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+principles+to+training+an+ensemble+of+small+neural+networks+for+regression+tasks.+Using+Markov+Chain+Monte+Carlo%252C+we+sample+from+the+posterior+distribution+of+neural+networks+that+have+a+single+hidden+layer.+To+create+an+ensemble+of+these%252C+we+apply+Gibbs+sampling+to+update+each+network+against+the+residual+target+value+(i.e.+subtracting+the+effect+of+the+other+networks).+We+demonstrate+the+effectiveness+of+this+technique+on+several+benchmark+regression+problems%252C+comparing+it+to+equivalent+shallow+neural+networks%252C+BART%252C+and+ordinary+least+squares.+Our+Bayesian+Additive+Regression+Networks+(BARN)+provide+more+consistent+and+often+more+accurate+results.+On+test+data+benchmarks%252C+BARN+averaged+between+5+to+20+percent+lower+root+mean+square+error.+This+error+performance+does+come+at+the+cost%252C+however%252C+of+greater+computation+time.+BARN+sometimes+takes+on+the+order+of+a+minute+where+competing+methods+take+a+second+or+less.+But%252C+BARN+without+cross-validated+hyperparameter+tuning+takes+about+the+same+amount+of+computation+time+as+tuned+other+methods.+Yet+BARN+is+still+typically+more+accurate.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.d176d65ddfc646edde2c9061f7857368%3frik%3dWxfRwjTpCAehMw%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Bayesian+Additive+Regression+Model+with+GPT+Image&FORM=IRPRST&ck=1F85C605BB12A9B942788348764BE34D&selectedIndex=4&itb=0)
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