The BBN Crosslingual Topic Detection and Tracking System

Size: px
Start display at page:

Download "The BBN Crosslingual Topic Detection and Tracking System"

Transcription

1 The BBN Crosslngual Topc Detecton and Trackng System Tm Leek, Hubert Jn, Sreenvasa Ssta, Rchard Schwartz BBN Technologes, Cambrdge, MA ABSTRACT Ths was the frst year that the TDT program ncluded a requred crosslngual test: Englsh and Mandarn. Most of our work, therefore, was to adapt our trackng and detecton systems to work on a corpus of documents n these two languages. To ths end, we worked both on quck, adequate translaton, and the modfcatons necessary to our systems to attan good performance n ths crosslngual doman. We started by buldng smple term translaton systems, and ended wth more complcated ones that made sensble use of knowledge of the target language. Workng from a parallel corpus of algned sentences, we estmated pror term translaton probabltes. Addtonally, we devsed an algorthm for teratvely refnng a translaton, va word co-occurrence statstcs, n order to choose the most consstent translaton. The trackng and detecton systems themselves were left largely unchanged, wth the excepton that we estmated score normalzaton statstcs separately for documents n dfferent languages. We were pleasantly surprsed to fnd that the performance on trackng and detecton usng our translaton system was about the same as when we avaled ourselves of the suppled machne translatons of Mandarn. 1. Translatng for TDT It was our belef that the ntroducton of cross-lngual tasks nto the TDT evaluaton meant we needed to buld a translaton system. It s worth notng that both tme and resources were lmted. We had only a few months to do ths work, and were provded the sort of resources you d expect when asked to work n a sparse language: an errorful translaton dctonary, a parallel corpus not qute from the rght doman, varous msmatched word lsts and concordances. But ths seemed to be the man thrust of TDT3: how well and how quckly can you adapt your TDT systems to work on an addtonal language, gven lmted resources? 1.1. A Smple Term Translaton System We decded that the frst pass at a soluton should be to translate all the Mandarn documents nto Englsh usng a blngual dctonary and then run our monolngual trackng and detecton systems as usual. Obvously, ths s not gong to gve the best result. But, snce t s the easest thng to do, t s mportant to have t as a benchmark aganst whch to compare other, more elaborate solutons. Our translaton system used a very crude algorthm. 1. Segment the orgnal Mandarn document nto words. 2. Look up each Mandarn word n the blngual dctonary. If t s n the dctonary, make a bag of all the Englsh words from all the translatons. Else, throw t away. 3. Each Mandarn document s just a bg bag of Englsh words. We were fortunate to have avalable two systems for segmentng Mandarn nto words, one provded by the LDC and another we at BBN had developed as part of a Mandarn Informaton Extracton system. Upon nspecton, the output of the LDC segmenter appeared more approprate for nput to a translaton system. The BBN segmenter tended to leave denttes (persons, locatons, organzaton, etc) unsegmented. Ths s a valuable behavour when namefndng, but t often renders these crucal terms untranslatable. In addton to tryng these dfferent programs for segmentng the Mandarn, we also expermented wth segmentng greedly (always take the longest word next that s n the dctonary), and segmentng all-ways at once (all substrngs of less than M characters). Notce at least two obvous but sgnfcant falngs of ths sort of smple-mnded approach to term translaton. 1. We are throwng away too much of the orgnal Mandarn document. Our estmate s that 25% of the words don t translate. Only about 5% are due to errors n segmentaton. About half are names. 2. By translatng a Mandarn word as the entrety of the Englsh half of ts dctonary entry, we are weghtng the words n the translaton n precsely the wrong way. Common words typcally translate many ways. Uncommon words typcally translate very few ways. Together, these two facts conspre to mean that we are ncreasng the weght for common words, and decreasng t for uncommon words. Ths s a bad dea. Common words are generally not useful for TDT, whle uncommon words are generally very mportant. The frst of these problems can only be addressed by ncreasng the coverage of the Mandarn words by the term translaton system. The second problem s best solved by ntroducng the noton of translatng wth probablty Extended Word Lookup Translaton We can solve the coverage problem by translatng and segment jontly,.e. choosng a segmentaton that ncreases dctonary coverage. We decded to start wth the LDC segmentaton and then repar t. Roughly half of the untranslated words are names. In many cases, the correct translaton for a Chnese name nto Englsh s smply the Pnyn spellng for the sequence of characters. We made use of ths target language knowledge as well as a lst of Chnese surnames, to refne our dctonary lookup algorthm.

