INTRODUCTION TO MACHINE LEARNING FOR MEDICINE
|
|
- Sydney Thompson
- 5 years ago
- Views:
Transcription
1 Fall 2017 INTRODUCTION TO MACHINE LEARNING FOR MEDICINE Carla E. Brdley Prfessr & Dean Cllege f Cmputer and Infrmatin Science Nrtheastern University
2 WHAT IS MACHINE LEARNING/DATA MINING? Figure is frm Fayyad, Piatetsky-Shapir, Smyth, and Uthurusamy. Advances in Knwledge Discvery and Data Mining, 1996; image fund at: www2.cs.uregina.ca/~dbd/cs831/ntes/kdd/kdd.gif
3 Fall 2017 SUPERVISED LEARNING NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 3
4 SUPERVISED LEARNING Given: eample < 1, 2, nn, ff( 1, 2, nn ) > fr sme unknwn functin ff Find: A gd apprimatin t ff Gal: Apply ff t previusly unseen data Eample Applicatins: Regressin: ff is a cntinuus variable (e.g., predicting EDSS fr MS patients) Classificatin: ff is a discrete variable (e.g., predicting whether a patient has unilateral r bilateral Meniere s)
5 CLASSIFICATION EXAMPLE: CITATION SCREENING FOR SYSTEMATIC REVIEWS Systematic review: an ehaustive assessment f all the published medical evidence regarding a precise clinical questin e.g., Is aspirin better than leeches in inducing mre than 50% relief in patients with tensin headaches? Must find all relevant studies
6 TYPICAL WORKFLOW 26M PubMed SEARCH 10,000 Ptentially eligible SCREEN 500 Relevant
7 CITATION SCREENING Dctrs read these. They d rather be ding smething else.
8 GENERATING TRAINING DATA FOR SUPERVISED LEARNING Epert labels randm subset Induce (train) a classifier C ver Apply C t unlabeled eamples -
9 A DETOUR INTO TEXT ENCODING Classificatin algrithms perate n vectrs Feature space: an n-dimensinal representatin A bag-f-wrds eample: S 1 = Bstn drivers are frequently aggressive S 2 = The Bstn Red S frequently hit line drives
10 TEXT ENCODING: STOP WORDS S 1 = Bstn drivers are frequently aggressive S 2 = The Bstn Red S frequently hit line drives
11 TEXT ENCODING: LOWERCASING S 1 = bstn drivers are frequently aggressive S 2 = The bstn red s frequently hit line drives
12 TEXT ENCODING: STEMMING S 1 = bstn drive are frequent aggressive S 2 = The bstn red s frequent hit line drive
13 TEXT ENCODING: VOILA hit red s line bstn frequent drive aggressive S 1 = S 2 = A new sentence, S 3, cmes alng: I hate the red s. Which sentence is it mst similar t? S 3 =
14 SUPPORT VECTOR MACHINES: A HAND-WAVING EXPLANATION margin supprt vectrs Minimize: ww. ww
15 SUPPORT VECTOR MACHINES: THE NON-LINEARLY SEPARABLE CASE ε 6 ε 2 ε 11 Minimize: ww. ww + CC εε RR kk=11 kk
16 SUPERVISED LEARNING Epert labels randm subset Induce (train) a classifier C ver Apply C t unlabeled eamples -
17 SUPERVISED LEARNING What if we are clever in what eamples we label? Induce (train) a classifier C ver Apply C t unlabeled eamples -
18 ACTIVE LEARNING Key idea: have the epert label eamples mst likely t be helpful in inducing a classifier Need fewer labels fr gd classificatin perfrmance = less time/wrk/mney Need a scring functin ff: epected value f labeling Mst ppular strategy: uncertainty sampling
