Local Decision Rules Research Articles

Risk-Adaptive Local Decision Rules

The decision rules developed in this paper help managers recognize relationships between data and decisions and prescribe courses of actions that are guaranteed near-optimal as well as transparent and interpretable. Transparency and interpretability are prerequisites for any decision support tool that needs to be conveyed, understood, and justified broadly. An understanding of the relationship between data and decisions is important for managers as they identify the critical factors, prioritize their focus, guide the resource allocation, and develop mitigation strategies for handling data uncertainty. The relationship between data and decision can be especially convoluted for combinatorial optimization problems. We consider simple decisions rules that ensure transparency and interpretability, but also allow nearly any continuous decision rule within a unified framework of analysis. Our preferred adaptive minimum decision rule prescribes decisions with 1% relative suboptimality gap, on average, even when facing distributional shifts in out-of-sample testing.

Target Detection in Underwater Sensor Networks by Fusion of Active and Passive Measurements

Underwater target detection plays an important role in the ocean exploration. However, the strong noise and weak communication properties of underwater environment make it challenging to achieve the detection task. This paper is concerned with a non-cooperative target detection issue by fusion of active and passive measurements in underwater sensor networks (USNs). The detection procedure is mainly divided into two phases, i.e., local decision and external fusion. For the first phase, the active and passive measurements are both employed to develop a Chi-square test based local decision rule, where the membership functions are conducted to bias the weight of each measurement in accordance with signal reliability. Based on this, we formulate the communication topology of USNs as a two-layer multi-group (2LMG) structure, such that a hybrid Bayesian fusion algorithm is designed in the second phase to fuse the detection decisions from different sensor nodes. It is worth mentioning that, our solution can integrate the active and passive measurements by local decision, and more importantly, it can improve the detection accuracy and reduce the communication load through the 2LMG-based fusion algorithm. Finally, simulation results are performed to validate the effectiveness of our solution in this paper.

Exploiting auto-encoders for explaining black-box classifiers

Recent years have witnessed the rise of accurate but obscure classification models that hide the logic of their internal decision processes. In this paper, we present a framework to locally explain any type of black-box classifiers working on any data type through a rule-based model. In the literature already exists local explanation approaches able to accomplish this task. However, they suffer from a significant limitation that implies representing data as a binary vectors and constraining the local surrogate model to be trained on synthetic instances that are not representative of the real world. We overcome these deficiencies by using autoencoder-based approaches. The proposed framework first allows to generate synthetic instances in the latent feature space and learn a latent decision tree classifier. After that, it selects and decodes the synthetic instances respecting local decision rules. Independently from the data type under analysis, such synthetic instances belonging to different classes can unveil the reasons for the classification. Also, depending on the data type, they can be exploited to provide the most useful kind of explanation. Experiments show that the proposed framework advances the state-of-the-art towards a comprehensive and widely usable approach that is able to successfully guarantee various properties besides interpretability.

Local Indiscernibility Relation Reduction for Information Tables

Attribute reduction comes from machine learning and is an important component of rough set theory. Research on attribute reduction has produced many important achievements. The aim of attribute reduction is to reduce the complexity of data while retaining its original characteristics to the greatest extent. The concept of attribute reduction is of great significance in machine learning research. In previous studies, a variety of attribute reduction definitions have been proposed according to different rules. Based on the binary relations among objects and local decision rules, this paper describes a local indiscernibility relation reduction for information tables. The discernibility matrix for the proposed reduction is established, and examples for single- and multi-decision classes are presented to illustrate that the proposed local indiscernibility relation reduction can be applied to decision tables. According to the reduction concept developed in this paper, and considering a heuristic algorithm for calculating the significance of attributes and a binary integer programming algorithm based on the discernibility matrix, three reduction algorithms are proposed. Experiments are conducted using four classifiers and a number of publicly available datasets. A comparison of the experimental results presented in this paper demonstrates the feasibility of the proposed algorithms.