2 1. If the untranslated word begns wth a Chnese surname, wrte out the surname and gven name n Pnyn. 2. Else greedly subsegment usng the dctonary. Ths soluton does ncrease coverage; every word n the orgnal now translates. However, we stll have the word-weghtng problem Probablstc Term Translaton A coarse soluton to the word weghtng problem s smply to mandate that the Englsh translaton have the same total number of words as the orgnal Mandarn. We can acheve ths by gvng each Englsh word a fractonal count proportonal to the total number of words n the Englsh translaton. Ths wll mean that the three character word that translates only one way (n the blngual dctonary we had to work wth), as Mao Zedong, wll result n two Englsh words wth half a sngle count each. Lkewse, the two character word that translates eght ways as varous forms of haven t and to not be wll result n thrteen Englsh words wth 1=13 of a count each. A better soluton nvolves estmatng non-unform pror translaton probabltes for these ndvdual words. Not all translatons are equally lkely. For nstance, the Chnese word for Amerca translates ten ways. Clearly, though, Amerca s a more lkely translaton than yankeedom. We mplemented an teratve procedure to estmate non-unform pror translaton probabltes usng the observatons of algned sentences n the parallel corpora of Hong Kong Laws. 1. Intalze P (E jjc) = 1 Nt(C) P 2. Count C(E j C)= P S c S e C2S c E j 2S e P (E j jc) 3. Re-estmate P (E jjc) = ap (E jjc) +(1; a) usng a = 4. Iterate. where x+p x. C(E C) E j s the j th translaton for Chnese word C. Nt(C) s the number of translatons for C. P (E jc) P C(E j C) C(E C) S c S e are a par of algned Chnese and Englsh sentences, x s a parameter that governs the rate at whch probabltes are updated. There are about 230,000 sentences and about 8 mllon Englsh words n ths parallel corpus. Unfortunately, ts doman s law, so we can expect t to be useful only for estmatng translaton probables for words lkely to occur n laws. In partcular, we noted that our procedure only assgned non-unform translaton probabltes to 4,979 of the 128,365 Mandarn entres. Ths s not qute as bad as t sounds; 95,511 of the Mandarn entres have only one possble translaton. Our re-estmaton procedure gave non-unform translaton probabltes to 15% of words that have more than one translaton Co-occurrence Statstcs Addtonally, we devsed an algorthm for teratvely mprovng a translaton usng co-occurrence statstcs. When we have alternate translatons for a Mandarn word, the algorthm tends to favor those that are consstent wth the rest of the document. 1. Estmate coocurrence probabltes from large background corpus. P (E 1 2 W je 2 2 W ). W s some wndow of words. 2. Create an ntal translaton usng pror term translaton probabltes. Translaton s a probablstc bag of words. 3. For each Mandarn word wth more than one translaton, estmate posteror probablty, P (E jjc T ~ ), of each Englsh translaton gven the orgnal Mandarn word and the rest of the probablstc translaton so far. 4. Iterate, replacng the pror term translaton probabltes wth the posteror probabltes. There are many ways of estmatng the posteror. One would be to use Bayes rule to rearrange thngs untl we have quanttes we can estmate well. P (E jjc ~ T ) P (E jjc) P (Ejj ~ T ) P (E j) P (E jjc) s just the pror translaton probablty. We can estmate P (E jj T ~ ) wth a generatve model. In ths model, frst, we choose a word C 0 from the orgnal Mandarn document, accordng to P (C 0 jorg). Second, we choose an Englsh translaton accordng to P (E 0 jc 0 ). Thrd and fnally, we choose to generate a dfferent, Englsh word E j, accordng to the co-occurrence probablty P (E j 2 W je 0 2 W ). The full equaton follows. P (E jj X X T ~ ) P (E jje 0 )P (E 0 jc 0 )P (C 0 jorg) (2) C 0 6=C E 0 6=E j 2. Crosslngual TDT Systems 2.1. Trackng System Overvew We have developed several approaches to topc trackng, all Bayesan. The two most successful are known as the topc spottng (TS) system, and the nformaton retreval (IR) system. These systems are descrbed n more detal n [3]. The TS trackng system s based upon our work developng the OnTopc topc classfcaton system [1]. The raw score s a loglkelhood rato, and t represents how much more probable a document s, under the hypothess that t s on the topc, compared wth how probable t s under the null hypothess,.e. that t s not relevant to the topc. Assumng that words are generated ndependently, we can approxmate ths log-lkelhood rato as score TS X P (DjT = log ) P (wjt log ) P (D) P (3) (w) w2d P (w) s the probablty of w estmated on some large, background corpus. P (wjt ) s formed by poolng the words n documents that have T as a topc, and then re-estmatng these probabltes usng (1)

