Showing papers presented at "Conference on Information Sciences and Systems in 2017"

Electric load forecasting in smart grids using Long-Short-Term-Memory based Recurrent Neural Network

Abstract: Electric load forecasting plays a vital role in smart grids. Short term electric load forecasting forecasts the load that is several hours to several weeks ahead. Due to the nonlinear, non-stationary and nonseasonal nature of the short term electric load time series in small scale power systems, accurate forecasting is challenging. This paper explores Long-Short-Term-Memory (LSTM) based Recurrent Neural Network (RNN) to deal with this challenge. LSTM-based RNN is able to exploit the long term dependencies in the electric load time series for more accurate forecasting. Experiments are conducted to demonstrate that LSTM-based RNN is capable of forecasting accurately the complex electric load time series with a long forecasting horizon. Its performance compares favorably to many other forecasting methods.

On deep learning-based channel decoding

Abstract: We revisit the idea of using deep neural networks for one-shot decoding of random and structured codes, such as polar codes. Although it is possible to achieve maximum a posteriori (MAP) bit error rate (BER) performance for both code families and for short codeword lengths, we observe that (i) structured codes are easier to learn and (ii) the neural network is able to generalize to codewords that it has never seen during training for structured, but not for random codes. These results provide some evidence that neural networks can learn a form of decoding algorithm, rather than only a simple classifier. We introduce the metric normalized validation error (NVE) in order to further investigate the potential and limitations of deep learning-based decoding with respect to performance and complexity.

Interest, energy and physical-aware coalition formation and resource allocation in smart IoT applications

Abstract: In this paper, the problem of coalition formation among Machine-to-Machine (M2M) communication type devices and the resource management problem is addressed. Each M2M device is characterized by its energy availability, as well as by differentiated interests to communicate with other devices based on the Internet of Things (IoT) application that they jointly serve. Physical ties among devices also exist based on their physical distance proximity and communication channel quality. Those three factors: energy availability, interest and physical ties, are considered into the coalition formation process and the coalition-head selection. Each M2M device is associated with a holistic utility function, which appropriately represents its degree of satisfaction with respect to Quality of Service (QoS) prerequisites fulfillment. Given the created coalitions among the M2M devices, a distributed power control framework is proposed towards determining each M2M device's optimal transmission power in order to fulfill its QoS prerequisites. The performance of the proposed approach is evaluated via modeling and simulation and its superiority compared to other state of the art approaches is illustrated.

Muscle tuning and preferred movement path - a paradigm shift

Abstract: In the last 40 years, the scientific debate around running injuries and running shoes has been dominated by two paradigms, the ‘impact’ and the ‘pronation’ paradigms. However, the development of running shoe technologies aimed at reducing impact forces and pronation has not led to a decline of running-related injuries. This article recommends to abandon the ‘impact’ and ‘pronation’ paradigms due to a lack of biomechanical and epidemiological evidence and instead suggests a shift to new paradigms: ‘Muscle tuning’ and the ‘preferred movement path’. These paradigms represent new approaches to understanding the biomechanical patterns of each individual runner and how they are controlled by the neuromuscular system. Experimental evidence in support of the ‘muscle tuning’ and ‘preferred movement path’ paradigms are presented and discussed regarding their relevance for running performance, injuries, and footwear. Finally, this paper proposes that the concept of ‘functional groups’ should be used and further developed to overcome the challenge that groups of individuals respond differently to footwear interventions. First, groups of individuals who behave similarly (functional groups) should be identified. Second, running shoes should be selected to match the characteristics of the identified functional groups in order to optimize the beneficial effects of running shoes for improving running performance and reducing the risk of running injuries.

Scientific approaches to technological officiating aids in game sports

Abstract: An increasing number of sports use, what we call, technological umpiring aids to support their umpires and referees respectively. In order to create a basis for further investigations, the aim of this review is to survey the respective literature to extract universal issues of these aids, which are used in different ways in a wide range of settings. Therefore we identified 23 studies, of which the majority was published in the current decade. These studies also embraced, beside empirical works, contributions of the fields of philosophy and jurisprudence. Based on the approaches and findings of the selected studies we identified seven major issues: the underlying phenomena, usage patterns, accuracy, standard of review, influence on the nature of the game, material as well as immaterial costs and the amount of authority that is granted to the umpiring aid. Further, we found regularly some overlapping between these issues, but also that some matters of interest haven’t even been touched so far, for example studying the influence of technological umpiring aids on stakeholders’ opinions. Empirical as well as theoretical evaluations of technological umpiring aids have to deal with this complexity. As this seems to be neglected currently, we suggest that further studies should show awareness of this in their approaches as well as in their conclusions.

