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Whats Strange About Recent Events (WSARE) Weng-Keen Wong (Carnegie Mellon University) Andrew Moore (Carnegie Mellon University) Gregory Cooper (University of Pittsburgh) Michael Wagner (University of Pittsburgh) DIMACS Tutorial on Statistical and Other Analytic Health Surveillance Methods

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Motivation Primary Key DateTimeHospitalICD9ProdromeGenderAgeHome Location Work Location Many more… 1006/1/039:121781FeverM20sNE?… 1016/1/0310:451787DiarrheaF40sNE … 1026/1/0311:031786RespiratoryF60sNEN… 1036/1/0311:072787DiarrheaM60sE?… 1046/1/0312:151717RespiratoryM60sENE… 1056/1/0313:013780ViralF50s?NW… 1066/1/0313:053487RespiratoryF40sSW … 1076/1/0313:572786UnmappedM50sSESW… 1086/1/0314:221780ViralM40s??… : : : : : : : : : : : Suppose we have access to Emergency Department data from hospitals around a city (with patient confidentiality preserved)

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The Problem From this data, can we detect if a disease outbreak is happening?

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The Problem From this data, can we detect if a disease outbreak is happening? Were talking about a non- specific disease detection

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The Problem From this data, can we detect if a disease outbreak is happening? How early can we detect it?

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The Problem From this data, can we detect if a disease outbreak is happening? How early can we detect it? The question were really asking: In the last n hours, has anything strange happened?

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Traditional Approaches What about using traditional anomaly detection? Typically assume data is generated by a model Finds individual data points that have low probability with respect to this model These outliers have rare attributes or combinations of attributes Need to identify anomalous patterns not isolated data points

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Traditional Approaches –Time series algorithms –Regression techniques –Statistical Quality Control methods Need to know apriori which attributes to form daily aggregates for! What about monitoring aggregate daily counts of certain attributes? Weve now turned multivariate data into univariate data Lots of algorithms have been developed for monitoring univariate data:

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Traditional Approaches What if we dont know what attributes to monitor?

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Traditional Approaches What if we dont know what attributes to monitor? What if we want to exploit the spatial, temporal and/or demographic characteristics of the epidemic to detect the outbreak as early as possible?

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Traditional Approaches We need to build a univariate detector to monitor each interesting combination of attributes: Diarrhea cases among children Respiratory syndrome cases among females Viral syndrome cases involving senior citizens from eastern part of city Number of children from downtown hospital Number of cases involving people working in southern part of the city Number of cases involving teenage girls living in the western part of the city Botulinic syndrome cases And so on…

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Traditional Approaches We need to build a univariate detector to monitor each interesting combination of attributes: Diarrhea cases among children Respiratory syndrome cases among females Viral syndrome cases involving senior citizens from eastern part of city Number of children from downtown hospital Number of cases involving people working in southern part of the city Number of cases involving teenage girls living in the western part of the city Botulinic syndrome cases And so on… Youll need hundreds of univariate detectors! We would like to identify the groups with the strangest behavior in recent events.

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Our Approach We use Rule-Based Anomaly Pattern Detection Association rules used to characterize anomalous patterns. For example, a two-component rule would be: Gender = Male AND 40 Age < 50 Related work: –Market basket analysis [Agrawal et. al, Brin et. al.] –Contrast sets [Bay and Pazzani] –Spatial Scan Statistic [Kulldorff] –Association Rules and Data Mining in Hospital Infection Control and Public Health Surveillance [Brossette et. al.]

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WSARE v2.0 Last 24 hours Ignore key Primary Key DateTimeHospitalICD9ProdromeGenderAgeHome Location Work Location Many more… 1006/1/039:121781FeverM20sNE?… 1016/1/0310:451787DiarrheaF40sNE … 1026/1/0311:031786RespiratoryF60sNEN… : : : : : : : : : : : Inputs: 1. Multivariate date/time-indexed biosurveillance- relevant data stream 2. Time Window Length 3. Which attributes to use? Emergency Department Data

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WSARE v2.0 Outputs: 1. Here are the records that most surprise me 2. Heres why 3. And heres how seriously you should take it Primary Key DateTimeHospitalICD9ProdromeGenderAgeHome Location Work Location Many more… 1006/1/039:121781FeverM20sNE?… 1016/1/0310:451787DiarrheaF40sNE … 1026/1/0311:031786RespiratoryF60sNEN… : : : : : : : : : : : Inputs: 1. Multivariate date/time-indexed biosurveillance- relevant data stream 2. Time Window Length 3. Which attributes to use?