3 an teratve EM-lke procedure that tends to ncrease the lkelhood of the data gven the model. The IR trackng system s based upon our work developng the BBN IR system [4]. We use the tranng documents for a topc to form a large query, and compute the posteror probablty that a test document s relevant gven the query. Usng Bayes rule to re-wrte ths n terms of quanttes that are easer to estmate, we have P (T jdsr) P (DsRjT )=P(DsR) P (T ) P (T ) s constant across test documents. Whle P (DsR), the pror probablty that a document s relevant, could be modeled so that t would dffer from document to document, we choose to leave t as a constant. So we can safely compose the IR trackng score smply out of the condtonal probablty of the query T beng generated, under the hypothess that D s a document relevant to the query. We construct P (T jdsr) as a mxture model, one state generatng the words n the query by drawng from the document, accordng to P (wjd), and the other by drawng from a background corpus, accordng to P (w): score IR(D T ) = log P (T jdsr) (5) X log(ap (wjd) +(1; a)p (w)) (6) w2t where a can be ether a constant or a functon of features of w. It s a requrement of TDT that the score we gve for a test document be comparable across topcs. We therefore normalze a document s score usng the statstcs of the scores of thousands of known offtopc or no documents. score(d T score 0 ) ; no (D T )= (7) no where no s the mean score of all no documents, and no s the standard devaton of no document scores. Our trackng system also adapts, unsupervsed, to test documents extremely lkely to be on-topc. Any test document wth a normalzed score that s hgher than some threshold s added to the set of tranng examples and we re-estmate P (wjt ) wth all the examples. We combne the scores from the TS and IR systems to form our fnal result, usng logstc regresson, tranng the combnaton weghts on prevous corpora and tests. Ths combnaton system gves the best results. Unless otherwse noted here that wll be the result reported Detecton System Overvew The Detecton system, descrbed n detal elsewhere [2], uses the trackng TS score to measure the dstance between a document and a cluster. But here, we must normalze twce f our score s to be comparable both across test documents and clusters (topcs). Only then wll t be a score we can use along wth a threshold to make a bnary decson about whether to add a test document to a cluster or to use t as the seed for a new cluster. Frst, we compute the IR scores of many background documents aganst the cluster, fnd the mean and standard devaton, NO D and NO D, and use equaton 7 to gve us a score that s normalzed wth respect to documents certan to be off-topc. (4) Not Translated Translated by SYSTRAN BBN Table 1: Effect of Translaton: Monolngual Chnese trackng. Translatng to Englsh results n a loss of 24% to 30%. Second, we compute the normalzed scores for the test document, wth respect to many background clusters, and agan fnd the mean and standard devaton, NO C and NO C, of those scores. Then we normalze a second tme, agan usng equaton 7, now wth respect to clusters of varous szes all of whch are unlkely to be on the same topc as the test document. Ths two-level normalzaton s crtcal to detecton performance Crosslngual TDT Issues We clamed, above, that our approach would be to translate all of the Mandarn documents nto Englsh and then smply use our monolngual trackng and detecton systems as-s. Ths s almost true. In fact, we keep track of the orgnal language of each document and make use of that nformaton whle trackng. We can t really expect the score for a translated Mandarn test document to have the same statstcs as the score for an Englsh test document. So, we compute normalzaton statstcs separately for the two languages and amend our normalzaton formula to score 0 (D T score(d T )= ) ; L(D) no (8) L(D) no where L(D) s the natve language for document D. 3. Performance We present results both for development experments and the TDT3 evaluaton. Note that ctrack numbers are ncomparable between development experments, snce corpus, test, and evaluaton measures were all n flux over the tme perod Effect of Translaton Our fnal cross-lngual system made use of the re-estmated probablstc translaton dctonary. We had better results when we smply chose the hghest probablty translaton for a Mandarn word, nstead of ncludng all translatons wth fractonal counts. There was not tme to run experments wth the co-occurrence re-estmaton translaton refnement algorthm. In order to understand the loss due to translaton, we ran trackng experments on just the Mandarn documents n the development corpus (TDT2). We ran our trackng system three tmes. The frst run was wthout translaton. The second was wth the suppled SYS- TRAN (commercal MT) translaton. And the thrd was wth BBN s term translaton system. Ths comparson s n table 1. The performance of the trackng system s worse by 30% relatve when we translate wth our system and worse by 24% relatve when we use the SYSTRAN translaton. So t s certanly true that translaton s hurtng. What s remarkable s that the dfference n performance between SYSTRAN and the BBN translaton s so small, consderng how much effort has gone nto developng SYSTRAN and how smple the BBN translaton was.

4 Normalzaton Tran Test one-way two-way ENG ENG+MAN MAN ENG+MAN ENG+MAN ENG+MAN Condton Translaton SYS BBN MUL E C Table 2: Wthn Language Score Normalzaton: Trackng results, usng the smple translaton system (no probabltes), TS trackng system only. Gan s largest when trackng nvolves constructng models only from translated Mandarn documents. It occurred to us as a result of ths analyss that t would be worthwhle to spend some tme and thought ntegratng our models of translaton and TDT. Because we chose to translate everythng nto Englsh and then smply work monolngually, we lose n several ways. Obvously, whenever we translate a document, we ntroduce nose. What s perhaps less obvous s that we are translatng far more often than we need to be. When we have tranng n both languages, surely t s preferable always to compare a test document to a model n the correct language, rather than one bult of translated examples. And even when we have tranng n only one language, once adaptaton has dscovered an on-topc example n the other language, t wll be better to use that for future comparsons. In fact, we concluded, we should take a symmetrc vew of the problem. We should translate every document nto the other language for when we need to make cross-lngual comparsons. And we should mantan dstnct topc models n both languages, beng careful always to compare a test document to a model n the approprate language. Ths means we would be translatng as lttle as possble and should mprove results dramatcally Wthn-Language Score Normalzaton Score normalzaton by language was an mportant gan (see table 2). When the tranng was translated Mandarn documents, two-way normalzaton mproved ctrack by 55%. When the tranng was Englsh documents, t mproved ctrack by 5%. The dramatc dfference between these two gans s probably due to the fact that the development corpus had a very small proporton of Mandarn documents Evaluaton Results The fnal evaluaton results for TDT3 were qute good. From table 3, we see that the trackng result, as n our development experments, s about the same when we use our own smple translaton Tranng Translaton SYS BBN E C E+C Table 3: Trackng Evaluaton Result: Performance s about the same for SYSTRAN and BBN translaton. Loss for usng Chnese nstead of Englsh tranng s small. There s a gan for addng Chnese tranng to Englsh. Englsh tranng s the prmary result here. Table 4: Detecton Evaluaton Result: Agan, performance s about the same for the two knds of translaton. Chnese monolngual performance s better than Englsh monolngual, for some reason. system as t s when we use SYSTRAN. As we d expect, our performance s worse the more we translate. But we see that our system s defntely able to make use of the translated examples, achevng a farly respectable ctrack of when all of the tranng examples are n Chnese, and always mprovng (from to for SYSTRAN and from to for BBN s translaton) when translated Chnese examples are added to the Englsh ones. The detecton eval result, shown n table 4 shows a smlar result as for trackng, wth respect to translaton. Performance usng SYS- TRAN s about on par wth the BBN translaton. In partcular, t s vrtually the same n the multlngual case. 4. Conclusons We have demonstrated that t s possble to buld a full-fledged crosslngual TDT system n a few months wth lmted resources. It s clear that t s not necessary to have a mature commercal machne translaton system embodyng deep lngustc knowledge for IR-lke applcatons such as TDT. Our TDT systems dd about as well usng our translaton as they dd usng the suppled SYSTRAN translaton. Smple term translaton wth a blngual dctonary and some care about word weghtng s as good, for the purposes of TDT, as commercal MT. Ths s lkely because all TDT systems, at some level, just count the number of word matches between documents. Successful TDT systems consder matches for very uncommon words better evdence than matches for common words. Term translaton makes the fewest errors when translatng uncommon words. Wth hndsght, t s obvous that ths sort of approach wll work farly well. However, at the same tme t s clear that there s much work left to be done. We have shown that translatng results n a loss of about 30% (table 1). So even though our term translaton s as good as SYSTRAN, t could be much better. And t appears that there s a loss of about 50% for workng crosslngually (table 4). It s lkely that the choce to translate everythng nto Englsh and work monolngually costs dearly. If ths s the case, future work should revolve around mplementng the symmetrc vew of the problem that ntegrates translaton and TDT, presented above. There, we proposed translatng every document nto the other language and always comparng a test document to a model n ts natve language, thus effectvely mnmzng the amount of translaton we are forced to do. 5. Acknowledgements Ths work was supported by the Defense Advanced Research Projects Agency and montored by Ft. Huachuca under contract No. DABT63-94-C-0063 and by the Defense Advanced Research Projects Agency and montored by NRaD under contract No.

