule based on as few features as possible. Making use of a set of 20 features (gathering ‘FIGO-like’ features, classical spectral features and recently proposed scale-free features), applied to two large-size (respectively ≃1800 and ≃500 subjects), well-documented databases, collected independently in French and Czech hospitals, the benefits of sparse learning are quantified in terms of: (i) accounting for class imbalance (few acidotic subjects), (ii) producing simple and interpretable decision rules, (iii) evidences for differences between the temporal dynamics of active pushing and dilation stages, and (iv) of validity/generalizability of decision rules learned on one database and applied to the other one.

The Likelihood of the Consistency of Collective Rankings Under Preferences Aggregation with Four Alternatives Using Scoring Rules: A General Formula and the Optimal Decision Rule

In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limit probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

Link-Quality Aware Path Selection in the Presence of Proactive Jamming in Fallible Wireless Sensor Networks

In this paper, we propose a mechanism to ensure the proper functioning of a wireless sensor network (WSN) in the presence of static and proactive jammer within the network. Existing research works have primarily focused on the detection of jammer node within the network and ameliorating its consequent effects on the network. However, these countermeasures to mitigate the effect of the jammer suffer from certain limitations as WSNs are primarily resource constrained and most of the countermeasures are computationally intensive. The objective of this paper is to prevent the disruption of the network in the presence of jamming by bypassing the jammed zone and setting up alternative paths. The alternative paths are chosen with the maximum link quality in order to maintain the quality of service of the network even after jamming. This paper proposes Link-quality Aware Path SElection ( LAPSE ) algorithm that chooses alternative paths based on the optimal link quality. LAPSE is based on optimal decision rule and its design considers the fallible nature of the nodes while choosing/rejecting a particular link. Finally, the performance of the proposed algorithm, LAPSE, is evaluated in terms of the network parameters—packet delivery rate, network throughput, transmission energy, node lifetime, and network lifetime. Results indicate that the performance of LAPSE is significantly better than the existing jamming avoidance algorithms.

GBOIN: A Unified Model-Assisted Phase I Trial Design Accounting for Toxicity Grades, and Binary or Continuous End Points

SummaryThe landscape of oncology drug development has recently changed with the emergence of molecularly targeted agents and immunotherapies. These new therapeutic agents appear more likely to induce multiple low or moderate grade toxicities rather than dose limiting toxicities. Various model-based dose finding designs and toxicity severity scoring systems have been proposed to account for toxicity grades, but they are difficult to implement because of the use of complicated dose–toxicity models and the requirement to refit the model at each decision of dose escalation and de-escalation. We propose a generalized Bayesian optimal interval design, gBOIN, that accommodates various existing toxicity grade scoring systems under a unified framework. As a model-assisted design, gBOIN derives its optimal decision rule on the basis of the exponential family of distributions but is carried out in a simple way as the algorithm-based design: its decision of dose escalation and de-escalation involves only a simple comparison of the sample mean of the end point with two prespecified dose escalation and de-escalation boundaries. No model fitting is needed. We show that gBOIN has the desirable finite property of coherence and a large sample property of consistency. Numerical studies show that gBOIN yields good performance that is comparable with or superior to that of some existing, more complicated model-based designs. A Web application for implementing gBOIN is freely available from http://www.trialdesign.org.

Necessary Condition-Based Detector for Generalized Space Shift Keying MIMO Systems

In this letter, we present a low-complexity detection algorithm for generalized space shift keying MIMO systems. First, the maximum likelihood detection is posed as a binary quadratic programming (BQP) problem. Then, we derive an optimal decision rule based on the necessary global optimality condition of BQP. Using this rule, most entries of solution can be determined optimally with only O(3N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ) per-bit complexity. Furthermore, taking advantage of the determined entries, the original programming can be reduced to a smaller-scale one only including the undetermined entries. Finally, we can use some conventional detectors to solve the remained small-scale problem with a lower complexity. Simulation results substantiate the performance of the proposed detector.