伯克利帕切特對(duì)barabasi的批判

憤怒的萊爾?帕切特【一】：裸奔的網(wǎng)絡(luò)皇帝已有189次閱讀2014-2-2521:22|系統(tǒng)分類:觀點(diǎn)評(píng)述2014年2月10,11,12日三天，加州大學(xué)伯克利分校數(shù)學(xué)系、分子與細(xì)胞生物學(xué)系和電子工程與計(jì)算機(jī)科學(xué)系的萊爾?帕切特(LiorPachter)教授在他的個(gè)人博客上連續(xù)發(fā)表了三篇博文，強(qiáng)烈抨擊2011年8月同時(shí)發(fā)表在NatureBiotechnology上的兩篇論文：ThenetworknonsenseofAlbert-LaszloBarabasiThenetworknonsenseofManolisKellisWhyIreadthenetworknonsensepapers被批評(píng)的兩篇NBT論文是：BarzelB1,BarabasiAL.(2013)Networklinkpredictionbyglobalsilencingofindirectcorrelations.NatBiotechnol.,31(8):720-5.FeiziS1,MarbachD,MedardM,KellisM.(2013)Networkdeconvolutionasageneralmethodtodistinguishdirectdependenciesinnetworks.NatBiotechnol.,31(8):726-33.LiorPachterAlbert-LaszloBarabasi其中，”nonsense”這個(gè)詞怎么精確的翻譯，讓我思考了很久。雖然有點(diǎn)兒不雅，但個(gè)人以為用南京方言里的形容詞“依壁雕鑿”來描述，是比較能夠貼合萊爾寫博客時(shí)憤怒的心境。在這三篇博文里，萊爾首先不屑的指出著名的“網(wǎng)絡(luò)皇帝”(networkemperor)、美國東北大學(xué)(NortheasternUniversity)物理系和計(jì)算機(jī)科學(xué)與生物系的復(fù)雜網(wǎng)絡(luò)研究中心的埃爾伯特-拉斯洛?巴拉巴西(Albert-LdszloBarabasi)教授的數(shù)學(xué)爛到掉底兒，痛批巴拉巴西那些所謂的“發(fā)現(xiàn)”其實(shí)狗屁不通，因此結(jié)論就是雖然網(wǎng)絡(luò)皇帝經(jīng)常在Nature,Science這些刊物上炫耀自己的新衣，但是全世界都真真切切地看著皇帝正在裸奔；當(dāng)然這不是高潮，萊爾在第二篇里繼續(xù)抨擊另一位生物信息領(lǐng)域的大牛、MIT計(jì)算生物學(xué)研究組負(fù)責(zé)人曼諾利斯?凱利斯(ManolisKellis)副教授(2011年“甜妞”)，并且使用了“不誠實(shí)和欺詐的”(dishonestandfraudulent)的字眼，這種指責(zé)在惜名如命的學(xué)術(shù)界里，幾乎是毀滅性的指控；當(dāng)然你如果認(rèn)為這就是高潮，那你就錯(cuò)了，萊爾在第三篇博文里洋洋得意的指出：兄弟我從2006年開始就痛恨曼諾利斯，一直想辦法抓他把柄，終于給我逮住了吧。這叫什么不怕什么偷，就怕什么惦記??？兄弟我就是惦記著這哥們，給我逮住算他倒霉。完了。三篇博文一出，整個(gè)生信領(lǐng)域像是被丟進(jìn)了顆重量級(jí)的核彈，眾皆嘩然：你要打曼諾利斯那就打吧，人家網(wǎng)絡(luò)皇帝招你啥事了??？(巴拉巴西小聲嘀咕：我招誰惹誰了？)還有，你打了人，還沾沾自喜說你一貫對(duì)人有成見，這都哪跟哪??？這下好了，美國的同行們一看見標(biāo)題，二話不說，先拿過來慢慢一桶的爆米花；歐洲的同行們也不看球了，叼著巧克力，拎著啤酒瓶；中國的同行們一看，我靠，這么震撼，趕緊點(diǎn)根煙壓壓驚：大家一邊吃零食、喝啤酒、抽煙，一邊搬個(gè)馬叉坐下來慢悠悠的看熱鬧。有啥熱鬧可看的？當(dāng)然是有。首先，生信這個(gè)圈子現(xiàn)在還不大，無論是國外還是國內(nèi)，就那些人，所以有個(gè)風(fēng)吹草動(dòng)的很快就能傳遍整個(gè)圈子；其次，搞生信的人生活一般比較簡單，工作、生活、寫博客或者看博客，領(lǐng)域里面一般沒啥大新聞，就算是整個(gè)大新聞，那也是跑出去忽悠圈兒外的人，自己人之間忽悠起來還是挺困難的；再次，這場架打的水平那真是不一般的高，高科技打架斗毆啊，高科技打仗這是現(xiàn)在的流行趨勢，高科技打架那還真是不多見，能明明白白看懂整場架的每一招一式，非常不容易，理論上來說需要有非常強(qiáng)悍的數(shù)學(xué)背景，物理背景要扎實(shí)，計(jì)算機(jī)水平要高，還得有相當(dāng)?shù)纳飳W(xué)功底。不要看我，我反正是沒本事看懂這架是咋打的，當(dāng)然我也很認(rèn)真的找各種資料，仔細(xì)閱讀博文和相應(yīng)的評(píng)論，從12號(hào)Shirley轉(zhuǎn)給我博文鏈接到今天，前后琢磨了兩周的時(shí)間。當(dāng)然即使這樣，這場架還是沒大看明白，于是到處請(qǐng)教各位同行朋友，結(jié)合大家的觀點(diǎn)，湊成這篇博文。當(dāng)然說實(shí)話，兄弟我這數(shù)學(xué)實(shí)在是太渣了，要是還有看走眼或者看錯(cuò)的招式，盡管補(bǔ)充哈。一、裸奔的“網(wǎng)絡(luò)皇帝”萊爾寫博客的時(shí)間不長，2013年8月開始，也就半年多的時(shí)間。但絕對(duì)絕對(duì)是博客界的奇葩。