19 UNCERTAINTY SAMPLING (W/ SVMS) Which eamples shuld we label net?
20 UNCERTAINTY SAMPLING (W/ SVMS) Uncertainty sampling: label the eamples nearest the separating plane
21 UNCERTAINTY SAMPLING (W/ SVMS)
22 WHY OFF-THE-SHELF AL DOESN T WORK FOR CITATION SCREENING Imbalanced data; relevant class is very small (~5%), but sensitivity t this class is paramunt Randm Active (uncertainty) Recall Accuracy
23 WHY MIGHT UNCERTAINTY SAMPLING FAIL? Randm sampling Uncertainty sampling Hasty generalizatin: uncertainty sampling may miss clusters Pre-clustering desn t help unreliable in high-dimensins small clusters f interest
24 GUIDING AL WITH DOMAIN KNOWLEDGE Labeled terms: terms r n-grams whse presence is indicative f class membership tensin headache, leeches, aspirin migraine headache, mice Is aspirin better than leeches in inducing mre than 50% relief in patients with tensin headaches?
25 CO-TESTING FRAMEWORK (MUSLEA ET AL., 2000) Mdel 1 Mdel 2 F 1 () F 2 () If mdel 1 disagrees with mdel 2 abut, then is a gd pint t label
26 LABELED TERMS + CO-TESTING Mdel 1: Standard BOW (linear kernel) SVM Mdel 2: Rati f #ps terms t #neg terms Query strategy: Find all dcuments abut which the mdels disagree Select fr labeling items f maimum disagreement
27 COPD: GENETIC ASSOCIATIONS WITH COPD
28 MOST IMPORTANT REQUIREMENT FOR MACHINE LEARNING TO WORK: THE DATA Are the features predictive f the class? Hw nisy is the data? (attribute nise vs. class nise) D yu have enugh (labeled) data? Are the training samples representative? NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 28
29 TRANSFER LEARNING A machine learning technique t imprve perfrmance leveraging n related knwledge A primary task n dataset TT An auiliary dataset TT aaaaaa TT and TT aaaaaa are usually related and have similar distributins Auiliary TT aaaaaa Primary TT
30 TRANSFER LEARNING EXAMPLES Predicting readmissin t hspitals Use data frm ther hspitals t predict fr yur hspital Predicting MS prgressin Cmbining data frm multiple physicians NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 30
31 Fall 2017 UNSUPERVISED LEARNING NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 31
32 CLUSTERING Given a set f data pints, each described by a set f attributes, find clusters such that: Inter-cluster similarity is maimized Intra-cluster similarity is minimized Requires the definitin f a similarity measure F1 F2
33 EXAMPLE: K-MEANS
34 EXAMPLE: K-MEANS
35 EXAMPLE: K-MEANS
36 EXAMPLE: K-MEANS
37 EXAMPLE: K-MEANS
38 EXAMPLE: K-MEANS
39 EXAMPLE: CONSTRAINED K-MEANS
40 EXAMPLE: CONSTRAINED K-MEANS
41 EXAMPLE: CONSTRAINED K-MEANS
42 CHALLENGES IN CLUSTERING MEDICAL DATA Cnfunding factr: One r a set f features whse effect will lead t undesirable clustering slutin if nt remved Clustering clinical data: Physician subjectivity Age fr neurlgical test scring in MS
43 EXAMPLE: VESTIBULAR DISORDERS Balance Functin Age
44 CLUSTERING WITH K = 2 Balance Functin Age
45 PROPOSED SOLUTION Remve the impact f cnfunding factr F via cnstraint-based clustering: 1. Bin the data int hmgeneus grups w.r.t. F 2. Apply clustering t each grup and generate pair-wise instance cnstraints 3. Apply cnstraint-based clustering t entire data
46 STEP 1: BINNING (STRATIFICATION) Categrical F: Create ne bin per categry Eample: ne bin per physician fr MS data Numeric F: Create bins f: Unifrm ranges r unifrm bin sizes Dmain knwledge Mre sphisticated binning methds, such as nnparametric density estimatin, etc
47 STEP 1: BINNING Balance Functin 40 Age
48 STEP 2: CLUSTER IN EACH BIN AND GENERATE CONSTRAINTS In each bin: Apply clustering (e.g., EM ver a miture f Gaussians) Number f clusters can be specified by dmain knwledge r inferred using criteria such as BIC Generate must-nt-link cnstraints fr pairs f instances in different clusters