A game theory based secure model against Black hole attacks in Opportunistic Networks

Abstract: Opportunistic Networks, a subset of Delay Tolerant Networks (DTNs), do not have a predefined source to destination end-to-end path and hence, offer a multitude of challenges with regard to security. In this paper a Potential Threat (PT) based security protocol has been developed which models the characters of the incoming nodes on the basis of swift delivery of messages, their reputation and history. Thus, it secures the network against malicious nodes. The PT based mechanism also trumps previous security based protocols as the basis of its conception is rooted in evolutionary game theory and in evaluating the malicious nodes as a player with certain goals and intentions. A comprehensive comparison with an existing protocol has also been done. The simulations of the protocol are run on the Opportunistic Network Environment (ONE) simulator with Spray and Wait as the base routing protocol. It is observed that the security of the network is much more vigorous with the proposed PT based security protocol. The network also benefits in terms of delivery probability, data packets dropped, network overhead ratio and the average transmission delay.

A game-theoretic analysis of label flipping attacks on distributed support vector machines

Abstract: Distributed machine learning algorithms play a significant role in processing massive data sets over large networks. However, the increasing reliance on machine learning on information and communication technologies makes it inherently vulnerable to cyber threats. This work aims to develop secure distributed algorithms to protect the learning from adversaries. We establish a game-theoretic framework to capture the conflicting goals of a learner who uses distributed support vector machines (DSVM) and an attacker who is capable of flipping training labels. We develop a fully distributed and iterative algorithm to capture real-time reactions of the learner at each node to adversarial behaviors. The numerical results show that DSVM is vulnerable to attacks, and their impact has a strong dependence on the network topologies.

A survey on Arabic Optical Character Recognition and an isolated handwritten Arabic Character Recognition algorithm using encoded freeman chain code

Abstract: Optical Character Recognition (OCR) is the process of identifying text in an image and convert it into a digital form. Several approaches have been attempted to accurately recognize characters in printed Arabic language. This survey focuses on OCR in handwritten Arabic language. We will describe the general difficulties in Arabic language text, the main process of a typical OCR system and some enhancements to Arabic OCR systems. We will also describe a novel approach for identifying handwritten isolated Arabic characters using encoded Freeman chain code. Several handwritten Arabic characters were trained and tested, and the preliminary experimental results are promising.

Improving ADMM-based optimization of Mixed Integer objectives

Abstract: We consider a class of mixed integer programs where the problem is convex except for a vector of discrete variables. Two methods based on the Alternating Direction Method of Multipliers (ADMM) are presented. The first, which has appeared in the recent literature, duplicates the discrete variable, with one copy allowed to vary continuously. This results in a simple projection, or rounding, to determine the discrete variable at each iteration. We introduce an alternate method, whereby part of the objective is replaced by a new variable instead. When the objective satisfies a certain condition, this allows the update of the discrete variables to be handled separately for each one, thus maintaining linear complexity of this update, while incorporating some of the objective into the update. Initial comparisons on examples for which both methods are applicable show that the latter exhibits clear improvements in both performance and run-time.

Fundamental limits of location privacy using anonymization

Abstract: In [1]–[3], the concept of perfect location privacy is defined and sufficient conditions for achieving it were obtained when anonymization is used. In this paper, necessary conditions for perfect privacy are obtained. Specifically, we prove that the previous sufficient bounds are tight, and thus we obtain the threshold for achieving perfect location privacy using anonymization. First, we assume that a user's current location is independent from her past locations. Using this i.i.d model, we show that if the adversary collects more than equation anonymous observations, then the adversary can successfully recover the users' locations with high probability. Here, n is the number of users in the network and r is the number of all possible locations that users can go to. Next, we model users' movements using Markov chains to better model real-world movement patterns. We show similar results if the adversary collects more than equation observations, where |E| is the number of edges in the user's Markov chain model.