萊爾寫博客的風(fēng)格非常鮮明，那就是無論如何上來先噼里啪啦一頓胖揍，揍的角度自然是他最拿手的數(shù)學(xué)（這不廢話嗎？人家是貨真價(jià)實(shí)的數(shù)學(xué)家），當(dāng)然嘍，個(gè)人以為你一個(gè)數(shù)學(xué)家譏笑人家物理學(xué)數(shù)學(xué)水平不咋地，這個(gè)實(shí)在有點(diǎn)兒不厚道。因?yàn)槿R爾本來的目的就要批曼諾利斯，但郁悶的是巴拉巴西正好與曼諾利斯“背靠背”的同一期發(fā)表對(duì)同一個(gè)問題的計(jì)算分析方法，再加上萊爾本來就對(duì)巴拉巴西不爽（這個(gè)也正常，網(wǎng)絡(luò)皇帝是個(gè)極其有爭議的人物，捧他的人是鐵桿誓死捍衛(wèi)，批他的人真是批到一錢不值），所以二話不說先逮住巴拉巴西，上去就是一頓暴打。等會(huì)兒，萊爾這么鬧騰了半天，究竟是個(gè)什么事兒？這話說起來有那么點(diǎn)兒復(fù)雜。這得講到網(wǎng)絡(luò)這個(gè)東西，最早的淵源呢，就是匈牙利有個(gè)天才數(shù)學(xué)家Erdos，跟他的小伙伴Renyi，在漫長的灌著水的學(xué)術(shù)生涯里，一不小心研究了一下隨機(jī)網(wǎng)絡(luò)發(fā)了八篇論文，后來覺得沒啥意思，就收于不玩了。后來巴拉巴西，真好也是匈牙利裔，一看這玩意兒不錯(cuò)，加了倆限制條件，即網(wǎng)絡(luò)生長模式和“強(qiáng)者恒強(qiáng)”的節(jié)點(diǎn)連接模式，這樣隨機(jī)網(wǎng)絡(luò)一下子就不隨機(jī)了，變成了一種奇怪的，被巴拉巴西稱為“無尺度”(Scale-free)網(wǎng)絡(luò)。從這個(gè)網(wǎng)絡(luò)里，學(xué)者們發(fā)現(xiàn)了很多很多有意思的現(xiàn)象，并且表明這個(gè)星球上，如果不是所有那也是絕大部分的網(wǎng)絡(luò)，都是無尺度網(wǎng)絡(luò)。所以巴拉巴西后來得意洋洋的主要根據(jù)自己的研究結(jié)果，寫了兩本暢銷并且極其忽悠的書：《鏈接》和《爆發(fā)》。問題就來了：巴拉巴西你這要干啥的？吃飽了撐得沒事干，寫兩本書出來娛樂娛樂大眾？你要這么想，那你就錯(cuò)了。巴拉巴西的目標(biāo)很明確：拿諾獎(jiǎng)?？墒菃栴}又來了：網(wǎng)絡(luò)這東西，給你發(fā)個(gè)啥獎(jiǎng)？跟化學(xué)不沾邊，那發(fā)個(gè)物理獎(jiǎng)吧。物理獎(jiǎng)？怎么可能啊，物理領(lǐng)域等著拿獎(jiǎng)的多了去了，你看人家希格斯辛辛苦苦的活著為的啥？還不是為了等著拿獎(jiǎng)。所以巴拉巴西要想在物理這個(gè)領(lǐng)域拿獎(jiǎng)，難度真的不是一般的高。所以，后面的事情就很容易理解了：生物。如果網(wǎng)絡(luò)的理念能夠解釋生物學(xué)的現(xiàn)象，并且像分子動(dòng)力學(xué)(MD)這樣扎扎實(shí)實(shí)的用到生物學(xué)和醫(yī)學(xué)里去，做出重大的貢獻(xiàn)，那既有可能拿生理學(xué)獎(jiǎng)，也可以仿照MD殺回去拿他的物理獎(jiǎng)。所以瞄準(zhǔn)生物就等于給網(wǎng)絡(luò)研究上了個(gè)雙保險(xiǎn)，反正只要上到應(yīng)用，跟諾獎(jiǎng)那幫評(píng)委們就有討價(jià)還價(jià)的余地了。當(dāng)然上面一段是大背景啦。具體到本例，那就是目前生物學(xué)網(wǎng)絡(luò)存在一個(gè)現(xiàn)象：我用芯片做基因表達(dá)譜的分析，觀測到有些基因表達(dá)與其他基因的表達(dá)是正相關(guān)或者負(fù)相關(guān)，但是生物分子存在直接或間接的相互作用關(guān)系，因此，怎么從這些關(guān)聯(lián)的數(shù)據(jù)里發(fā)現(xiàn)直接的調(diào)控關(guān)系？好吧，我知道這個(gè)問題描述的有點(diǎn)兒抽象，舉個(gè)形象點(diǎn)兒的例子：我和小伙伴們一起在操場上踢球，老馬控球，以嫻熟的技術(shù)過了我，我不高興了，二話不說上去一腳直接把老馬踹翻。其他小伙伴諸如老貓、老狗、老羊等一看：哇，這么兇猛！嚇得腿發(fā)軟，紛紛自動(dòng)躺地上不動(dòng)了。好，小兔子正好經(jīng)過，一看，哇？這小子一腳踹翻這么多？第二天科學(xué)網(wǎng)博客頭條：華工某教授神功蓋世一腳踹翻數(shù)十位同事?？闯鰡栴}了吧？就直接的關(guān)聯(lián)來說，我的腳只踹到老馬身上，就這一個(gè)是直接的“相互作用”，其他人躺地上不動(dòng)了關(guān)我毛事??？那都是醬油，不算數(shù)的(本例隆重感謝老馬友情客串，故事純屬虛構(gòu)，模仿有礙團(tuán)結(jié))。所以生物學(xué)家們關(guān)心的，是直接的相互作用關(guān)系，因?yàn)橹苯拥年P(guān)系才可能發(fā)現(xiàn)重要的調(diào)控關(guān)系，并有助于進(jìn)一步的功能研究。而間接的關(guān)系一般來說木有任何的說服力，所以這種信息屬于垃圾信息。因此，這兩篇文章要解決的問題，就是從關(guān)聯(lián)數(shù)據(jù)里尋找直接或間接的分子間互相作用，也就是網(wǎng)絡(luò)里關(guān)鍵“邊”(linkageoredge)的預(yù)測。第一篇論文2012年10月22日投稿，2013年4月23日接收；第二篇論文2012年9月12日投稿，2013年6月11日接收。兩篇論文在線發(fā)表了之后，立即引來各種爭議，其中咱國內(nèi)一位數(shù)學(xué)功底奇好的前輩高人，看見這兩篇論文氣的暴跳如雷：這也能叫數(shù)學(xué)？