5 N D The vews and fndngs contaned n ths materal are those of the authors and do not necessarly reflect the poston or polcy of the Government and no offcal endorsement should be nferred. References 1. Schwartz, R., Ima, T., Nguyen, L., and Makhoul, J., A maxmum Lkelhood Model for Topc Calssfcaton of Broadcast News, n Proc. Eurospeech, Rhodes, Greece, September, Walls, F., Jn, H., Ssta, S., and Schwartz, R., Topc Detecton n Broadcast News, n Proceedngs of the DARPA Broadcast News Workshop, Herndon, Va, Jn, H., Schwartz, R., Ssta, S., and Walls, F., Topc Trackng for Rado, TV Broadcast, and Newswre, n Proceedngs of the DARPA Broadcast News Workshop, Herndon, Va, Mller, D., Leek, T., and Schwartz, R., A Hdden Markov Model Informaton Retreval System, n Proceedngs of the ACM Sgr 99.

Note on EM-training of IBM-model 1

Note on EM-training of IBM-model 1 Note on EM-tranng of IBM-model INF58 Language Technologcal Applcatons, Fall The sldes on ths subject (nf58 6.pdf) ncludng the example seem nsuffcent to gve a good grasp of what s gong on. Hence here are

More information

Kernel Methods and SVMs Extension

Kernel Methods and SVMs Extension Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general

More information

Evaluation for sets of classes

Evaluation for sets of classes Evaluaton for Tet Categorzaton Classfcaton accuracy: usual n ML, the proporton of correct decsons, Not approprate f the populaton rate of the class s low Precson, Recall and F 1 Better measures 21 Evaluaton

More information

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

Homework Assignment 3 Due in class, Thursday October 15

Homework Assignment 3 Due in class, Thursday October 15 Homework Assgnment 3 Due n class, Thursday October 15 SDS 383C Statstcal Modelng I 1 Rdge regresson and Lasso 1. Get the Prostrate cancer data from http://statweb.stanford.edu/~tbs/elemstatlearn/ datasets/prostate.data.

More information

A Robust Method for Calculating the Correlation Coefficient

A Robust Method for Calculating the Correlation Coefficient A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal

More information

For now, let us focus on a specific model of neurons. These are simplified from reality but can achieve remarkable results.

For now, let us focus on a specific model of neurons. These are simplified from reality but can achieve remarkable results. Neural Networks : Dervaton compled by Alvn Wan from Professor Jtendra Malk s lecture Ths type of computaton s called deep learnng and s the most popular method for many problems, such as computer vson

More information

Limited Dependent Variables

Limited Dependent Variables Lmted Dependent Varables. What f the left-hand sde varable s not a contnuous thng spread from mnus nfnty to plus nfnty? That s, gven a model = f (, β, ε, where a. s bounded below at zero, such as wages

More information

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)

ANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U) Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of

More information

Gaussian Mixture Models

Gaussian Mixture Models Lab Gaussan Mxture Models Lab Objectve: Understand the formulaton of Gaussan Mxture Models (GMMs) and how to estmate GMM parameters. You ve already seen GMMs as the observaton dstrbuton n certan contnuous

More information

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

Vapnik-Chervonenkis theory

Vapnik-Chervonenkis theory Vapnk-Chervonenks theory Rs Kondor June 13, 2008 For the purposes of ths lecture, we restrct ourselves to the bnary supervsed batch learnng settng. We assume that we have an nput space X, and an unknown

More information

Motion Perception Under Uncertainty. Hongjing Lu Department of Psychology University of Hong Kong

Motion Perception Under Uncertainty. Hongjing Lu Department of Psychology University of Hong Kong Moton Percepton Under Uncertanty Hongjng Lu Department of Psychology Unversty of Hong Kong Outlne Uncertanty n moton stmulus Correspondence problem Qualtatve fttng usng deal observer models Based on sgnal

More information

10-701/ Machine Learning, Fall 2005 Homework 3

10-701/ Machine Learning, Fall 2005 Homework 3 10-701/15-781 Machne Learnng, Fall 2005 Homework 3 Out: 10/20/05 Due: begnnng of the class 11/01/05 Instructons Contact questons-10701@autonlaborg for queston Problem 1 Regresson and Cross-valdaton [40

More information

Generalized Linear Methods

Generalized Linear Methods Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set

More information

Statistics II Final Exam 26/6/18

Statistics II Final Exam 26/6/18 Statstcs II Fnal Exam 26/6/18 Academc Year 2017/18 Solutons Exam duraton: 2 h 30 mn 1. (3 ponts) A town hall s conductng a study to determne the amount of leftover food produced by the restaurants n the

More information

Grover s Algorithm + Quantum Zeno Effect + Vaidman

Grover s Algorithm + Quantum Zeno Effect + Vaidman Grover s Algorthm + Quantum Zeno Effect + Vadman CS 294-2 Bomb 10/12/04 Fall 2004 Lecture 11 Grover s algorthm Recall that Grover s algorthm for searchng over a space of sze wors as follows: consder the

More information

Split alignment. Martin C. Frith April 13, 2012

Split alignment. Martin C. Frith April 13, 2012 Splt algnment Martn C. Frth Aprl 13, 2012 1 Introducton Ths document s about algnng a query sequence to a genome, allowng dfferent parts of the query to match dfferent parts of the genome. Here are some

More information

Assortment Optimization under MNL

Assortment Optimization under MNL Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.