Equilibrium strategies for an OFDM network that might be under a jamming attack

Abstract: Wireless networks are vulnerable to many malicious attacks, like active interference, due to the shared and open-access nature of the wireless medium. One difficulty in dealing with interference attacks is the lack of knowledge about whether the attack will be present or not. In this paper, we investigate how the lack of knowledge of whether jamming will or will not be used against an OFDM communication impacts the anti-jamming strategy one should use. Our model can be applied more generally to jamming attacks with a fixed frequency where, at each time slot, it is unknown whether the interference will be used or not. We have derived the equilibrium strategy in waterfilling form, and shown that the obtained solution includes as boundary cases two classical solutions in OFDM transmission for the case where there is no adversary, and the case where the adversary attacks with certainty. Uniqueness of the equilibrium strategies is proven, and an algorithm for finding the parameters of the waterfilling equations is developed. The efficiency of the algorithm is illustrated by numerical examples.

Towards a macromodel for Packetized Energy Management of resistive water heaters

Abstract: This paper presents a state bin transition (macro)model for a large homogeneous population of thermostatically controlled loads (TCLs). The energy use of these TCLs is coordinated with a novel bottom-up asynchronous, anonymous, and randomizing control paradigm called Packetized Energy Management (PEM). A macro-model for a population of TCLs is developed and then augmented with a timer to capture the duration and consumption of energy packets and with exit-ON/OFF dynamics to ensure consumer quality of service. PEM permits a virtual power plant (VPP) operator to interact with TCLs through a packet request mechanism. The VPP regulates the proportion of accepted packet requests to allow tight tracking of balancing signals. The developed macro-model compares well with (agent-based) micro-simulations of TCLs under PEM and can be represented by a controlled Markov chain.

Network topology risk assessment of stealthy cyber attacks on advanced metering infrastructure networks

Abstract: Advanced Metering Infrastructure (AMI) plays a crucial role in Demand Side Management (DSM) in Smart Grid systems. It provides real-time, two-way communication capabilities between a utility/load aggregator and consumers. The communication infrastructure, by virtue of topological weaknesses, is vulnerable to cyber attacks that are undetectable or stealthy. This work investigates the topological vulnerabilities of AMI networks that could result in potential theft of electricity through hacked smart meters. In particular, a provably correct risk assessment protocol is proposed to identify completely the individual nodes in mesh network based AMIs that are potential targets of such economically motivated stealthy cyber attacks. The protocol proposed utilizes knowledge of the network topology and data obtained from existing system monitoring technologies. A case study is provided to demonstrate the protocol and its effectiveness.

Polar codes for covert communications over asynchronous Discrete Memoryless Channels

Abstract: We develop a covert communication scheme for binary-input asynchronous Discrete Memoryless Channels based on binary polar codes, in which legitimate parties exploit uncertainty created by both the channel noise and the time of transmission. The proposed code jointly ensures reliable communication for a legitimate receiver and low probability of detection with respect to an adversary, both observing noisy versions of the codewords. Binary polar codes are used to shape the weight distribution of codewords and ensure that the average weight decays as the block length grows. The performance of the proposed code is limited by the speed of polarization, which in turns controls the decay of the average codeword weight with the block length. Although the proposed construction falls short of achieving the performance of random codes, it inherits the low-complexity properties of polar codes.

A hierarchical Stackelberg-coalition formation game theoretic framework for cooperative spectrum leasing

Abstract: The problem of cooperative spectrum leasing among multiple primary users (PUs) and secondary users (SUs) is considered. A hybrid Stackelberg-coalition formation game theoretic algorithm is proposed that enables the PUs to identify a group of cooperative SUs by looking at the reputation history of their cooperative behavior. The coalition formation approach also promotes collaboration among the SUs to provide them with a higher chance of spectrum access. The Stackelberg game determines the optimum time allocation among the PUs and SUs individual transmission as well as cooperation time. The results show the performance enhancement of spectrum leasing model, particularly in mobile and dynamic network with a diverse range of SUs initial credits and channel conditions.

