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+designed+and+trained+to+predict+the+evolution+of+a+stochastic+dynamical+system%252C+using+wildfire+prediction+as+a+case+study.+We+show+that+traditional+evaluation+methods+based+on+threshold+based+classification+metrics+and+error-based+scoring+rules+assess+a+DNN%27s+ability+to+replicate+the+observed+ground+truth+(GT)%252C+but+do+not+measure+the+fidelity+of+the+DNN%27s+learning+of+the+underlying+stochastic+process.+To+address+this+gap%252C+we+propose+a+new+system+property%3a+Statistic-GT%252C+representing+the+GT+of+the+stochastic+process%252C+and+an+evaluation+metric+that+exclusively+assesses+fidelity+to+Statistic-GT.+Utilizing+a+synthetic+dataset%252C+we+introduce+a+stochastic+framework+to+characterize+this+property+and+establish+criteria+for+a+metric+to+be+a+valid+measure+of+the+proposed+property.+We+formally+show+that+Expected+Calibration+Error+(ECE)+tests+the+necessary+condition+for+fidelity+to+Statistic-GT.+We+perform+empirical+experiments%252C+differentiating+ECE%27s+behavior+from+conventional+metrics+and+demonstrate+that+ECE+exclusively+measures+fidelity+to+the+stochastic+process.+Extending+our+analysis+to+real-world+wildfire+data%252C+we+highlight+the+limitations+of+traditional+evaluation+methods+and+discuss+the+utility+of+evaluating+fidelity+to+the+stochastic+process+alongside+existing+metrics.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.d84b86b38b7dc111d20d68d1ff3e7329%3frik%3dPdMaFuqCYzLhxQ%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Stochastic+Neural+Networks&FORM=IRPRST&ck=15DC0363478EF53A13752BFBEFA8B653&selectedIndex=28&itb=0)
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