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Using Predictive Analytics to Forecast Drone Attacks in Pakistan
Adailson de CastroMarcio Mendes
Uzma AfzalFederal Urdu University ofArts Science & TechnologyKarachi, Pakistan
Dr. Tariq MahmoodPAF - Karachi Institute ofEconomics & TechnologyKarachi, Pakistan
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Roteiro
• Contextualização• Objetivo• Dados• Ferramentas• Preprocessamento• Modelagem e Forecasting• Conclusão
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Drones• Unmanned Aerial Vehicles (UAV) or• Remotely Piloted Aerial Systems (RPAS).
• São empregados, no âmbito militar, em condições onde o vôo tripulado é considerado difícil e arriscado.
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Drones
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Drones
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Objetivo• Aplicar tecnicas de previsão para medir futuros danos
• E prever ataques futuros para salvar vidas inocentes
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Os Ataques
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Fontes1. Pakistan Body Count (PBC) Website2. Cruzamentos das correspondencias
com1. entradas na wikipedia2. South Asia Terrorism Portal (SATP)
Website
• Cerca de 340 ataques registrados, desde Junho/2004 até junho/2013
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Atributos
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Atributos
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Atributos
Curtose
Obliquidade
Média
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Atributos
Número de ataques
JUN 2004 JUN 2013
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Atributos
Mortes de Militantes
JUN 2004 JUN 2013
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Atributos
Mortes de civis
JUN 2004 JUN 2013
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Atributos
Feridos
JUN 2004 JUN 2013
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AtributosSobreposição
JUN 2004 JUN 2013
Numero de ataquesMortes de civisMortes de militantes
Obs.: Escala Aproximada
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Série temporal EstacionáriaUma série temporal é dita estacionária quando ela se desenvolve no tempo aleatoriamente ao redor de uma média constante, refletindo alguma forma de equilíbrio estável. O que facilita a previsão.
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TransformaçãoNâo Estacionária -> estacionária
Diferenças sucessivas da série original
Primeira diferença:
Segunda diferença:
N-ésima diferença:
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TransformaçãoEstacionária -> Não estacionária
Diferenças sucessivas da série original
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Trend
Trend, ou tendência , é o movimento de uma serie tempo a longo prazo
Exemplo
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SeasonSeasonality, ou sazonalidade , é o movimento de uma serie temporal em intervalos menores que um ano. Mensalmente, semanalmente, diariamente , e.g.
Exemplo
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TransformaçãoEstacionária -> Não estacionária
Não é dito no artigo, mas provavelmente foram feitos testes de estacionaridade nas series temporais dos 4 parâmetros. Provavelmente também foi descoberto que as mesmas eram não estacionárias (um tanto quanto óbvio pelos gráficos), por isso a necessidade de se aplicar a transformação por uma função de diferenciação. Como é dito no artigo:
“In all four graphs, the mean value ischanging across different time periods, signaling the need to
apply a differencing function across consecutive timePeriods [...]”
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Partial Autocorrelation function (PACF)
É usado uma função de auto correção parcial(Partial Auto correlation function, PACF) para identificar a extensão do “lag”(atraso) no modelo
Seja um valor da serie temporal no tempo t:
Auto correlação parcial do lag 1:
Auto correlação parcial do lag k:
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Partial Autocorrelation function (PACF)
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IBM SPSS Tool
Exponential Smoothing
Autoregressive Integrated Moving Average (ARIMA)
AutomatedExpert Modeler
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Exponential Smoothing
+(1- )
𝑆0=𝑋 0
0<<1
Smoothing Factor (“Fator Suavizante”, tradução livre)
Previsão no tempo “t”
Valor observado no instante inicial
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ARIMAAutoregressive Integrated Moving Average
(1−∑𝑖=1𝑝
𝜑𝑖𝐿𝑖) (1− 𝐿)𝑑𝑋 𝑡=𝛿+(1+∑𝑖=1
𝑞
𝜃𝑖𝐿𝑖)𝜀𝑡
Modelo ARIMA (p, d, q) ARIMA (autoregressive, Integrated, Moving)
Lag Operator Erro
Número de parâmetrosauto-regressivos,
Número de diferenças número de parâmetros da média móvel
𝐿𝑖=𝑋 𝑡 −𝑖/ 𝑋 𝑡𝑋 𝑡−𝑋 𝑡− 1=𝜀𝑡
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ARIMAAutoregressive Integrated Moving Average
(1−∑𝑖=1𝑝
𝜑𝑖𝐿𝑖) (1− 𝐿)𝑑𝑌 𝑡=𝛿+(1+∑𝑖=1
𝑞
𝜃𝑖𝐿𝑖)𝜀𝑡
𝑌 𝑡 ¿ (1−𝐿 )𝑑 𝑋 𝑡
𝑌 𝑡=(𝛿+(1+∑𝑖=1𝑞
𝜃 𝑖𝐿𝑖)𝜀𝑡) /((1−∑𝑖=1
𝑝
𝜑𝑖𝐿𝑖)(1−𝐿 )𝑑 )
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Dados observados vs Forecast
Dados observadosForecast
Expert Modeler
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Dados observadosForecast
ARIMA Modelado Manualmente
Dados observados vs Forecast
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Comparação de erros
Root Mean Squared Error (RMSE)
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Dados observados Forecast
Expert Modeler
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ARIMA Modelado Manualmente
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Forecast
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Forecast• Julho 2013: 2(ataques), 17
(militantes), 2(estrangeiros), 0 (feridos)
• Agosto 2013: Não houve ataques• Setembro 2013: 3(ataques), 6
(militantes), 12(civis e estrangeiros), 9 (feridos)
• Outubro 2013: 2(ataques), 5 (militantes), 3(civis), 5 (feridos)
• Novembro 2013: 2(ataques), 2 (militantes), 6(civis e estrangeiros), 10 (feridos)
• Dezembro 2013: 2(ataques), 0 (militantes), 9(civis), 3 (feridos)
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Comparação do ARIMA e EM em 2012
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Conclusão• O Expert Modeler, no IBM SPSS, se mostrou melhor, com menos erros que o ARIMA Modelado Manualmente.
• Os ataques tem grande número de civis mortos comparados com as mortes de militantes.
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Obrigado, dúvidas?