SEIR: A Stackelberg game based approach for energy-aware and incentivized routing in selfish Opportunistic Networks

Abstract: Opportunistic Networks (OppNets) are a sub-class of wireless Delay Tolerant Networks (DTNs) that can be utilized in areas of sporadic network connectivity. OppNets consist of a network of mobile devices that cooperate with each other to forward messages from the source to the destination. However, in a practical real-world setting, nodes behave selfishly and do not choose to be cooperative all throughout. This selfish behavior could be exhibited due to a variety of reasons, ranging from lower energy levels of the node to memory or buffer shortages. Thus, it is imperative to develop incentivizing mechanisms that reward nodes that are cooperative and penalize nodes that are selfish. In this paper, we present a novel routing protocol called SEIR that is able to reduce energy consumption of nodes as well as incentivize them to participate in message routing. SEIR is based on the Stackelberg game theoretic model and decides the optimal reward to give relay nodes to eliminate their selfishness and improve chances of successful message delivery. Subsequent simulations performed show that SEIR outperforms existing routing protocols in terms of energy efficiency and message delivery in an OppNet with selfish nodes.

Examining the functionality of peripheral vision: From fundamental understandings to applied sport science

Abstract: In sports, it is important not only to locate gaze on the right location to utilize the high acuity of foveal vision, but also to attend to other objects in the environment without looking directly at them, accordingly, using peripheral vision. Peripheral vision becomes especially important if, for example, the processing of information from more than one location (e.g. players) is decisive in making accurate decisions. Since such decisions generally must be made under high spatio-temporal demands, costly eye-movements might be advantageously avoided by using peripheral vision for information pick-up from multiple cues. In a series of studies, we aimed to translate the demands found in sports and to investigate the functionality of peripheral vision in a well-controlled experimental paradigm, the multiple object tracking (MOT) task. MOT was implemented in a dual task, along with an additional event-detection task. The present article first presents an overview of sport-specific studies focusing on the functionality of peripheral vision and following, summarizes a series of three published MOT studies. These studies show that peripheral vision is used for simultaneous target monitoring and target-change detection and that visual and attentional demands affect gaze anchoring and change-detection rates. Results also reveal a dysfunctionality of saccades, and further suggest an event- and distance-optimized gaze-anchoring position. In the final portion of this article, we derive specific applications for future sports-specific research. Specifically, we suggest to: (a) use dual-task situations in sport-specific settings, such as monitoring multiple players in soccer and playing a pass at specific moments, (b) investigate the costs of saccades in sports situations with high spatio-temporal demands, as in martial arts, and finally, (c) manipulate attentional and visual demands. For each of these avenues of research, we sketch sports-specific experiments currently being conducted in our research group.

Head movements during visual exploration of natural images in virtual reality

Abstract: During natural visual exploration, both head and eye movements can be used to redirect gaze to new points of interest. In order to better understand the role of head movements in this process, we recorded subjects' head orientations while they explored a set of natural images from five different categories using virtual reality head-mounted displays. While head movements are likely influenced by image content or image saliency, here we focus on their stereotyped patterns, which have a consistent relationship between the amplitude, duration, and peak velocity of movements. We find that most head movements occur along the cardinal directions, and furthermore, the head position and head velocity distributions are similar across image categories. Our results provide greater insight into the kinematics of head movements during visual exploration in virtual reality environments.

Massive MIMO for 5G: Overview and the road ahead

Abstract: Massive MIMO is the currently most compelling sub-6 GHz wireless access technology for 5G. Since its inception about a decade ago, it has evolved from a wild “academic” idea to one of the most vibrant research topics in the wireless communications community, as well as a main work item in 5G standardization. The concept is to equip base stations with arrays of many antennas that serve many terminals simultaneously, in the same time-frequency resource. The arrays have attractive form factors: in the 2 GHz band, a halfwave-length-spaced rectangular array with 200 dual-polarized elements is about 1.5 × 0.75 meters large. Massive MIMO operates in TDD mode and the downlink beamforming exploits the uplink-downlink reciprocity of radio propagation. Specifically, the base station array uses channel estimates obtained from uplink pilots transmitted by the terminals to learn the channel in both directions. This makes Massive MIMO entirely scalable with respect to the number of base station antennas. Base stations operate autonomously, with no sharing of payload data or channel state information with other cells. In this talk I will discuss the development of Massive MIMO over the last five years, and outline the most important research problems ahead.