二話不說把自己正在做的東西也投了Bioinformatics：YuX1,LiG,ChenL.(2013)Predictionandearlydiagnosisofcomplexdiseasesbyedge-network.Bioinformatics.2013Nov29.[Epubaheadofprint]這篇論文怎么樣，我反正不說。當(dāng)然你要是認(rèn)為發(fā)在NBT上的論文怎么說都應(yīng)該比Bioinformatics的好，那我只能呵呵了。陳老師雖然是咱華工電信系的校友，可是他跟數(shù)學(xué)界鼎鼎有名的大家章先生合作多年，數(shù)學(xué)的水準(zhǔn)絕對(duì)的專業(yè)級(jí)的，發(fā)NBT這兩位的數(shù)學(xué)，呵呵，加起來也未必趕得上。所以咱國內(nèi)的生信學(xué)者，牛人照樣有的是。說正事，說正事。因?yàn)榘屠臀髦皇菍儆凇斑B帶”，所以萊爾其實(shí)批評(píng)的很客氣。上來先吹捧一下，說這個(gè)鏈預(yù)測很重要啊，所以巴拉巴西弄個(gè)矩陣變換，變換完了這個(gè)計(jì)算的時(shí)間復(fù)雜度是O(n%)，萊爾看到這二話不說先去了趟茅房，回來二話不說重新推了遍公式，簡單一約簡，發(fā)現(xiàn)算法復(fù)雜度已經(jīng)降到O(n^3)了！因此評(píng)論道：這玩意兒的難度充其量也就是本科生線性幾何的家庭作業(yè)(theentireexercisewouldbesuitableforanundergraduatelinearalgebrahomeworkproblem)。當(dāng)然這不算晚，萊爾還順道指出，巴拉巴西這個(gè)算法沒有辦法直接從實(shí)驗(yàn)里估算參數(shù)；陳老師當(dāng)然是繼續(xù)指出：這個(gè)算法還要求樣本的規(guī)模比變量多(注：陳老師近年來以“小樣本、無重復(fù)”的理念名震領(lǐng)域，主要是生物學(xué)實(shí)驗(yàn)一般都比較費(fèi)錢、費(fèi)時(shí)間，巴拉巴西的模型里參數(shù)超多，樣本如果比參數(shù)多，那基本上是不具有任何實(shí)用價(jià)值的?！靶颖尽o重復(fù)”，或者少重復(fù)，這是計(jì)算生物學(xué)者必須面對(duì)也必須盡力解決的問題，無限實(shí)驗(yàn)是不可能的)。最后，萊爾指出，這玩意兒吧，其實(shí)準(zhǔn)確性比已有的算法提高的非常有限，也就是巴拉巴西論文里Fig.3C里說的，AROC從0.67上升到0.68(不解釋了成不？總之就是改進(jìn)了一個(gè)百分點(diǎn)，就一個(gè))，所以根本就不能稱為啥新算法。因此，巴拉巴西的網(wǎng)絡(luò)是“依壁雕鑿”的。在第一篇博文即將結(jié)尾的時(shí)候，萊爾充分的展現(xiàn)了其作為一個(gè)數(shù)學(xué)家的嚴(yán)密推導(dǎo)能力，力圖證明網(wǎng)絡(luò)皇帝這么多年其實(shí)一直是在裸奔：巴拉巴西以“BA模型”(無尺度網(wǎng)絡(luò)模型，最早用在互聯(lián)網(wǎng)分析上)出名(BarabdsiandAlbert‘EmergenceofScalinginRandomNetworks"，Science,Vol.28615October1999,pp.509-512)。LadaAdamic和BernardoHuberman(不了解)立即指出這個(gè)模型其實(shí)與實(shí)際觀測到的網(wǎng)頁鏈接結(jié)構(gòu)是不符合的。Willinger,Alderson和Doyle指出，無尺度網(wǎng)絡(luò)的確具有某些有趣的數(shù)學(xué)特性，但這些數(shù)學(xué)不是巴拉巴西，而是Bollobds和Riordan做的。巴拉巴西反復(fù)的強(qiáng)調(diào)代謝網(wǎng)絡(luò)是無尺度網(wǎng)絡(luò)里的一個(gè)代表性的例子，但是ReikoTanaka的論文"ScaleRichMetabolicNetworks”指出說代謝網(wǎng)絡(luò)里木有尺度是扯淡，尺度是rich的。RekaAlbert,HawoongJeong&Albert-LoszloBarabdsi2000年發(fā)表在Nature的論文里，指出復(fù)雜網(wǎng)絡(luò)面對(duì)錯(cuò)誤的耐受性和面對(duì)攻擊的脆弱性（《鏈接》這本書里的最核心的理念）。JohnDoyle在PNAS上專門發(fā)了篇文章，指出這種“耐受性”其實(shí)也極為脆弱，從頭到尾把巴拉巴西批個(gè)遍。巴拉巴西在2005年發(fā)表的Nature論文”Theoriginofburstsandheavytailsinhumandynamics”，指出人類的活動(dòng)具有爆發(fā)性的特征（《爆發(fā)》這本書里的核心理念）。DanielStouffer,DeanMalmgrenandLuisAmaral在隨后的評(píng)論里指出這玩意兒就是個(gè)人造的（artifact）的結(jié)果，并且被分析的電子郵件模式也不具有代表性。Liu,SlotineandBarabdsi在2011年發(fā)表的Nature論文"Controllabilityofcomplexnetworks”，指出致密的、均一的網(wǎng)絡(luò)可以通過少數(shù)幾個(gè)驅(qū)動(dòng)節(jié)點(diǎn)來調(diào)控。