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WSARE v2.0 Overview 2.Search for rule with best score 3.Determine p-value of best scoring rule through randomization test All Data 4.If p-value is less than threshold, signal alert Recent Data Baseline 1.Obtain Recent and Baseline datasets

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Step 1: Obtain Recent and Baseline Data Recent Data Baseline Data from last 24 hours Baseline data is assumed to capture non-outbreak behavior. We use data from 35, 42, 49 and 56 days prior to the current day

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Step 2. Search for Best Scoring Rule For each rule, form a 2x2 contingency table eg. Perform Fishers Exact Test to get a p-value for each rule => call this p-value the score Take the rule with the lowest score. Call this rule R BEST. This score is not the true p-value of R BEST because we are performing multiple hypothesis tests on each day to find the rule with the best score Count Recent Count Baseline Age Decile = 34845 Age Decile 3 86220

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The Multiple Hypothesis Testing Problem Suppose we reject null hypothesis when score <, where = 0.05 For a single hypothesis test, the probability of making a false discovery = Suppose we do 1000 tests, one for each possible rule Probability(false discovery) could be as bad as: 1 – ( 1 – 0.05) 1000 >> 0.05

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Step 3: Randomization Test Take the recent cases and the baseline cases. Shuffle the date field to produce a randomized dataset called DB Rand Find the rule with the best score on DB Rand. June 4, 2002C2 June 5, 2002C3 June 12, 2002C4 June 19, 2002C5 June 26, 2002C6 June 26, 2002C7 July 2, 2002C8 July 3, 2002C9 July 10, 2002C10 July 17, 2002C11 July 24, 2002C12 July 30, 2002C13 July 31, 2002C14 July 31, 2002C15 June 4, 2002C2 June 12, 2002C3 July 31, 2002C4 June 26, 2002C5 July 31, 2002C6 June 5, 2002C7 July 2, 2002C8 July 3, 2002C9 July 10, 2002C10 July 17, 2002C11 July 24, 2002C12 July 30, 2002C13 June 19, 2002C14 June 26, 2002C15

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Step 3: Randomization Test Repeat the procedure on the previous slide for 1000 iterations. Determine how many scores from the 1000 iterations are better than the original score. If the original score were here, it would place in the top 1% of the 1000 scores from the randomization test. We would be impressed and an alert should be raised. Estimated p-value of the rule is: # better scores / # iterations

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Two Kinds of Analysis Day by Day If we want to run WSARE just for the current day… …then we end here. Historical Analysis If we want to review all previous days and their p- values for several years and control for some percentage of false positives… …then well once again run into overfitting problems …we need to compensate for multiple hypothesis testing because we perform a hypothesis test on each day in the history

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We only need to do this for historical analysis! False Discovery Rate [Benjamini and Hochberg] Can determine which of these p-values are significant Specifically, given an α FDR, FDR guarantees that Given an α FDR, FDR produces a threshold below which any p-values in the history are considered significant

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WSARE v3.0

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WSARE v2.0 Review 2.Search for rule with best score 3.Determine p-value of best scoring rule through randomization test All Data 4.If p-value is less than threshold, signal alert Recent Data Baseline 1.Obtain Recent and Baseline datasets

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Obtaining the Baseline Recall that the baseline was assumed to be captured by data that was from 35, 42, 49, and 56 days prior to the current day. Baseline

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Obtaining the Baseline Recall that the baseline was assumed to be captured by data that was from 35, 42, 49, and 56 days prior to the current day. Baseline We would like to determine the baseline automatically! What if this assumption isnt true? What if data from 7, 14, 21 and 28 days prior is better?