Optimal fusion rule for distributed detection with channel errors taking into account sensors' unreliability probability when protecting coastlines

In this paper, algorithms that make decisions on the presence or absence of penetration on a protected object with both ideal and non-ideal communication channels are synthesised and analysed. Local sensor decision rules based on an energy detector and its performance characteristics are presented. We determine the dependencies of the total error probability on the energy parameter taking into account the energy emitted from the target at the level of local sensors and the channel's signal-to-noise ratio. The gain of the optimal fusion rule in efficiency compared to known fusion rules such as the LRT-BER and Chair-Varshney fusion rule is shown. The detection algorithm under possible sensor failure and its detection performance is also presented. With the unknown target location on a coastline, the detection rules are given and the detection performance is analysed.

GLocalX - From Local to Global Explanations of Black Box AI Models

Artificial Intelligence (AI) has come to prominence as one of the major components of our society, with applications in most aspects of our lives. In this field, complex and highly nonlinear machine learning models such as ensemble models, deep neural networks, and Support Vector Machines have consistently shown remarkable accuracy in solving complex tasks. Although accurate, AI models often are “black boxes” which we are not able to understand. Relying on these models has a multifaceted impact and raises significant concerns about their transparency. Applications in sensitive and critical domains are a strong motivational factor in trying to understand the behavior of black boxes. We propose to address this issue by providing an interpretable layer on top of black box models by aggregating “local” explanations. We present GLocalX, a “local-first” model agnostic explanation method. Starting from local explanations expressed in form of local decision rules, GLocalX iteratively generalizes them into global explanations by hierarchically aggregating them. Our goal is to learn accurate yet simple interpretable models to emulate the given black box, and, if possible, replace it entirely. We validate GLocalX in a set of experiments in standard and constrained settings with limited or no access to either data or local explanations. Experiments show that GLocalX is able to accurately emulate several models with simple and small models, reaching state-of-the-art performance against natively global solutions. Our findings show how it is often possible to achieve a high level of both accuracy and comprehensibility of classification models, even in complex domains with high-dimensional data, without necessarily trading one property for the other. This is a key requirement for a trustworthy AI, necessary for adoption in high-stakes decision making applications.

Dependent Randomization in Parallel Binary Decision Fusion

We consider a parallel decentralized detection system employing a bank of local detectors (LDs) to access a commonly-observed phenomenon. The system makes a binary decision about the phenomenon, accepting one of two hypotheses (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (“absent” ) or H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (“present” )). The kth LD uses a local decision rule to compress its local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> into a binary local decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ; u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> =0 if the kth LD accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = 1 accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . The kth LD sends its decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> over a noiseless dedicated channel to a Data Fusion Center (DFC). The DFC combines the local decisions it receives from n LDs (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,...,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) into a single binary global decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0=</sub> 0 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> =1 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ). If each LD uses a single deterministic local decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> from the local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) and the DFC uses a single deterministic global decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> from n local decisions), the team receiver operating characteristic (ROC) curve is in general non-concave. The system's performance under a Neyman-Pearson criterion may then be suboptimal in the sense that a mixed strategy may yield a higher probability of detection when the probability of false alarm is constrained not to exceed a certain value, α>0. Specifically, a “dependent randomization” detection scheme can be applied in certain circumstances to improve the system's performance by making the ROC curve concave. This scheme requires a coordinated and synchronized action between the DFC and the LDs. In this study, we specify when dependent randomization is needed, and discuss the proper response of the detection system if synchronization between the LDs and the DFC is temporarily lost.

Detection Fusion of Weak Signal under Chaotic Noise Based on Distributed System

In this paper, the problem of signal detection under chaotic noise was considered in the distributed detection fusion system. The problem which is urgent and difficult has important research value. A new detection and fusion mechanism for weak signal under chaotic noise based on a distributed system is proposed. Due to the short‐term predictability of chaotic signals and their sensitivity to small disturbances, observation of each local sensor is reconstructed in phase space according to the Takens delay embedding theorem. The locally weighted regression (LOWESS) model is used to fit the observation of each local sensor in the phase space. Thus, the chaotic noise is stripped out from the observation, and the fitting error without chaotic noise is regarded as the new observation of each local sensor. Based on the new observation without chaotic noise, an optimization model aiming at minimizing the Bayesian risk of the fusion center is established. Under the condition that the observations of local sensors are conditionally independent, the fusion rule and the sensor decision rules are derived. An algorithm is proposed to obtain the fusion rule and local decision rules. The simulation results show that the proposed signal detection and fusion algorithm can effectively detect weak signals under chaotic noise background. Specifically, the fusion performance is obviously better than that of local sensors with low SNR.