49 STEP 2: CLUSTER EACH BIN Balance Functin 40 Age
50 STEP 2: GENERATE CONSTRAINTS Balance Functin 40 Age
51 STEP 3: APPLY CONSTRAINT BASED CLUSTERING TO THE ENTIRE DATA Balance Functin Age
52 Fall 2017 ANOMALY DETECTION NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 52
53 ANOMALY DETECTION Given a set f data pints, each described by a set f attributes, pints that are far away frm mst f the ther pints als called utliers Requires the definitin f a similarity measure F1 F2
54 TYPES OF ANOMALY DETECTION Supervised Labelled nrmal and anmalus data Similar t rare (minrity) class mining Semi-supervised Labels available nly fr nrmal data Unsupervised N labelled data Assumptin: anmalies are rare cmpared t nrmal data
55 COMPLEXITIES OF ANOMALY DETECTION Where des the nrmal data cme frm? Feature selectin Metric Different parts f the space may have different densities NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 55
56 COMPLEXITIES OF ANOMALY DETECTION Which f P1, P2 and P3 are anmalies? Distance frm p 3 t nearest neighbr p 3 Distance frm p 2 t nearest neighbr p 2 p 1
57 ANOMALY DETECTION EXAMPLE: DETECTING CORTICAL LESIONS 50 millin affected by epilepsy wrldwide One-third remain refractry t treatment One f the mst cmmn causes f TRE: Fcal Crtical Dysplasia (FCD) Treatment: Surgical resectin f the abnrmal crtical tissue (aka lesin) Visual MRI Eam Lesin Identificatin & Tracing Inter-Cranial EEG Analysis Resective Surgery 70-80% f histlgically verified FCD cases have nrmal MRI Chances f being seizure free after surgery: MRI-Psitive: 66% MRI-Negative: 29%
58 MACHINE LEARNING CHALLENGES Input data Surfaces f FCD patients (MRI) Resected tissue (MRI-Negatives): histpathlgically verified Generus margins t ensure cmplete lesin remval Eact lcatin f the lesin is unknwn Labels Resectin znes fr MRI-negatives Lesin tracings by neurradilgists fr MRI-psitives False psitives in training data False negatives in training data frm lng untreated epilepsy, trauma, etc.
59 PROPOSED SOLUTION Hierarchical Cnditinal Randm Fields fr Outlier Detectin Discard piel-level labels and use nly image-level labels Redefine FCD lesin as: a crtical regin which is an utlier when cmpared t the same regin acrss a ppulatin f nrmal cntrls Hierarchical Cnditinal Randm Field
60 RESULTS Tested n fifteen MRI-negative patients with successful surgery High detectin rate (80%) fr MRInegative patients with higher average recall and precisin
61 MY LAST WORDS There are many, many different learning algrithms, but the key t success is in having the right training data. MLHC is a great cnference. NORTHEASTERN UNIVERSITY COLLEGE OF COMPUTER AND INFORMATION SCIENCE 61
Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff
Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised
More informationLecture 2: Supervised vs. unsupervised learning, bias-variance tradeoff
Lecture 2: Supervised vs. unsupervised learning, bias-variance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised
More informationk-nearest Neighbor How to choose k Average of k points more reliable when: Large k: noise in attributes +o o noise in class labels
Mtivating Example Memry-Based Learning Instance-Based Learning K-earest eighbr Inductive Assumptin Similar inputs map t similar utputs If nt true => learning is impssible If true => learning reduces t
More informationChapter 3: Cluster Analysis
Chapter 3: Cluster Analysis } 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries } 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA
More informationPattern Recognition 2014 Support Vector Machines
Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft
More informationIAML: Support Vector Machines
1 / 22 IAML: Supprt Vectr Machines Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester 1 2 / 22 Outline Separating hyperplane with maimum margin Nn-separable training data Epanding the input int
More informationAgenda. What is Machine Learning? Learning Type of Learning: Supervised, Unsupervised and semi supervised Classification
Agenda Artificial Intelligence and its applicatins Lecture 6 Supervised Learning Prfessr Daniel Yeung danyeung@ieee.rg Dr. Patrick Chan patrickchan@ieee.rg Suth China University f Technlgy, China Learning
More informationThe Kullback-Leibler Kernel as a Framework for Discriminant and Localized Representations for Visual Recognition
The Kullback-Leibler Kernel as a Framewrk fr Discriminant and Lcalized Representatins fr Visual Recgnitin Nun Vascncels Purdy H Pedr Mren ECE Department University f Califrnia, San Dieg HP Labs Cambridge
More informationElements of Machine Intelligence - I
ECE-175A Elements f Machine Intelligence - I Ken Kreutz-Delgad Nun Vascncels ECE Department, UCSD Winter 2011 The curse The curse will cver basic, but imprtant, aspects f machine learning and pattern recgnitin
More informationPart 3 Introduction to statistical classification techniques
Part 3 Intrductin t statistical classificatin techniques Machine Learning, Part 3, March 07 Fabi Rli Preamble ØIn Part we have seen that if we knw: Psterir prbabilities P(ω i / ) Or the equivalent terms
More informationIn SMV I. IAML: Support Vector Machines II. This Time. The SVM optimization problem. We saw:
In SMV I IAML: Supprt Vectr Machines II Nigel Gddard Schl f Infrmatics Semester 1 We sa: Ma margin trick Gemetry f the margin and h t cmpute it Finding the ma margin hyperplane using a cnstrained ptimizatin
More informationx 1 Outline IAML: Logistic Regression Decision Boundaries Example Data
Outline IAML: Lgistic Regressin Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester Lgistic functin Lgistic regressin Learning lgistic regressin Optimizatin The pwer f nn-linear basis functins Least-squares
More informationCOMP 551 Applied Machine Learning Lecture 11: Support Vector Machines
COMP 551 Applied Machine Learning Lecture 11: Supprt Vectr Machines Instructr: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted fr this curse
More informationResampling Methods. Cross-validation, Bootstrapping. Marek Petrik 2/21/2017
Resampling Methds Crss-validatin, Btstrapping Marek Petrik 2/21/2017 Sme f the figures in this presentatin are taken frm An Intrductin t Statistical Learning, with applicatins in R (Springer, 2013) with
More informationSupport-Vector Machines
Supprt-Vectr Machines Intrductin Supprt vectr machine is a linear machine with sme very nice prperties. Haykin chapter 6. See Alpaydin chapter 13 fr similar cntent. Nte: Part f this lecture drew material
More informationMACHINE LEARNING FOR CLUSTER- GALAXY CLASSIFICATION
MACHINE LEARNING FOR CLUSTER- GALAXY CLASSIFICATION Silvia de Castr García Directres: Dr. Ricard Pérez Martínez, Dra. Ana María Pérez García 16/03/2018 Machine Learning fr cluster-galaxy classificatin
More informationMATCHING TECHNIQUES. Technical Track Session VI. Emanuela Galasso. The World Bank
MATCHING TECHNIQUES Technical Track Sessin VI Emanuela Galass The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Emanuela Galass fr the purpse f this wrkshp When can we use
More informationChecking the resolved resonance region in EXFOR database
Checking the reslved resnance regin in EXFOR database Gttfried Bertn Sciété de Calcul Mathématique (SCM) Oscar Cabells OECD/NEA Data Bank JEFF Meetings - Sessin JEFF Experiments Nvember 0-4, 017 Bulgne-Billancurt,
More informationWhat is Statistical Learning?