More information

9 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations

9 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations Physcs 171/271 - Chapter 9R -Davd Klenfeld - Fall 2005 9 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys a set

More information

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys

More information

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)

See Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition) Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes

More information

Problem Set 9 Solutions

Problem Set 9 Solutions Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem

More information

Boostrapaggregating (Bagging)

Boostrapaggregating (Bagging) Boostrapaggregatng (Baggng) An ensemble meta-algorthm desgned to mprove the stablty and accuracy of machne learnng algorthms Can be used n both regresson and classfcaton Reduces varance and helps to avod

More information

Errors for Linear Systems

Errors for Linear Systems Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch

More information

Supporting Information

Supporting Information Supportng Informaton The neural network f n Eq. 1 s gven by: f x l = ReLU W atom x l + b atom, 2 where ReLU s the element-wse rectfed lnear unt, 21.e., ReLUx = max0, x, W atom R d d s the weght matrx to

More information

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA

4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA 4 Analyss of Varance (ANOVA) 5 ANOVA 51 Introducton ANOVA ANOVA s a way to estmate and test the means of multple populatons We wll start wth one-way ANOVA If the populatons ncluded n the study are selected

More information

Composite Hypotheses testing

Composite Hypotheses testing Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter

More information

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore

Predictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.

More information

Question Classification Using Language Modeling

Question Classification Using Language Modeling Queston Classfcaton Usng Language Modelng We L Center for Intellgent Informaton Retreval Department of Computer Scence Unversty of Massachusetts, Amherst, MA 01003 ABSTRACT Queston classfcaton assgns a

More information

CSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography

CSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography CSc 6974 and ECSE 6966 Math. Tech. for Vson, Graphcs and Robotcs Lecture 21, Aprl 17, 2006 Estmatng A Plane Homography Overvew We contnue wth a dscusson of the major ssues, usng estmaton of plane projectve

More information

Lecture 10 Support Vector Machines II

Lecture 10 Support Vector Machines II Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed

More information

Retrieval Models: Language models

Retrieval Models: Language models CS-590I Informaton Retreval Retreval Models: Language models Luo S Department of Computer Scence Purdue Unversty Introducton to language model Ungram language model Document language model estmaton Maxmum

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

Checking Pairwise Relationships. Lecture 19 Biostatistics 666

Checking Pairwise Relationships. Lecture 19 Biostatistics 666 Checkng Parwse Relatonshps Lecture 19 Bostatstcs 666 Last Lecture: Markov Model for Multpont Analyss X X X 1 3 X M P X 1 I P X I P X 3 I P X M I 1 3 M I 1 I I 3 I M P I I P I 3 I P... 1 IBD states along

More information

Finding Dense Subgraphs in G(n, 1/2)

Finding Dense Subgraphs in G(n, 1/2) Fndng Dense Subgraphs n Gn, 1/ Atsh Das Sarma 1, Amt Deshpande, and Rav Kannan 1 Georga Insttute of Technology,atsh@cc.gatech.edu Mcrosoft Research-Bangalore,amtdesh,annan@mcrosoft.com Abstract. Fndng

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

CS47300: Web Information Search and Management

CS47300: Web Information Search and Management CS47300: Web Informaton Search and Management Probablstc Retreval Models Prof. Chrs Clfton 7 September 2018 Materal adapted from course created by Dr. Luo S, now leadng Albaba research group 14 Why probabltes

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

Expectation Maximization Mixture Models HMMs

Expectation Maximization Mixture Models HMMs -755 Machne Learnng for Sgnal Processng Mture Models HMMs Class 9. 2 Sep 200 Learnng Dstrbutons for Data Problem: Gven a collecton of eamples from some data, estmate ts dstrbuton Basc deas of Mamum Lelhood

More information

Markov Chain Monte Carlo (MCMC), Gibbs Sampling, Metropolis Algorithms, and Simulated Annealing Bioinformatics Course Supplement

Markov Chain Monte Carlo (MCMC), Gibbs Sampling, Metropolis Algorithms, and Simulated Annealing Bioinformatics Course Supplement Markov Chan Monte Carlo MCMC, Gbbs Samplng, Metropols Algorthms, and Smulated Annealng 2001 Bonformatcs Course Supplement SNU Bontellgence Lab http://bsnuackr/ Outlne! Markov Chan Monte Carlo MCMC! Metropols-Hastngs

More information

THE SUMMATION NOTATION Ʃ

THE SUMMATION NOTATION Ʃ Sngle Subscrpt otaton THE SUMMATIO OTATIO Ʃ Most of the calculatons we perform n statstcs are repettve operatons on lsts of numbers. For example, we compute the sum of a set of numbers, or the sum of the

More information

Ensemble Methods: Boosting

Ensemble Methods: Boosting Ensemble Methods: Boostng Ncholas Ruozz Unversty of Texas at Dallas Based on the sldes of Vbhav Gogate and Rob Schapre Last Tme Varance reducton va baggng Generate new tranng data sets by samplng wth replacement