Economic viability, energy and nutrient balances of site-specific fertilisation for citrus

Core objectives of precision agriculture are to improve the economic and environmental performance of agricultural systems. This study used a long-term experiment in citrus to assess whether site-specific nutrient management was successful from these two perspectives. Variable and uniform rate fertilisation treatments were implemented in intercalated strips across two 25 ha citrus groves in São Paulo state, Brazil. To generate variable rate recommendations, information from soil fertility and yield maps were fed into a traditional recommendation formula used by growers. The experiment was carried out for five growing seasons. An economic, energy and nutrient balance analysis was conducted. Variable rate application increased average yield in grove 1 but sometimes reduced yield in grove 2. As a consequence, profit was increased by 34.7% (US$ ∗ 318.5 ha −1 year −1 ) in grove 1. In grove 2, profit was reduced by 8.5% (US$ −97.4 ha −1 year −1 ). Embodied fertiliser energy was reduced by 34% in grove 1 and by 29% in grove 2. Nutrient surplus after harvest was reduced by approximately 20–70% depending on the nutrient. Maps of economic and environmental indicators showed that site-specific management did not reduce the spatial variability of the system's performance. The variable rate strategy tested could be improved by using local decision rules rather than generalised recommendation formulas. Site-specific analysis of profit, embodied energy and nutrient balance help to assess system performance and can potentially improve decisions in site-specific nutrient management. • A five-year study was used to evaluate variable rate fertilisation in orange groves. • Economic and environmental performance were spatially variable within orange groves. • Environmental indicators were usually superior with variable rate application. • Mixed economic results were found for variable rate application. • Variable rate application must not rely on global recommendation rules.

Local temporal-spatial multi-granularity learning for sequential three-way granular computing

Based on multiple levels of granularity, the notion of sequential three-way granular computing focuses on a multiple stages of thinking, problem-solving, and information processing in threes. This paper interprets, represents, and implements sequential three-way granular computing by a framework of temporal-spatial multi-granularity learning, which is described with the temporality of data and the spatiality of parameters. In real-world decision-making, such a sequential approach is useful to make faster decisions for some objects with the lower cost of decision process and the acceptable accuracy when information is insufficient or unavailable. However, the cost of time-consuming computation for hierarchical multilevel granularity is our concern. To address this issue, we utilize a local strategy to accelerate a sequence of neighborhood-based granulation induced by Gaussian kernel function. Subsequently, local three-way decision rules are investigated based on the Bayesian minimum risk criterion. Moreover, by the construction of a novel local trisection model, we propose a local sequential approach of three-way granular computing under a temporal-spatial multilevel granular structure. Finally, a series of comparative experiments between global and local perspectives is carried out to verify the effectiveness of our proposed models.

Fusion-Based Cooperative Support Identification for Compressive Networked Sensing

This paper proposes a fusion-based cooperative support identification scheme for distributed compressive sparse signal recovery via resource-constrained wireless sensor networks. The proposed support identification protocol involves: (i) local sparse sensing for economizing data gathering and storage, (ii) local binary decision making for partial support knowledge inference, (iii) binary information exchange among active nodes, and (iv) binary data aggregation for support estimation. Then, with the aid of the estimated signal support, a refined local decision is made at each node. Only the measurements of those informative nodes will be sent to the fusion center, which employs a weighted $\ell_1$-minimization for global signal reconstruction. The design of a Bayesian local decision rule is discussed, and the average communication cost is analyzed. Computer simulations are used to illustrate the effectiveness of the proposed scheme.