CarlBergstrom和同事認(rèn)為對(duì)于絕大多數(shù)網(wǎng)絡(luò)，其實(shí)只需要控制一個(gè)節(jié)點(diǎn)，就能調(diào)控整個(gè)網(wǎng)絡(luò)。寫到這里，兄弟我真想大吼一聲，萊爾你有完沒完？這架你打的累不累??？就為你這場架，我寫的都寫累死了，你難道真的不累？本部分結(jié)論：第一，萊爾從算法的角度嚴(yán)謹(jǐn)?shù)淖C明了網(wǎng)絡(luò)皇帝的數(shù)學(xué)也就是本科生的水平（我要哭出來了，兄弟我看不懂啊，好多同行看的也是稀里糊涂的，難道咱這幫都是中學(xué)的水平？我的自尊受到了森森的傷害）；第二，巴拉巴西的幾個(gè)主要概念，比如BA模型，代謝網(wǎng)絡(luò)的無尺度性，網(wǎng)絡(luò)容錯(cuò)性、爆發(fā)特征和絡(luò)可控性，都被同行們批的焦頭爛額，所以；第三，陛下你還是穿上衣服吧，別光著屁股受涼了。不好意思，本來準(zhǔn)備今天一天寫完。寫的實(shí)在太累了。尤其是“光腚五條”，我的的確確是木有精力挨篇看完，就算是萊爾指責(zé)巴拉巴西的算法有問題，看的也是稀里糊涂，所以，看到這兒，我想你能夠明白：萊爾真是超牛?。‘?dāng)然你還得清楚，萊爾的打擊目標(biāo)是曼諾利斯，所以，接下來的場面，比上述的要?jiǎng)疟亩啵鸷车牧考?jí)大為提升。最后，雖然我數(shù)學(xué)是個(gè)渣，但我圈兒里同行們可基本上都比我的數(shù)學(xué)好，所以寫這篇博文之前我專門請(qǐng)教了各位同行好友，這里特此鳴謝：Shirley，陳老師，師兄，丹丹師弟，和世華兄。都是高手啊，三兩句一點(diǎn)撥，馬上茅塞頓開，佩服佩服啊!ThenetworknonsenseofAlbert-LdszloBarabdsiFebruary10,2014inphysics,reviews,sophistry|Tags:Barabasi,Barzel,Biham,DREAM5,Medard,network,partialcorrelation,regulatorynetworkIntheAugust2013issueofNatureBiotechnologythereweretwoback-to-backmethodspaperspublishedintheareaofnetworktheory:BaruchBarzel&Albert-LaszloBarabasi,Networklinkpredictionbyglobalsilencingofindirectcorrelations,NatureBiotechnology31(8),2013,p720-725.doi:10.1038/nbt.2601.SoheilFeizi,DanielMarbach,MurielMedard&ManolisKellis,Networkdeconvolutionasageneralmethodtodistinguishdirectdependenciesinnetworks,NatureBiotechnology31(8),2013,p726-733.doi:10.1038/nbt.2635.Thispostisthefirstofatrilogypart2,part3)inwhichmystudentNicolasBrayandItellthestoryofthesepapersandwhywetookthetimetoreadthemandcritiquethem.WestartwiththeBarzel-BarabfisipaperthatisabouttheapplicationsofamodelproposedbyBarzelandhisPh.D.adviso,OferBiham(althoughalllastnamesstartwithaB,BihamisnottobeconfusedwithBarabasi):Inordertoquantifyconnectivityinbiologicalnetworks,BarzelandBihamproposedanexperimentalperturbationmodelinthepaperBaruchBarzel&OferBiham,Quantifyingtheconnectivityofanetwork:Thenetworkcorrelationfunctionmetho,Phys.Rev.E80,046104(2009)thatformsthebasisfornetworklinkpredictioninBarzel-Barabasi.Inthecontextofbiology,linkpredictionreferstotheproblemofidentifyingfunctionallinksbetweengenesfromdatathatmaybeconfoundedbyindirecteffects.Forexample,ifgeneAinhibitstheexpressionofgeneB,andalsogeneBinhibitstheexpressionofgeneC,theniftheexpressionofAincreases,itwilldecreasetheexpressionofB,whichinturnincreaseC.ThereforeonemightobservecorrelationintheexpressionlevelsofgeneAandC,eventhoughthereisnodirectinteractionbetweenthem.TheBarzel-Bihammodelisbasedonperturbation