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Temporal Trends But health care data has many different trends due to –Seasonal effects in temperature and weather –Day of Week effects –Holidays –Etc. Allowing the baseline to be affected by these trends may dramatically alter the detection time and false positives of the detection algorithm

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Temporal Trends From: Goldenberg, A., Shmueli, G., Caruana, R. A., and Fienberg, S. E. (2002). Early statistical detection of anthrax outbreaks by tracking over-the-counter medication sales. Proceedings of the National Academy of Sciences (pp. 5237-5249)

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WSARE v3.0 Generate the baseline… Taking into account recent flu levels… Taking into account that today is a public holiday… Taking into account that this is Spring… Taking into account recent heatwave… Taking into account that theres a known natural Food- borne outbreak in progress… Bonus: More efficient use of historical data

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Conditioning on observed environment: Well understood for Univariate Time Series Time Signal Example Signals: Number of ED visits today Number of ED visits this hour Number of Respiratory Cases Today School absenteeism today Nyquil Sales today

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An easy case Time Signal Dealt with by Statistical Quality Control Record the mean and standard deviation up the the current time. Signal an alarm if we go outside 3 sigmas Mean Upper Safe Range

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Conditioning on Seasonal Effects Time Signal

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Time Signal Fit a periodic function (e.g. sine wave) to previous data. Predict todays signal and 3-sigma confidence intervals. Signal an alarm if were off. Reduces False alarms from Natural outbreaks. Different times of year deserve different thresholds. Conditioning on Seasonal Effects

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Weekly counts of P&I from week 1/98 to 48/00 Example [Tsui et. Al] From: Value of ICD 9–Coded Chief Complaints for Detection of Epidemics, Fu-Chiang Tsui, Michael M. Wagner, Virginia Dato, Chung- Chou Ho Chang, AMIA 2000

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Seasonal Effects with Long-Term Trend Weekly counts of IS from week 1/98 to 48/00. From: Value of ICD 9–Coded Chief Complaints for Detection of Epidemics, Fu-Chiang Tsui, Michael M. Wagner, Virginia Dato, Chung- Chou Ho Chang, AMIA 2000

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Fit a periodic function (e.g. sine wave) plus a linear trend: E[Signal] = a + bt + c sin(d + t/365) Good if theres a long term trend in the disease or the population. Weekly counts of IS from week 1/98 to 48/00. From: Value of ICD 9–Coded Chief Complaints for Detection of Epidemics, Fu-Chiang Tsui, Michael M. Wagner, Virginia Dato, Chung- Chou Ho Chang, AMIA 2000 Called the Serfling Method [Serfling, 1963] Seasonal Effects with Long-Term Trend

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Day-of-week effects From: Goldenberg, A., Shmueli, G., Caruana, R. A., and Fienberg, S. E. (2002). Early statistical detection of anthrax outbreaks by tracking over-the- counter medication sales. Proceedings of the National Academy of Sciences (pp. 5237-5249)

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Day-of-week effects From: Goldenberg, A., Shmueli, G., Caruana, R. A., and Fienberg, S. E. (2002). Early statistical detection of anthrax outbreaks by tracking over-the- counter medication sales. Proceedings of the National Academy of Sciences (pp. 5237-5249) Fit a day-of-week component E[Signal] = a + delta day E.G: delta mon = +5.42, delta tue = +2.20, delta wed = +3.33, delta thu = +3.10, delta fri = +4.02, delta sat = - 12.2, delta sun = -23.42 Another simple form of ANOVA

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Analysis of variance (ANOVA) Good news: If youre tracking a daily aggregate (univariate data)…then ANOVA can take care of many of these effects. But… What if youre tracking a whole joint distribution of events?