Uncovering the decision rules behind collective foraging in spider monkeys

Unlike animals living in cohesive groups, those in groups with high fission–fusion dynamics can separate temporarily from other group members. While mechanisms underlying collective decisions are not well understood, it is possible that these separations occur by a divergence of interests between individuals. We evaluated the collective foraging decisions made by a group of Geoffroy's spider monkeys, Ateles geoffroyi, in a tropical forest in the Yucatan peninsula, Mexico. We assessed whether each individual's centrality in the social network, years living in the group, age, sex and social relationships affected the collective decisions. We examined two collective dynamics: foraging movements and arrivals to novel food patches, and in the latter, identified knowledgeable and naive individuals. In both dynamics, spider monkeys exhibited partially shared leadership influenced by individual attributes, particularly the centrality in the social network, age and time in the group. These attributes have been associated with ecological knowledge. In arrivals to novel food patches, individuals most likely to have information about food resources (i.e. central individuals and males) had a greater likelihood to be followed, suggesting an influence of social information on the tendency to follow others. Also, we show evidence that social information could accelerate the arrival of naive individuals to these patches. Collective foraging dynamics in our study group seem to arise from local rules that each individual follows when foraging: when a naive individual needs social information to forage, it will follow the individual that is more likely to have this information, i.e. a central individual or a male; otherwise, when it is not possible or necessary to use social information, naive individuals will follow a partner with which they have a strong social relationship. Thus, the interaction between local decision rules and the structure of the social network could drive collective coordination in fission–fusion dynamics.

Hierarchical copula-based distributed detection

Abstract Detection is one of the main tasks of wireless sensor networks (WSN) in many applications. The data of network nodes are usually assumed to be statistically independent since considering dependence results in intractable decision rules. However, detection performance degrades when the correlation rises. In this paper, a practically popular configuration of WSNs is considered where homogeneous nodes - each of them consisting of several heterogeneous sensors - send their processed data to a fusion center (FC). Here, data fusion should be implemented in two levels: 1. Nodes fuse the data of their sensors. 2. The FC takes the final decision by fusing the data of the nodes. We propose to implement a copula-based local decision rule in nodes. At the FC, it is shown that the correlation among nodes’ decisions can be resolved by simply adding the logarithm of the sum of nodes’ decisions to the statistic of the FC. The proposed distributed detection scheme is evaluated in a practical example of fire detection. Simulations show that considering correlation by implementing the proposed methods would improve detection performance.

Coded Quickest Classification With Applications in Bandwidth-Efficient Smart Grid Monitoring

Cyber-physical systems, such as smart grids, have received lots of attention recently. Unfortunately, security breaches in cyber-physical systems can result in catastrophic consequences, thus needing to be carefully monitored. For example, abnormal voltage quality events, which are more likely to happen because of unstable renewable energy sources in smart grids, harm delicate electronic devices. We thus focus on the quickest classification, or multi-hypothesis quickest change detection, which jointly detects and classifies multiple abnormal events. Both the classification delay and misclassification probability need to be low. Multiple smart meters are adopted, where each meter transmits its local decision to a fusion center for making the final decision. For energy saving, the bandwidth (link capacity) between each meter and the fusion center is limited to be one bit. Moreover, some meters may be faulty and mislead the final decision. To combat these faulty meters under the limited bandwidth, a code-based framework for quickest classification is proposed. Our contribution is two-fold. First, a new local decision rule based on the stochastic ordering theory is proposed. Compared with existing matrix-cumulative-sums algorithm, the newly proposed local decision rule has lower complexity and comparable performance. Second, a new fusion method based on codebook switching and minimum Hamming distance rule is developed. Compared with existing fault-tolerant methods, the newly-developed method can significantly lower the misclassification probabilities.

Independent Log-Linear Learning in Potential Games With Continuous Actions

Game theoretic learning in multiagent systems is a rapidly developing area of research. It gained popularity since the wide range of optimization problems in multiagent systems can be reformulated in terms of potential games, where the set of potential function maximizers represents the set of optimal states. The crucial point of such approach is the design of local decision rules that leads the system to a potential function maximizer. In this paper, we consider the independent log-linear learning procedure applicable to continuous action potential games. We provide the analysis of the stochastic stability of potential function maximizers in case of continuous action games. To analyze the behavior of the underlying Markov chain, we develop a new method for approximating the initial chain with continuous states by chains whose long run properties can be established. After that, we study the finite time behavior of the algorithm with a definite time-dependent parameter and obtain settings that guarantee an efficient implementation of the learning procedure under consideration.

Toward Information Privacy for the Internet of Things: A Nonparametric Learning Approach

In an Internet of things network, multiple sensors send information to a fusion center for it to infer a public hypothesis of interest. However, the same sensor information may be used by the fusion center to make inferences of a private nature that the sensors wish to protect. To model this, we adopt a decentralized hypothesis testing framework with binary public and private hypotheses. Each sensor makes a private observation and utilizes a local sensor decision rule or privacy mapping to summarize that observation independently of the other sensors. The local decision made by a sensor is then sent to the fusion center. Without assuming knowledge of the joint distribution of the sensor observations and hypotheses, we adopt a nonparametric learning approach to design local privacy mappings. We introduce the concept of an empirical normalized risk, which provides a theoretical guarantee for the network to achieve information privacy for the private hypothesis with high probability when the number of training samples is large. We develop iterative optimization algorithms to determine an appropriate privacy threshold and the best sensor privacy mappings, and show that they converge. Finally, we extend our approach to the case of a private multiple hypothesis. Numerical results on both synthetic and real data sets suggest that our proposed approach yields low error rates for inferring the public hypothesis, but high error rates for detecting the private hypothesis.

Synthesizing decision rules from multiple information sources: a neighborhood granulation viewpoint

In the big data era, data are usually described by multiple information sources in many practical application fields, and it is infeasible way to mine interesting knowledge from a centralized huge source directly after aggregating all information sources, due to the problems of massive data, privacy concerns, and potential transmission cost. To mine decision rules from multiple information sources, therefore, we can mine local decision rules at different local information sources, and then put these rules to form a set of global decision rules. In this paper, we first present a formal representation of decision rule, which depends on the neighborhood granulation of each sample from the viewpoint of granular computing. Then, we obtain the weight of each local information source based on the consensus measure principle between local information sources. Finally, a weighting model for mining global decision rules via synthesizing all local decision rules is proposed. Extensive experimental results demonstrate that the proposed decision rules synthesization model is effective and scalable.

A multi-agent system based on reactive decision rules for solving the caregiver routing problem in home health care

Home Health Care (HHC) services are growing worldwide. HHC providers that employ their caregivers have to manage operational decisions such as assigning patients to caregivers and planning the caregivers’ routes. Centralized “off-line” approaches are generally used to deal with both these problems. In this paper, we solved the caregiver routing problem in a dynamic and distributed way using a Multi-agent system (MAS) to simulate caregiver behavior. Four decision rules were developed for the caregivers: NPR (Nearest Patient Rule), NRR (No-wait Route Rule), SRR (Shortest Route Rule), and BRR (Balanced Route Rule). These decision rules were implemented and tested on a multi-agent platform to assess their performances. We designed an experimental plan based on case studies that represent different sizes of HHC provider inspired from real-world examples. The results obtained show the relevance of using local decision rules to plan the caregiver's route.

LD approach to asymptotically optimum sensor fusion

Sensor fusion maybe used to improve detection performance in applications. The idea is to make decisions locally, and then transmit them to a global fusion centre where the global decision is made. For global decision making, Bayes or Neyman–Pearson reasoning determines the optimal use of the local decision variables. However, the determination of the local decision variables that minimise global error probability is intractable. In this study, the authors design local decisions that maximise the mutual information between a binary decision variable and the underlying binary state. This serves as a benchmark against which globally optimum solutions maybe compared. Then, they use the theory of large deviations (LDs) to determine a local decision rule that minimises asymptotic global error probability. The use of LD produces a one-dimensional search on a receiver operating characteristic curve to equalise the error exponents for local false alarm and miss probabilities. Many interesting properties of the LD solution are proved. Numerical results illustrate the performance of the asymptotically optimum decision rule for finite collections of sensors.

Optimal local sensor decision rule for target detection with channel fading statistics in multi-sensor networks

In this paper, we investigate the optimal local sensor decision rule based on non-ideal transmission channels between local sensors and the fusion center for distributed target detection system. The optimality of a likelihood-ratio test (LRT)-based local decision rule at local sensor, which requires only the knowledge of channel statistics instead of instantaneous channel state information (CSI), is established. The coupled local decision rule at each sensor is derived in a closed-form for coherent BPSK and OOK and non-coherent OOK. The iterative person-by-person optimization (PBPO) algorithm is employed to solve the coupled local thresholds. Simulation analysis reveals that the derived thresholds according to the local decision rule are consistent to the exhaustive searching. Furthermore, the detection performance of the system with the proposed optimal local decision rule for different reception modes and modulations is analyzed and compared.