experiments.Assumingthatasystemofgenesisinequilibrium,itisamodelforthechangeinexpressionofonegeneinresponsetoasmallperturbationinanother.TheparametersintheBarzel-Bihammodelareentriesinwhattheycalla“l(fā)ocalresponsematrix”S(anymatrixwith二..：foralli).Physicalargumentspertainingtoperturbationsatequilibriumleadtotheequations■-(offthediagonal)and-:■-foralli.(1)fora“globalresponsematrix”Gthatcan,inprinciple,beobservedandusedtoinferthematrixS.TheinnovationofBarzelandBarabasiistoprovideanapproximateformulaforrecoveringSfromG,specificallytheformulaS/approx{G-ID[[G-丁)&))一〔(2)whereD(M)denotestheoperationsettingoff-diagonalelementsofMtozero.Asignificantpartofthepaperisdevotedtoshowingthattheapproximation(2)isgood.Thentheysuggestthat(2)canbeusedtoinferdirectcausallinksinregulatorynetworksfromcollectionsofexpressionexperiments.BarzelandBarabasiclaimthattheapproximationformula(2)is■jnecessarybecauseexactinferenceofSfromGrequiressolvingtheintractablesystemof：-equations■-'f-(offthediagonal)and「foralli.(3)Theassertionofintractabilityisbasedontheclaimthattheequationsarecoupled.Theyreasonthatsincethenaivematrixinversionalgorithmrequires；operationsformequations,thesolutionof(3)wouldrequiretime''■:.Whenwelookedatthissystem,ourfirstthoughtwasthatwhileitislarge,itisalsostructured.Wesatdownandstartedexaminingitbywritingdowntheequationsforasimplecase:amatrixSforagraphon3nodes.Weimmediatelynoticedtheequationsdecoupledintonsystemsofnequationswhere':■,:-.，'」-；、；,withthen':■,:-.，'」-；、；,withthenunknowns1—,oreven*byand'：?：?-■■-亡.，：.Thisimmediatelyreducesthecomplexityto-',orevensimpleparallelization.Inotherwords,thesystemistriviallytractable.Butthereismore:whilelookingatthepaperIhadtotakeaquickbathroombreak,andbythetimeIreturnedNickhadrealizedhecouldapplythSherman-Morrisonformulatoobtainthefollowingformulafortheexactsolution:s=i-nii/G-1)^-1.(4)Heretheoperator"/"denoteselement-wisedivision,asimpleoperationtoexecute,sothatinferringSfromGrequiresnomorethaninvertingGandscalingit,aformulathatisalsomuchsimplerandmoreefficienttocomputethan(2).[Added2/23:JordanEllenbergpointedouttheobviousfactthat「'■1■offthediagonalmeansthat"「1■■''forsomediagonalmatrix；',andtherefore；3■'andsincethediagonalentriesof-mustbezeroitfollowsthat=以心).Inotherwords,theSherman-Morrisonformulaisnotevenneeded].WhileitwouldbeniceforustoclaimthatourmanagingtoquicklysupersedethemainresultofapaperpublishedinNatureBiotechnologywasduetosomesortofgenius,infacttheentireexercisewouldbesuitableforanundergraduatelinearalgebrahomeworkproblem.BarabasilikestocomparehimselftothegreatphysicistandnobellaureateSubrahmanyanChandrasekha,butitisdifficulttoimaginethegreatChandrasekharhavingsimilardifficulties.Theapproachtosolving(4)hasanimplicationthatisevenmoreimportantthanthesolutionitself.ItprovidesadualformulaforcomputingsfromSaccordingto(1),i.e.tosimulatefromthemodel.Usingthesameideasasabove,onefindsthat"*where；.UnlikeBarzel&BarabasithatresortedtosimulatingwithMichaelis-Mentendynamicsintheirstudyofperformanceoftheirapproximation,using(4)wecanefficientlysimulatedatadirectlyfromthemodel.OneissuewithMichaelis-Mentendynamicsisthattheymakemoresenseforenzymaticnetworksasopposedtoregulatorynetworks(formoreonthisseeKarlebach,G.&Shamir,R.Modellingandanalysisofgeneregulatorynetworks,NatRevMolCellBiol9,770-780(2008)),butinanycaseperformanceonsuchdynamicsishardlyavalidationof(2)sinceitsmixingapplesandoranges.SowhathappenswhenonesimulatesdatafromtheBarzel-Bihammodelandthentriestorecovertheparameters?AcomparisonofthestandardmethodofregularizedpartialcorrelationswithexactinferencefortheBarzel-Bihammodel.RandomsparsegraphsweregeneratedaccordingtotheErdos-RenyigraphmodelG(5000,p)wherepwasvariedtoassessperformanceatdifferentgraphdensities(shownonx-axis)They-axisshowstheaverageAUROCobtainedfrom75randomtrialsateachdensity.WhenexaminingsimulationsfromtheBarzel-Bihammodelwithgraphson5,000nodes(seeFigureabove),weweresurprisedtodiscoverthatwhenaddingevensmallamountsofnoise,theexactalgorithm(4)failedtorecoverthelocalresponsematrixfromG(wealsoanalyzedtheapproximation(3)andobservedthatitalwaysresultedinperformanceinferiorto(4),andthat5%ofthetimethecorrelationwiththeexactsolutionwasnegative).Thissensitivitytonoiseisduetotheterm二?intheexactformulawhichbecomesproblematicifthediagonalentriesof一areclosetozero.Someintuitionforthebehaviorof一maybegainedfromnotingthatifSissuchthatitsgeometricsumconverges,thediagonalof—isequaltothatof?：「'二.-.fshasmixedsignsandthereissignificantfeedbackwithinthenetwork,thediagonalof一maybeclosetozeroandanynoiseinthemeasurementofGcouldcreateverylargefluctuationsintheinferredS.ThismeansthattheresultsinFigure1arenotdependentonthegraphmodelchosen(Erdos-Renyi)andwilloccurforanyreasonablemodelofgeneregulatorynetworksincludingthemodelingofbothenhancersandrepressors.FromFigure2aintheirpaper,itappearsthatBarzelandBarabasiusedintheirsimulationanSwithonlypositiveentriesthatwouldprecludesucheffects.Suchanassumptionisbiologicallyunrealistic.However,thedifficultieswithnoisefortheBarzel-Bihammodelgomuchdeeper.Whileaconstantsignal-to-noiseratio,asassumedbyBarzelandBarabasi,isacommonlyusedmodelforerrorsinexperiments,itisimportanttorememberthatthereisnoexperimentfordirectlymeasuringtheelementsofG.Obtaining'fromanexperimentisdonebymakingasmallperturbationofsizeetogenei,observingthechangeingenej,andthendividingthatchangebye.Thislaststepincreasesthenoiseontheestimateof'byafactorof1/e(alargenumbe,foraperturbativeexperiment)abovethenoisealreadypresentinthemeasurements.Increasingeactstoremovethesystemfromtheperturbativeregimeandtherebyincreasestheintrinsicerrorinestimating?.ItisthereforethecasethatattainingreasonableerroronGwillrequireverylownoiseintheoriginalmeasurements.Inthiscaseofbiologicalnetworksthiswouldmeanperformingmanyreplicatesoftheexperiments.However,asBarzel&Barabasiacknowledgeintheirpaper,evenasinglereplicateofaperturbationexperimentisnotcurrentlyfeasible.Whiletheexactalgorithm(4)forinvertingtheBarzel-Bihammodelperformspoorly,wefoundthatawidelyusedshrinkagemethodbasedonpartialcorrelation(Schafer,J.&Strimmer,K.AShrinkageApproachtoLarge-ScaleCovarianceMatrixEstimationandImplicationsforFunctionalGenomics,StatisticalApplicationsinGeneticsandMolecularBiology4,(2005))outperformstheexactalgorithm(bluecurveinFigureabove).Thissuggeststhatthereisnoinputforwhich(4)mightbeuseful.Themethodisnotevenidealforinferencefromdatageneratedbythemodelitisbasedon.Thisbringsustothe“results”sectionofthepaper.TodemonstratetheirmethodcalledSilencer,Barzel&BarabasiranitononlyoneofthreedatasetsfromtheDREAM5data.TheythencomparedtheperformanceofSilencertothreeoutofthirtyfivemethodsbenchmarkedinDREAM5.TheBarzel-Bihammodelisforperturbationexperiments,butBarzel&Barabasijustthrewindatafromanotheruniverse(e.g.mutualinformationmatrices).Butletsjustgowiththatforamoment.Theirresultsareshowninthefigurebelow:Figure3fromBarzel-Barabasi.ThethreemethodstestedpotentialimprovementsonarePearson,SpearmanandMutualInformation.PearsonandSpearmanrank16/35and18/35respectivelyintheDREAM5benchmarks.TheremaybesomereasonwhySilencerappliedontopofthesemethodsimprovesperformance:inthecasewhereGisacorrelationmatrix,thepathinterpretationgivenbyBarzelandBarabasiconnectstheinferenceproceduretoSeawallWright’spathcoefficients(ca.1920),whichinturnsuggestsaninterpretationintermsofpartialcorrelation.Howeverinthecaseofmutualinformation,amethodthatisranked19/35intheDREAM5benchmarks,thereisnostatisticallysignificantimprovementatall.TheimprovementisfromanAUROCof0.67to0.68.Amazingly,BarzelandBarabfisicharacterizetheseresultsbyremarkingthatthey"improveuponthetop-performinginferencemethods”(emphasisontopisours).Consideringthatthebestoftheserank16/35theuseoftheword“top"seems,shallwesay,unconventional.Wehavetoask:howdidBarzel&BarabasigettopublishapaperinthejournalNatureBiotechnologyonregulatorynetworkinferencewithoutimprovementortestingonanythingbutahandfulofmediocreDREAM5methodsfromasingledataset?ToputtheBarzel-Barabasiresultsincontext,itisworthconsideringthestandardstheFeizietal.paperwereheldto.InthatpapertheauthorscomparedtheirmethodtoDREAM5dataaswell,excepttheytestedonall3datasetsand9methods(andevenonacommunitybasedmethod).WethinkitsfairtoconcludethatsignificantlymoretestingwouldhavetobedonetoarguethatSilencerimprovesonexistingmethodsforbiologicalnetworkinference.Wethereforedon’tseeanycurrentpracticalutilityfortheBarzel-Bihammodel,exceptpossiblyforperturbationexperimentsinsmallsub-networks.Eventhen,wedontbelieveitispracticaltoperformthenumberofexperimentsthatwouldbenecessarytoovercomesignaltonoiseproblems.UnfortunatelytheproblemsinBarzel-Barabasispilloverintoafollowuparticlepublishedbytheduo:Barzel,Baruch,andAlbert-LaszloBarabasi,“UniversalityinNetworkDynamics."NaturePhysics9(2013).InthepapertheyassumethatthelocalresponsematrixShasentriesthatareallpositive,i.e.theydonotallowforinhibitoryinteractions.Sucharestrictionimmediatelyrenderstheresultsofthepaper,iftheyaretobebelieved,mootintermsofbiologicalsignificance.Moreover,therestrictionsonSappeartobeimposedinordertoprovideapproximationstoGthatareunnecessaryinlightof(5).Giventheseimmediateissues,wesuspectthatwerewetoreadtheUniversalitypapercarefully,itisquitelikelythispostwouldhavetobelengthenedconsiderably.ThesearenotthefirstofBarabasi’spaperstopackagemeaninglessandincoherentresultsinNature/Sciencepublications.Infact,thereisalonghistoryofBarabasipublishingwithfanfareintopjournalsonlytohaveothersrespondbypublishingtechnicalcommentsonhispapers,inmanycasesrefutingcompletelytheclaimshemakes.UnfortunatelymanyofthecritiquesarenotwellknownbecausetheyarerejectedfromthejournalswhereBarabasiissuccessful,andinsteadfindtheirwaytopreprintserversormorespecializedpublications.HereisapartiallistofBarabasifinestandtheresponse(s):Barabasiisfamousforthe“BAmodel",proposedinBarabasiandAlbertEmergenceofScalinginRandomNetworks“,Science,Vol.28615October1999,pp.509-512.LadaAdamicandBernardoHubermanimmediatelyrefutedthepracticalapplicationsofthemodel.Moreover,aspointedoutbyWillinger,AldersonandDoyle,whileitistruethatscale-freenetworksexhibitsomeinterestingmathematicalproperties(specificallytheyareresilienttorandomattackyetvulnerabletoworst-case),eve