What is Statistical Learning? Sales 5 10 15 20 25 Sales 5 10 15 20 25 Sales 5 10 15 20 25 0 50 100 200 300 TV 0 10 20 30 40 50 Radi 0 20 40 60 80 100 Newspaper Shwn are Sales vs TV, Radi and Newspaper,
More informationTime, Synchronization, and Wireless Sensor Networks
Time, Synchrnizatin, and Wireless Sensr Netwrks Part II Ted Herman University f Iwa Ted Herman/March 2005 1 Presentatin: Part II metrics and techniques single-hp beacns reginal time znes ruting-structure
More informationHypothesis Tests for One Population Mean
Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be
More informationInternal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.
Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.
More informationThe general linear model and Statistical Parametric Mapping I: Introduction to the GLM
The general linear mdel and Statistical Parametric Mapping I: Intrductin t the GLM Alexa Mrcm and Stefan Kiebel, Rik Hensn, Andrew Hlmes & J-B J Pline Overview Intrductin Essential cncepts Mdelling Design
More informationSimple Linear Regression (single variable)
Simple Linear Regressin (single variable) Intrductin t Machine Learning Marek Petrik January 31, 2017 Sme f the figures in this presentatin are taken frm An Intrductin t Statistical Learning, with applicatins
More informationthe results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must
M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins
More informationMATCHING TECHNIQUES Technical Track Session VI Céline Ferré The World Bank
MATCHING TECHNIQUES Technical Track Sessin VI Céline Ferré The Wrld Bank When can we use matching? What if the assignment t the treatment is nt dne randmly r based n an eligibility index, but n the basis
More informationT Algorithmic methods for data mining. Slide set 6: dimensionality reduction
T-61.5060 Algrithmic methds fr data mining Slide set 6: dimensinality reductin reading assignment LRU bk: 11.1 11.3 PCA tutrial in mycurses (ptinal) ptinal: An Elementary Prf f a Therem f Jhnsn and Lindenstrauss,
More informationYou need to be able to define the following terms and answer basic questions about them:
CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f
More informationLesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.
Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are
More informationFive Whys How To Do It Better
Five Whys Definitin. As explained in the previus article, we define rt cause as simply the uncvering f hw the current prblem came int being. Fr a simple causal chain, it is the entire chain. Fr a cmplex
More informationMidwest Big Data Summer School: Machine Learning I: Introduction. Kris De Brabanter
Midwest Big Data Summer Schl: Machine Learning I: Intrductin Kris De Brabanter kbrabant@iastate.edu Iwa State University Department f Statistics Department f Cmputer Science June 24, 2016 1/24 Outline
More informationChapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms
Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical
More informationCOMP 551 Applied Machine Learning Lecture 9: Support Vector Machines (cont d)
COMP 551 Applied Machine Learning Lecture 9: Supprt Vectr Machines (cnt d) Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Class web page: www.cs.mcgill.ca/~hvanh2/cmp551 Unless therwise
More informationTree Structured Classifier
Tree Structured Classifier Reference: Classificatin and Regressin Trees by L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stne, Chapman & Hall, 98. A Medical Eample (CART): Predict high risk patients
More informationAnomalous State of Knowledge. Administrative. Relevance Feedback Query Expansion" computer use in class J hw3 out assignment 3 out later today
Relevance Feedback Query Epansin" David Kauchak cs458 Fall 2012 adapted frm: http://www.stanfrd.edu/class/cs276/handuts/lecture9-queryepansin.ppt Kevin Knight, http://www.isi.edu/natural-language/peple/pictures/ieee-epert-1.gif
More informationTrigonometric Ratios Unit 5 Tentative TEST date
1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin
More informationLim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?
THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,
More informationResampling Methods. Chapter 5. Chapter 5 1 / 52
Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and
More informationReinforcement Learning" CMPSCI 383 Nov 29, 2011!
Reinfrcement Learning" CMPSCI 383 Nv 29, 2011! 1 Tdayʼs lecture" Review f Chapter 17: Making Cmple Decisins! Sequential decisin prblems! The mtivatin and advantages f reinfrcement learning.! Passive learning!