Subset-codebook precoding for 1-bit massive multiuser MIMO

Abstract: We consider a massive multiuser MIMO downlink scenario with 1-bit digital-to-analog converters. QPSK information symbols are transmitted to the users by a channel-dependent mapping of the symbols to 1-bit DAC signals that are transmitted from each base station (BS) antenna. The mapping is selected to emulate the desired information bearing QPSK symbols at the users. Non-linear precoding is considered, where the mapping from the information symbols to the transmit antenna signals is selected based on the combination of information symbols. First, a linear quantized precoder is used to create tentative transmit symbols. For each combination of information symbols, a subset of antennas is selected, and an exhaustive search over a limited size codebook of precoding alternatives is performed. The resulting method significantly lowers the error floor caused by quantization, with a complexity that is linear in the number of transmit antennas.

Adaptive non-uniform compressive sampling for time-varying signals

Abstract: In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among coefficients more intelligently. To this aim, a Bayesian inference method is proposed that does not require any prior knowledge of importance levels of coefficients or sparsity of the signal. Our numerical simulations show that ANCS is able to achieve the desired non-uniform recovery of the signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce the number of required measurements significantly.

The economics of competition and cooperation between MNOs and MVNOs

Abstract: In this work, we consider the economics of the interaction between Mobile Virtual Network Operators (MVNOs) and Mobile Network Operators (MNOs). We investigate the incentives of an MNO for offering some of her resources to an MVNO instead of using the resources for her own. We formulate the problem as a sequential game. We consider a market with one MNO and one MVNO, and a continuum of undecided endusers. We assume that EUs have different preferences for the MNO and the MVNO. These preferences can be because of the differences in the service they are offering or the reluctance of an EU to buy her plan from one of them. We assume that the preferences also depend on the investment level the MNO and the MVNO. We show that there exists a unique interior SPNE, i.e. the SPNE by which both SPs receive a positive mass of EUs, and characterize it. We also consider a benchmark case in which the MNO and the MVNO do not cooperate, characterize the unique SPNE of this case, and compare the results of our model to the benchmark case to assess the incentive of the MNO to invest in her infrastructure and to offer it to the MVNO.

Distribution network management based on optimal power flow: Integration of discrete decision variables

Abstract: Recent developments in the optimal power flow (OPF) problem for radial networks open the promise of a more sophisticated management of the distribution end of the power grid. Such sophistication is required to operate efficiently new, dynamic energy resources being introduced at the micro scale. To be useful, however, optimization tools must also accommodate pre-existing management technologies which involve discrete decisions. In particular for topology reconfiguration, we extend recent references to provide a new, exact characterization of admissible topologies, explaining in detail its integration with OPF. We also propose methods to include discrete decisions on transformer taps and capacitor banks, as well as ON/OFF loads, to yield mixed-integer nonlinear programs with convex integer relaxations. We report simulation results on the application of this methodology to a distribution network in Uruguay.

Centralized class specific dictionary learning for wearable sensors based physical activity recognition

Abstract: With recent progress in pervasive healthcare, physical activity recognition with wearable body sensors has become an important and challenging area in both research and industrial communities. Here, we address a novel technique for a sensor platform that performs physical activity recognition by leveraging a class specific regularizer term into the dictionary pair learning objective function. The proposed algorithm jointly learns a synthesis dictionary and an analysis dictionary in order to simultaneously perform signal representation and classification once the time-domain features have been extracted. Specifically, the class specific regularizer term ensures that the sparse codes belonging to the same class will be concentrated thereby proving beneficial for the classification stage. In order to develop a more practical approach, we employ a combination of an alternating direction method of multipliers and a l 1 − l s minimization method to approximately minimize the objective function. We validate the effectiveness of our proposed model by employing it on two activity recognition problem and an intensity estimation problem, both of which include a large number of physical activities. Experimental results demonstrate that classifiers built in this dictionary learning based framework outperforms state of art algorithms by using simple features, thereby achieving competitive results when compared with classical systems built upon features with prior knowledge.

Soft-decision based distributed detection over correlated sensing channels

Abstract: This paper proposes a new framework that performs spectrum sensing in soft decision based distributed detection systems while considering correlated sensors' readings. The main contribution is formulating the problem into a nonlinear integer programming problem for which the genetic algorithm is further applied to find a suboptimal solution. This framework is able to handle both soft and hard decisions while assuming correlation for any number of sensors, and hence largely extends the scenarios being considered in previous works. The results show that our scheme outperforms previous schemes and approaches the centralized detection scheme performance in terms of probability of error.

Why do referees end their careers and which factors determine the duration of a referee’s career?