More information

P R. Lecture 4. Theory and Applications of Pattern Recognition. Dept. of Electrical and Computer Engineering /

P R. Lecture 4. Theory and Applications of Pattern Recognition. Dept. of Electrical and Computer Engineering / Theory and Applcatons of Pattern Recognton 003, Rob Polkar, Rowan Unversty, Glassboro, NJ Lecture 4 Bayes Classfcaton Rule Dept. of Electrcal and Computer Engneerng 0909.40.0 / 0909.504.04 Theory & Applcatons

More information

Lecture Nov

Lecture Nov Lecture 18 Nov 07 2008 Revew Clusterng Groupng smlar obects nto clusters Herarchcal clusterng Agglomeratve approach (HAC: teratvely merge smlar clusters Dfferent lnkage algorthms for computng dstances

More information

Lecture 4: Universal Hash Functions/Streaming Cont d

Lecture 4: Universal Hash Functions/Streaming Cont d CSE 5: Desgn and Analyss of Algorthms I Sprng 06 Lecture 4: Unversal Hash Functons/Streamng Cont d Lecturer: Shayan Oves Gharan Aprl 6th Scrbe: Jacob Schreber Dsclamer: These notes have not been subjected

More information

Notes on Frequency Estimation in Data Streams

Notes on Frequency Estimation in Data Streams Notes on Frequency Estmaton n Data Streams In (one of) the data streamng model(s), the data s a sequence of arrvals a 1, a 2,..., a m of the form a j = (, v) where s the dentty of the tem and belongs to

More information

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced,

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced, FREQUENCY DISTRIBUTIONS Page 1 of 6 I. Introducton 1. The dea of a frequency dstrbuton for sets of observatons wll be ntroduced, together wth some of the mechancs for constructng dstrbutons of data. Then

More information

Hopfield networks and Boltzmann machines. Geoffrey Hinton et al. Presented by Tambet Matiisen

Hopfield networks and Boltzmann machines. Geoffrey Hinton et al. Presented by Tambet Matiisen Hopfeld networks and Boltzmann machnes Geoffrey Hnton et al. Presented by Tambet Matsen 18.11.2014 Hopfeld network Bnary unts Symmetrcal connectons http://www.nnwj.de/hopfeld-net.html Energy functon The

More information

8 Derivation of Network Rate Equations from Single- Cell Conductance Equations

8 Derivation of Network Rate Equations from Single- Cell Conductance Equations Physcs 178/278 - Davd Klenfeld - Wnter 2015 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons We consder a network of many neurons, each of whch obeys a set of conductancebased,

More information

This column is a continuation of our previous column

This column is a continuation of our previous column Comparson of Goodness of Ft Statstcs for Lnear Regresson, Part II The authors contnue ther dscusson of the correlaton coeffcent n developng a calbraton for quanttatve analyss. Jerome Workman Jr. and Howard

More information

THE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens

THE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens THE CHINESE REMAINDER THEOREM KEITH CONRAD We should thank the Chnese for ther wonderful remander theorem. Glenn Stevens 1. Introducton The Chnese remander theorem says we can unquely solve any par of

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

Case A. P k = Ni ( 2L i k 1 ) + (# big cells) 10d 2 P k.

Case A. P k = Ni ( 2L i k 1 ) + (# big cells) 10d 2 P k. THE CELLULAR METHOD In ths lecture, we ntroduce the cellular method as an approach to ncdence geometry theorems lke the Szemeréd-Trotter theorem. The method was ntroduced n the paper Combnatoral complexty

More information

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010 Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton

More information

18.1 Introduction and Recap

18.1 Introduction and Recap CS787: Advanced Algorthms Scrbe: Pryananda Shenoy and Shjn Kong Lecturer: Shuch Chawla Topc: Streamng Algorthmscontnued) Date: 0/26/2007 We contnue talng about streamng algorthms n ths lecture, ncludng

More information

= z 20 z n. (k 20) + 4 z k = 4

= z 20 z n. (k 20) + 4 z k = 4 Problem Set #7 solutons 7.2.. (a Fnd the coeffcent of z k n (z + z 5 + z 6 + z 7 + 5, k 20. We use the known seres expanson ( n+l ( z l l z n below: (z + z 5 + z 6 + z 7 + 5 (z 5 ( + z + z 2 + z + 5 5

More information

Lecture Notes on Linear Regression

Lecture Notes on Linear Regression Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume

More information

since [1-( 0+ 1x1i+ 2x2 i)] [ 0+ 1x1i+ assumed to be a reasonable approximation

since [1-( 0+ 1x1i+ 2x2 i)] [ 0+ 1x1i+ assumed to be a reasonable approximation Econ 388 R. Butler 204 revsons Lecture 4 Dummy Dependent Varables I. Lnear Probablty Model: the Regresson model wth a dummy varables as the dependent varable assumpton, mplcaton regular multple regresson

More information

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY 2006 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE THE ROYAL STATISTICAL SOCIETY 6 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutons to assst canddates preparng for the eamnatons n future years and for

More information

STAT 511 FINAL EXAM NAME Spring 2001

STAT 511 FINAL EXAM NAME Spring 2001 STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte

More information

Natural Images, Gaussian Mixtures and Dead Leaves Supplementary Material

Natural Images, Gaussian Mixtures and Dead Leaves Supplementary Material Natural Images, Gaussan Mxtures and Dead Leaves Supplementary Materal Danel Zoran Interdscplnary Center for Neural Computaton Hebrew Unversty of Jerusalem Israel http://www.cs.huj.ac.l/ danez Yar Wess

More information

CIS526: Machine Learning Lecture 3 (Sept 16, 2003) Linear Regression. Preparation help: Xiaoying Huang. x 1 θ 1 output... θ M x M

CIS526: Machine Learning Lecture 3 (Sept 16, 2003) Linear Regression. Preparation help: Xiaoying Huang. x 1 θ 1 output... θ M x M CIS56: achne Learnng Lecture 3 (Sept 6, 003) Preparaton help: Xaoyng Huang Lnear Regresson Lnear regresson can be represented by a functonal form: f(; θ) = θ 0 0 +θ + + θ = θ = 0 ote: 0 s a dummy attrbute

More information

Basically, if you have a dummy dependent variable you will be estimating a probability.