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Idea: Bayesian Networks On Cold Tuesday Mornings the folks coming in from the North part of the city are more likely to have respiratory problems Patients from West Park Hospital are less likely to be young On the day after a major holiday, expect a boost in the morning followed by a lull in the afternoon Bayesian Network: A graphical model representing the joint probability distribution of a set of random variables The Viral prodrome is more likely to co-occur with a Rash prodrome than Botulinic

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WSARE Overview 2.Search for rule with best score 3.Determine p-value of best scoring rule through randomization test All Data 4.If p-value is less than threshold, signal alert Recent Data Baseline 1.Obtain Recent and Baseline datasets

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Obtaining Baseline Data Baseline All Historical Data Todays Environment 1.Learn Bayesian Network 2. Generate baseline given todays environment

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Obtaining Baseline Data Baseline All Historical Data Todays Environment 1.Learn Bayesian Network 2. Generate baseline given todays environment What should be happening today given todays environment

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Step 1: Learning the Bayes Net Structure Involves searching over DAGs for the structure that maximizes a scoring function. Most common algorithm is hillclimbing. Initial Structure Add an arcDelete an arcReverse an arc 3 possible operations:

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Step 1: Learning the Bayes Net Structure Involves searching over DAGs for the structure that maximizes a scoring function. Most common algorithm is hillclimbing. Initial Structure Add an arcDelete an arcReverse an arc 3 possible operations: But hillclimbing is too slow and single link modifications may not find the correct structure (Xiang, Wong and Cercone 1997). We use Optimal Reinsertion (Moore and Wong 2002).

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T 1. Select target node in current graph T 2. Remove all arcs connected to T Optimal Reinsertion

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T 3. Efficiently find new in/out arcs T 4. Choose best new way to connect T ? ? ? ?? ? ? ?

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The Outer Loop Until no change in current DAG: Generate random ordering of nodes For each node in the ordering, do Optimal Reinsertion

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The Outer Loop For NumJolts: Begin with randomly corrupted version of best DAG so far Until no change in current DAG: Generate random ordering of nodes For each node in the ordering, do Optimal Reinsertion

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For NumJolts: Begin with randomly corrupted version of best DAG so far The Outer Loop Until no change in current DAG: Generate random ordering of nodes For each node in the ordering, do Optimal Reinsertion Conventional hill-climbing without maxParams restriction

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How is Optimal Reinsertion done efficiently? 1.Create an efficient cache of NodeScore(PS->T) values using ADSearch [Moore and Schneider 2002] 2.Restrict PS->T combinations to those with CPTs with maxParams or fewer parameters 3.Additional Branch and Bound is used to restrict space an additional order of magnitude Scoring functions can be decomposed: P1P2P3 T Efficiency Tricks

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Environmental Attributes Divide the data into two types of attributes: Environmental attributes: attributes that cause trends in the data eg. day of week, season, weather, flu levels Response attributes: all other non- environmental attributes

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Environmental Attributes When learning the Bayesian network structure, do not allow environmental attributes to have parents. Why? We are not interested in predicting their distributions Instead, we use them to predict the distributions of the response attributes Side Benefit: We can speed up the structure search by avoiding DAGs that assign parents to the environmental attributes SeasonDay of WeekWeatherFlu Level

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Step 2: Generate Baseline Given Todays Environment SeasonDay of WeekWeatherFlu Level TodayWinterMondaySnowHigh Season = Winter Day of Week = Monday Weather = Snow Flu Level = High Suppose we know the following for today: We fill in these values for the environmental attributes in the learned Bayesian network Baseline We sample 10000 records from the Bayesian network and make this data set the baseline

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Step 2: Generate Baseline Given Todays Environment SeasonDay of WeekWeatherFlu Level TodayWinterMondaySnowHigh Season = Winter Day of Week = Monday Flu Level = High Suppose we know the following for today: We fill in these values for the environmental attributes in the learned Bayesian network Baseline We sample 10000 records from the Bayesian network and make this data set the baseline Sampling is easy because environmental attributes are at the top of the Bayes Net Weather = Snow

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Why not use inference? With sampling, we create the baseline data and then use it to obtain the p-value of the rule for the randomization test If we used inference, we will not be able to perform the same randomization test and we need to find some other way to correct for the multiple hypothesis testing Sampling was chosen for its simplicity

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Why not use inference? With sampling, we create the baseline data and then use it to obtain the p-value of the rule for the randomization test If we used inference, we will not be able to perform the same randomization test and we need to find some other way to correct for the multiple hypothesis testing Sampling was chosen for its simplicity But there may be clever things to do with inference which may help us. File this under future work