Abstract: Against the background that the number of referees has been falling in recent years, the German Football Association (DFB) needs to answer two key questions: (i) Why do referees end their careers, and, (ii) which factors determine the duration of referee careers? We studied these questions using data from a questionnaire study of former referees. Results of estimating linear regression models and a Cox model show that the duration of a typical referee career depends, among other factors, on how a referee thinks that the career developing according to his or her plan, and on whether the referee is successful in coping with insults, threats, and violence. The “survival rate” of a referee increases in the subjective evaluation of the importance of football-specific know-how. Approximately 39 % of the former referees stated that the end of their referee career could have been prevented.

An adaptive neural network approach for automatic modulation recognition

Abstract: This paper presents a novel adaptive approach to automatic modulation recognition (AMR) using artificial neural networks (ANN). Two types of features have been combined to ensure the robustness of detection for all types of modulations. An adaptive system of feature extraction and neural network is designed to distinguish the target modulation between 5 different modulation types namely AM, ASK, FSK, PSK and QAM, distinctly. In a novel approach by introducing modulation pairs, the decision is made based on the majority of each individual output of the 10 minimally complex - binary ANNs which have been trained using sufficient and wide range of modulation parameters for each pair of modulation types. We have made safe error criterions to indicate the performance of our design, and simulation results express the performance and accuracy of proposed system model according to detection error versus signal level, and detection error versus number of iterations through convergence.

Spectrum efficiency maximization using primal-dual adaptive algorithm for distributed mobile devices caching over edge computing networks

Abstract: The information-centric network techniques enable the in-network caching mechanism to cache the popular data contents in the mobile devices. Even though each mobile device's caching memory can be limited, caching in mobile devices offers the great potential of caching capability because of the massive mobile devices. Using caching in mobile devices, a mobile user can obtain its requested files from other mobile users through device-to-device (D2D) communication instead of the remote data-source provider, which significantly reduces the duplicate data traffics in the core network and through base stations. In this paper, we use the distributed mobile devices caching, where we randomly distribute and store the popular data contents in mobile devices of a cellular network. To avoid the interference among D2D communications, we partition the entire wireless cell into several squarelets and only activate the D2D connections within each squarelet. Then, we derive the expected number of mobile users in a squarelet and develop a primal-dual adaptive algorithm to maximize the overall spectrum efficiency for these mobile users with unknown wireless channel conditions. To evaluate the performance of our proposed adaptive algorithm, we compare our obtained spectrum efficiency with the spectrum efficiency under the optimal situation where all wireless channel conditions are given. Our proposed algorithm can guarantee the smallest ratio for the obtained spectrum efficiency under these two situations, showing the performance lower bound of our proposed adaptive algorithm.

The IOC and Olympic bids from democracies and authoritarian regimes – A socioeconomic analysis and strategic insights

Abstract: In this socio-economic study, the bidding processes for the Winter Olympic Games in 2022 and the Summer Games in 2024 and 2028 serve as case studies to scrutinize the decisions linked to the bidding process in democratic countries and authoritarian states. Transaction cost economics is employed as a lens to outline the problems that the findings pose for the IOC and to understand why the organization has to keep a certain proximity to authoritarian states for strategic reasons. This measure can be considered an insurance policy because of the high and likely sunk ex ante transaction costs that characterize bids from democratic countries. It will become apparent that keeping good working relations with authoritarian governments helps the IOC to secure the future of its main revenue driver, the Olympic Games, thus providing for its own future. Furthermore, the IOC’s decision to include the Summer Olympic Games in 2028 in the bidding process originally geared towards the Games in 2024 will be outlined as a logical consequence of the developments that are analysed in this study. This strategic move will turn out to be a logical consequence of the developments that are analysed in this paper.

Efficient computation of the Fisher information matrix in the EM algorithm

Abstract: The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. When the MLE is available, we naturally want the Fisher information matrix (FIM) of unknown parameters. However, one of the limitations of the EM algorithm is that the FIM is not an automatic by-product of the algorithm. In this paper, we construct a simple Monte Carlo-based method requiring only the gradient values of the function we obtain from the E step and basic operations. The key part of our method is to utilize the simultaneous perturbation stochastic approximation method to estimate the Hessian matrix from the gradient of the conditional expectation of the complete-data log-likelihood function.