More informationChapter 3 Digital Transmission Fundamentals
Chapter 3 Digital Transmissin Fundamentals Errr Detectin and Crrectin CSE 3213, Winter 2010 Instructr: Frhar Frzan Mdul-2 Arithmetic Mdul 2 arithmetic is perfrmed digit y digit n inary numers. Each digit
More informationModelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA
Mdelling f Clck Behaviur Dn Percival Applied Physics Labratry University f Washingtn Seattle, Washingtn, USA verheads and paper fr talk available at http://faculty.washingtn.edu/dbp/talks.html 1 Overview
More informationCOMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification
COMP 551 Applied Machine Learning Lecture 5: Generative mdels fr linear classificatin Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Jelle Pineau Class web page: www.cs.mcgill.ca/~hvanh2/cmp551
More informationA New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation
III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationCOMP 551 Applied Machine Learning Lecture 4: Linear classification
COMP 551 Applied Machine Learning Lecture 4: Linear classificatin Instructr: Jelle Pineau (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationDistributions, spatial statistics and a Bayesian perspective
Distributins, spatial statistics and a Bayesian perspective Dug Nychka Natinal Center fr Atmspheric Research Distributins and densities Cnditinal distributins and Bayes Thm Bivariate nrmal Spatial statistics
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More informationLinear Classification
Linear Classificatin CS 54: Machine Learning Slides adapted frm Lee Cper, Jydeep Ghsh, and Sham Kakade Review: Linear Regressin CS 54 [Spring 07] - H Regressin Given an input vectr x T = (x, x,, xp), we
More informationWriting Guidelines. (Updated: November 25, 2009) Forwards
Writing Guidelines (Updated: Nvember 25, 2009) Frwards I have fund in my review f the manuscripts frm ur students and research assciates, as well as thse submitted t varius jurnals by thers that the majr
More informationProfessional Development. Implementing the NGSS: High School Physics
Prfessinal Develpment Implementing the NGSS: High Schl Physics This is a dem. The 30-min vide webinar is available in the full PD. Get it here. Tday s Learning Objectives NGSS key cncepts why this is different
More informationThe blessing of dimensionality for kernel methods
fr kernel methds Building classifiers in high dimensinal space Pierre Dupnt Pierre.Dupnt@ucluvain.be Classifiers define decisin surfaces in sme feature space where the data is either initially represented
More informationCS 109 Lecture 23 May 18th, 2016
CS 109 Lecture 23 May 18th, 2016 New Datasets Heart Ancestry Netflix Our Path Parameter Estimatin Machine Learning: Frmally Many different frms f Machine Learning We fcus n the prblem f predictin Want
More informationAdministrativia. Assignment 1 due thursday 9/23/2004 BEFORE midnight. Midterm exam 10/07/2003 in class. CS 460, Sessions 8-9 1
Administrativia Assignment 1 due thursday 9/23/2004 BEFORE midnight Midterm eam 10/07/2003 in class CS 460, Sessins 8-9 1 Last time: search strategies Uninfrmed: Use nly infrmatin available in the prblem
More informationSUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis
SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical mdel fr micrarray data analysis David Rssell Department f Bistatistics M.D. Andersn Cancer Center, Hustn, TX 77030, USA rsselldavid@gmail.cm
More informationNAME: Prof. Ruiz. 1. [5 points] What is the difference between simple random sampling and stratified random sampling?
CS4445 ata Mining and Kwledge iscery in atabases. B Term 2014 Exam 1 Nember 24, 2014 Prf. Carlina Ruiz epartment f Cmputer Science Wrcester Plytechnic Institute NAME: Prf. Ruiz Prblem I: Prblem II: Prblem
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationThe standards are taught in the following sequence.