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Simulation NW 100 N 400 NE 500 W 100 C 200 E 300 SW 200 S 200 SE 600 City with 9 regions and different population in each region For each day, sample the citys environment from the following Bayesian Network Date Day of Week Previous Weather Season Previous Flu Level Previous Region Food Condition Previous Region Anthrax Concentration Region Food Condition Region Anthrax Concentration Weather Flu Level

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Simulation DATE DAY OF WEEK SEASON FLU LEVEL WEATHER REGION AGE GENDER Region Grassiness Region Anthrax Concentration Region Food Condition Immune System Outside Activity Has Anthrax Has Flu Has Allergy Has Heart Attack Has Sunburn Has Cold Heart Health Has Food Poisoning Disease ACTION Actual Symptom REPORTED SYMPTOM DRUG For each person in a region, sample their profile

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Visible Environmental Attributes DATE DAY OF WEEK SEASON FLU LEVEL WEATHER REGION AGE GENDER Region Grassiness Region Anthrax Concentration Region Food Condition Immune System Outside Activity Has Anthrax Has Flu Has Allergy Has Heart Attack Has Sunburn Has Cold Heart Health Has Food Poisoning Disease ACTION Actual Symptom REPORTED SYMPTOM DRUG

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Simulation DATE DAY OF WEEK SEASON FLU LEVEL WEATHER REGION AGE GENDER Region Grassiness Region Anthrax Concentration Region Food Condition Immune System Outside Activity Has Anthrax Has Flu Has Allergy Has Heart Attack Has Sunburn Has Cold Heart Health Has Food Poisoning Disease ACTION Actual Symptom REPORTED SYMPTOM DRUG Diseases: Allergy, cold, sunburn, flu, food poisoning, heart problems, anthrax (in order of precedence)

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Simulation DATE DAY OF WEEK SEASON FLU LEVEL WEATHER REGION AGE GENDER Region Grassiness Region Anthrax Concentration Region Food Condition Immune System Outside Activity Has Anthrax Has Flu Has Allergy Has Heart Attack Has Sunburn Has Cold Heart Health Has Food Poisoning Disease ACTION Actual Symptom REPORTED SYMPTOM DRUG Actions: None, Purchase Medication, ED visit, Absent. If Action is not None, output record to dataset.

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Simulation Plot

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Anthrax release (not highest peak)

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Simulation 100 different data sets Each data set consisted of a two year period Anthrax release occurred at a random point during the second year Algorithms allowed to train on data from the current day back to the first day in the simulation Any alerts before actual anthrax release are considered a false positive Detection time calculated as first alert after anthrax release. If no alerts raised, cap detection time at 14 days

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Other Algorithms used in Simulation Time Signal Mean Upper Safe Range 1. Standard algorithm 2. WSARE 2.0 3. WSARE 2.5 Use all past data but condition on environmental attributes

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Results on Simulation

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Conclusion One approach to biosurveillance: one algorithm monitoring millions of signals derived from multivariate data instead of Hundreds of univariate detectors WSARE is best used as a general purpose safety net in combination with other detectors Modeling historical data with Bayesian Networks to allow conditioning on unique features of today Computationally intense unless we use clever algorithms

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Conclusion WSARE 2.0 deployed during the past year WSARE 3.0 about to go online WSARE now being extended to additionally exploit over the counter medicine sales

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For more information References: Wong, W. K., Moore, A. W., Cooper, G., and Wagner, M. (2002). Rule-based Anomaly Pattern Detection for Detecting Disease Outbreaks. Proceedings of AAAI-02 (pp. 217-223). MIT Press. Wong, W. K., Moore, A. W., Cooper, G., and Wagner, M. (2003). Bayesian Network Anomaly Pattern Detection for Disease Outbreaks. Proceedings of ICML 2003. Moore, A., and Wong, W. K. (2003). Optimal Reinsertion: A New Search Operator for Accelerated and More Accurate Bayesian Network Structure Learning. Proceedings of ICML 2003. AUTON lab website:http://www.autonlab.org/wsare Email: wkw@cs.cmu.edu

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