Basically, if you have a dummy dependent variable you will be estimating a probability. ECON 497: Lecture Notes 13 Page 1 of 1 Metropoltan State Unversty ECON 497: Research and Forecastng Lecture Notes 13 Dummy Dependent Varable Technques Studenmund Chapter 13 Bascally, f you have a dummy

More information

1 The Mistake Bound Model

1 The Mistake Bound Model 5-850: Advanced Algorthms CMU, Sprng 07 Lecture #: Onlne Learnng and Multplcatve Weghts February 7, 07 Lecturer: Anupam Gupta Scrbe: Bryan Lee,Albert Gu, Eugene Cho he Mstake Bound Model Suppose there

More information

8 Derivation of Network Rate Equations from Single- Cell Conductance Equations

8 Derivation of Network Rate Equations from Single- Cell Conductance Equations Physcs 178/278 - Davd Klenfeld - Wnter 2019 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons Our goal to derve the form of the abstract quanttes n rate equatons, such as synaptc

More information

Online Appendix to: Axiomatization and measurement of Quasi-hyperbolic Discounting

Online Appendix to: Axiomatization and measurement of Quasi-hyperbolic Discounting Onlne Appendx to: Axomatzaton and measurement of Quas-hyperbolc Dscountng José Lus Montel Olea Tomasz Strzaleck 1 Sample Selecton As dscussed before our ntal sample conssts of two groups of subjects. Group

More information

Linear Feature Engineering 11

Linear Feature Engineering 11 Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19

More information

Module 9. Lecture 6. Duality in Assignment Problems

Module 9. Lecture 6. Duality in Assignment Problems Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept

More information

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6

Department of Quantitative Methods & Information Systems. Time Series and Their Components QMIS 320. Chapter 6 Department of Quanttatve Methods & Informaton Systems Tme Seres and Ther Components QMIS 30 Chapter 6 Fall 00 Dr. Mohammad Zanal These sldes were modfed from ther orgnal source for educatonal purpose only.

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor

Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data

More information

Manning & Schuetze, FSNLP (c)1999, 2001

Manning & Schuetze, FSNLP (c)1999, 2001 page 589 16.2 Maxmum Entropy Modelng 589 Mannng & Schuetze, FSNLP (c)1999, 2001 a decson tree that detects spam. Fndng the rght features s paramount for ths task, so desgn your feature set carefully. Exercse

More information

Chapter 6. Supplemental Text Material

Chapter 6. Supplemental Text Material Chapter 6. Supplemental Text Materal S6-. actor Effect Estmates are Least Squares Estmates We have gven heurstc or ntutve explanatons of how the estmates of the factor effects are obtaned n the textboo.

More information

Probabilistic Information Retrieval CE-324: Modern Information Retrieval Sharif University of Technology

Probabilistic Information Retrieval CE-324: Modern Information Retrieval Sharif University of Technology Probablstc Informaton Retreval CE-324: Modern Informaton Retreval Sharf Unversty of Technology M. Soleyman Fall 2016 Most sldes have been adapted from: Profs. Mannng, Nayak & Raghavan (CS-276, Stanford)

More information

A Bayes Algorithm for the Multitask Pattern Recognition Problem Direct Approach

A Bayes Algorithm for the Multitask Pattern Recognition Problem Direct Approach A Bayes Algorthm for the Multtask Pattern Recognton Problem Drect Approach Edward Puchala Wroclaw Unversty of Technology, Char of Systems and Computer etworks, Wybrzeze Wyspanskego 7, 50-370 Wroclaw, Poland

More information

Week 5: Neural Networks

Week 5: Neural Networks Week 5: Neural Networks Instructor: Sergey Levne Neural Networks Summary In the prevous lecture, we saw how we can construct neural networks by extendng logstc regresson. Neural networks consst of multple

More information

Logistic Regression. CAP 5610: Machine Learning Instructor: Guo-Jun QI

Logistic Regression. CAP 5610: Machine Learning Instructor: Guo-Jun QI Logstc Regresson CAP 561: achne Learnng Instructor: Guo-Jun QI Bayes Classfer: A Generatve model odel the posteror dstrbuton P(Y X) Estmate class-condtonal dstrbuton P(X Y) for each Y Estmate pror dstrbuton

More information

Chapter 5 Multilevel Models

Chapter 5 Multilevel Models Chapter 5 Multlevel Models 5.1 Cross-sectonal multlevel models 5.1.1 Two-level models 5.1.2 Multple level models 5.1.3 Multple level modelng n other felds 5.2 Longtudnal multlevel models 5.2.1 Two-level

More information

Density matrix. c α (t)φ α (q)

Density matrix. c α (t)φ α (q) Densty matrx Note: ths s supplementary materal. I strongly recommend that you read t for your own nterest. I beleve t wll help wth understandng the quantum ensembles, but t s not necessary to know t n

More information

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers

Psychology 282 Lecture #24 Outline Regression Diagnostics: Outliers Psychology 282 Lecture #24 Outlne Regresson Dagnostcs: Outlers In an earler lecture we studed the statstcal assumptons underlyng the regresson model, ncludng the followng ponts: Formal statement of assumptons.

More information

Bayesian predictive Configural Frequency Analysis

Bayesian predictive Configural Frequency Analysis Psychologcal Test and Assessment Modelng, Volume 54, 2012 (3), 285-292 Bayesan predctve Confgural Frequency Analyss Eduardo Gutérrez-Peña 1 Abstract Confgural Frequency Analyss s a method for cell-wse

More information

We present the algorithm first, then derive it later. Assume access to a dataset {(x i, y i )} n i=1, where x i R d and y i { 1, 1}.

We present the algorithm first, then derive it later. Assume access to a dataset {(x i, y i )} n i=1, where x i R d and y i { 1, 1}. CS 189 Introducton to Machne Learnng Sprng 2018 Note 26 1 Boostng We have seen that n the case of random forests, combnng many mperfect models can produce a snglodel that works very well. Ths s the dea

More information

Hidden Markov Models

Hidden Markov Models CM229S: Machne Learnng for Bonformatcs Lecture 12-05/05/2016 Hdden Markov Models Lecturer: Srram Sankararaman Scrbe: Akshay Dattatray Shnde Edted by: TBD 1 Introducton For a drected graph G we can wrte

More information

3.1 ML and Empirical Distribution

3.1 ML and Empirical Distribution 67577 Intro. to Machne Learnng Fall semester, 2008/9 Lecture 3: Maxmum Lkelhood/ Maxmum Entropy Dualty Lecturer: Amnon Shashua Scrbe: Amnon Shashua 1 In the prevous lecture we defned the prncple of Maxmum

More information

2.3 Nilpotent endomorphisms

2.3 Nilpotent endomorphisms s a block dagonal matrx, wth A Mat dm U (C) In fact, we can assume that B = B 1 B k, wth B an ordered bass of U, and that A = [f U ] B, where f U : U U s the restrcton of f to U 40 23 Nlpotent endomorphsms

More information

CHAPTER IV RESEARCH FINDING AND DISCUSSIONS

CHAPTER IV RESEARCH FINDING AND DISCUSSIONS CHAPTER IV RESEARCH FINDING AND DISCUSSIONS A. Descrpton of Research Fndng. The Implementaton of Learnng Havng ganed the whole needed data, the researcher then dd analyss whch refers to the statstcal data

More information

Hidden Markov Models

Hidden Markov Models Hdden Markov Models Namrata Vaswan, Iowa State Unversty Aprl 24, 204 Hdden Markov Model Defntons and Examples Defntons:. A hdden Markov model (HMM) refers to a set of hdden states X 0, X,..., X t,...,

More information

Lecture 6: Introduction to Linear Regression

Lecture 6: Introduction to Linear Regression Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6

More information

Bayesian Learning. Smart Home Health Analytics Spring Nirmalya Roy Department of Information Systems University of Maryland Baltimore County

Bayesian Learning. Smart Home Health Analytics Spring Nirmalya Roy Department of Information Systems University of Maryland Baltimore County Smart Home Health Analytcs Sprng 2018 Bayesan Learnng Nrmalya Roy Department of Informaton Systems Unversty of Maryland Baltmore ounty www.umbc.edu Bayesan Learnng ombnes pror knowledge wth evdence to

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

Hopfield Training Rules 1 N

Hopfield Training Rules 1 N Hopfeld Tranng Rules To memorse a sngle pattern Suppose e set the eghts thus - = p p here, s the eght beteen nodes & s the number of nodes n the netor p s the value requred for the -th node What ll the

More information

Topic 23 - Randomized Complete Block Designs (RCBD)

Topic 23 - Randomized Complete Block Designs (RCBD) Topc 3 ANOVA (III) 3-1 Topc 3 - Randomzed Complete Block Desgns (RCBD) Defn: A Randomzed Complete Block Desgn s a varant of the completely randomzed desgn (CRD) that we recently learned. In ths desgn,

More information

Mixture o f of Gaussian Gaussian clustering Nov

Mixture o f of Gaussian Gaussian clustering Nov Mture of Gaussan clusterng Nov 11 2009 Soft vs hard lusterng Kmeans performs Hard clusterng: Data pont s determnstcally assgned to one and only one cluster But n realty clusters may overlap Soft-clusterng:

More information

STATISTICS QUESTIONS. Step by Step Solutions.

STATISTICS QUESTIONS. Step by Step Solutions. STATISTICS QUESTIONS Step by Step Solutons www.mathcracker.com 9//016 Problem 1: A researcher s nterested n the effects of famly sze on delnquency for a group of offenders and examnes famles wth one to

More information

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh Computatonal Bology Lecture 8: Substtuton matrces Saad Mnemneh As we have ntroduced last tme, smple scorng schemes lke + or a match, - or a msmatch and -2 or a gap are not justable bologcally, especally

More information

Learning from Data 1 Naive Bayes

Learning from Data 1 Naive Bayes Learnng from Data 1 Nave Bayes Davd Barber dbarber@anc.ed.ac.uk course page : http://anc.ed.ac.uk/ dbarber/lfd1/lfd1.html c Davd Barber 2001, 2002 1 Learnng from Data 1 : c Davd Barber 2001,2002 2 1 Why

More information

Bit Juggling. Representing Information. representations. - Some other bits. - Representing information using bits - Number. Chapter

Bit Juggling. Representing Information. representations. - Some other bits. - Representing information using bits - Number. Chapter Representng Informaton 1 1 1 1 Bt Jugglng - Representng nformaton usng bts - Number representatons - Some other bts Chapter 3.1-3.3 REMINDER: Problem Set #1 s now posted and s due next Wednesday L3 Encodng

More information