B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and
More informationCOMP9444 Neural Networks and Deep Learning 3. Backpropagation
COMP9444 Neural Netwrks and Deep Learning 3. Backprpagatin Tetbk, Sectins 4.3, 5.2, 6.5.2 COMP9444 17s2 Backprpagatin 1 Outline Supervised Learning Ockham s Razr (5.2) Multi-Layer Netwrks Gradient Descent
More informationPhysical Layer: Outline
18-: Intrductin t Telecmmunicatin Netwrks Lectures : Physical Layer Peter Steenkiste Spring 01 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital Representatin f Infrmatin Characterizatin f Cmmunicatin
More informationSAMPLING DYNAMICAL SYSTEMS
SAMPLING DYNAMICAL SYSTEMS Melvin J. Hinich Applied Research Labratries The University f Texas at Austin Austin, TX 78713-8029, USA (512) 835-3278 (Vice) 835-3259 (Fax) hinich@mail.la.utexas.edu ABSTRACT
More informationLHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers
LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the
More informationSection 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law
Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential
More informationSURVIVAL ANALYSIS WITH SUPPORT VECTOR MACHINES
1 SURVIVAL ANALYSIS WITH SUPPORT VECTOR MACHINES Wlfgang HÄRDLE Ruslan MORO Center fr Applied Statistics and Ecnmics (CASE), Humbldt-Universität zu Berlin Mtivatin 2 Applicatins in Medicine estimatin f
More information7 TH GRADE MATH STANDARDS
ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,
More informationINSTRUMENTAL VARIABLES
INSTRUMENTAL VARIABLES Technical Track Sessin IV Sergi Urzua University f Maryland Instrumental Variables and IE Tw main uses f IV in impact evaluatin: 1. Crrect fr difference between assignment f treatment
More informationQuery Expansion. Lecture Objectives. Text Technologies for Data Science INFR Learn about Query Expansion. Implement: 10/24/2017
Tet Technlgies fr Data Science INFR11145 Query Epansin Instructr: Walid Magdy 24-Oct-2017 Lecture Objectives Learn abut Query Epansin Query epansin methds Relevance feedback in IR Rcchi s algrithm PRF
More informationData Mining: Concepts and Techniques. Classification and Prediction. Chapter February 8, 2007 CSE-4412: Data Mining 1
Data Mining: Cncepts and Techniques Classificatin and Predictin Chapter 6.4-6 February 8, 2007 CSE-4412: Data Mining 1 Chapter 6 Classificatin and Predictin 1. What is classificatin? What is predictin?
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationActivity 2 Dimensional Analysis
Activity 2 Dimensinal Analysis Gals! Develp cnversin factrs frm cmmn equalities.! Use cnversin factrs t cnvert between different units f measure.! Apply the cncept f dimensinal analysis t string tgether
More informationMisc. ArcMap Stuff Andrew Phay
Misc. ArcMap Stuff Andrew Phay aphay@whatcmcd.rg Prjectins Used t shw a spherical surface n a flat surface Distrtin Shape Distance True Directin Area Different Classes Thse that minimize distrtin in shape
More informationChapter 16. Capacitance. Capacitance, cont. Parallel-Plate Capacitor, Example 1/20/2011. Electric Energy and Capacitance
summary C = ε A / d = πε L / ln( b / a ) ab C = 4πε 4πε a b a b >> a Chapter 16 Electric Energy and Capacitance Capacitance Q=CV Parallel plates, caxial cables, Earth Series and parallel 1 1 1 = + +..
More informationA Matrix Representation of Panel Data
web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins
More informationAircraft Performance - Drag
Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce
More informationCAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank
CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal
More information1b) =.215 1c).080/.215 =.372
Practice Exam 1 - Answers 1. / \.1/ \.9 (D+) (D-) / \ / \.8 / \.2.15/ \.85 (T+) (T-) (T+) (T-).080.020.135.765 1b).080 +.135 =.215 1c).080/.215 =.372 2. The data shwn in the scatter plt is the distance
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationCOMP9414/ 9814/ 3411: Artificial Intelligence. 14. Course Review. COMP3411 c UNSW, 2014
COMP9414/ 9814/ 3411: Artificial Intelligence 14. Curse Review COMP9414/9814/3411 14s1 Review 1 Assessment Assessable cmpnents f the curse: Assignment 1 10% Assignment 2 8% Assignment 3 12% Written Eam
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationThe Law of Total Probability, Bayes Rule, and Random Variables (Oh My!)
The Law f Ttal Prbability, Bayes Rule, and Randm Variables (Oh My!) Administrivia Hmewrk 2 is psted and is due tw Friday s frm nw If yu didn t start early last time, please d s this time. Gd Milestnes:
More informationAP Physics Kinematic Wrap Up
AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x
More information[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )
(Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well
More informationStandard Title: Frequency Response and Frequency Bias Setting. Andrew Dressel Holly Hawkins Maureen Long Scott Miller
Template fr Quality Review f NERC Reliability Standard BAL-003-1 Frequency Respnse and Frequency Bias Setting Basic Infrmatin: Prject number: 2007-12 Standard number: BAL-003-1 Prject title: Frequency
More information24 Multiple Eigenvectors; Latent Factor Analysis; Nearest Neighbors
Multiple Eigenvectrs; Latent Factr Analysis; Nearest Neighbrs 47 24 Multiple Eigenvectrs; Latent Factr Analysis; Nearest Neighbrs Clustering w/multiple Eigenvectrs [When we use the Fiedler vectr fr spectral
More informationMedium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]
EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just
More informationData mining/machine learning large data sets. STA 302 or 442 (Applied Statistics) :, 1
Data mining/machine learning large data sets STA 302 r 442 (Applied Statistics) :, 1 Data mining/machine learning large data sets high dimensinal spaces STA 302 r 442 (Applied Statistics) :, 2 Data mining/machine
More informationLecture 02 CSE 40547/60547 Computing at the Nanoscale
PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements
More informationI. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is
Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,
More informationMath 10 - Exam 1 Topics
Math 10 - Exam 1 Tpics Types and Levels f data Categrical, Discrete r Cntinuus Nminal, Ordinal, Interval r Rati Descriptive Statistics Stem and Leaf Graph Dt Plt (Interpret) Gruped Data Relative and Cumulative
More informationMath 9 Year End Review Package. (b) = (a) Side length = 15.5 cm ( area ) (b) Perimeter = 4xside = 62 m
Math Year End Review Package Chapter Square Rts and Surface Area KEY. Methd #: cunt the number f squares alng the side ( units) Methd #: take the square rt f the area. (a) 4 = 0.7. = 0.. _Perfect square
More informationMaximum A Posteriori (MAP) CS 109 Lecture 22 May 16th, 2016
Maximum A Psteriri (MAP) CS 109 Lecture 22 May 16th, 2016 Previusly in CS109 Game f Estimatrs Maximum Likelihd Nn spiler: this didn t happen Side Plt argmax argmax f lg Mther f ptimizatins? Reviving an
More informationAdmin. MDP Search Trees. Optimal Quantities. Reinforcement Learning
Admin Reinfrcement Learning Cntent adapted frm Berkeley CS188 MDP Search Trees Each MDP state prjects an expectimax-like search tree Optimal Quantities The value (utility) f a state s: V*(s) = expected
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More information2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS
2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.
More informationPhys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1
Crdinatr: Al-Shukri Thursday, May 05, 2011 Page: 1 1. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0 x 10 6 electrns are transferred frm particle A t particle B, the magnitude
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationEngineering Decision Methods
GSOE9210 vicj@cse.unsw.edu.au www.cse.unsw.edu.au/~gs9210 Maximin and minimax regret 1 2 Indifference; equal preference 3 Graphing decisin prblems 4 Dminance The Maximin principle Maximin and minimax Regret
More information1 PreCalculus AP Unit G Rotational Trig (MCR) Name:
1 PreCalculus AP Unit G Rtatinal Trig (MCR) Name: Big idea In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin will invlve the unit circle which will
More informationExam #1. A. Answer any 1 of the following 2 questions. CEE 371 October 8, Please grade the following questions: 1 or 2
CEE 371 Octber 8, 2009 Exam #1 Clsed Bk, ne sheet f ntes allwed Please answer ne questin frm the first tw, ne frm the secnd tw and ne frm the last three. The ttal ptential number f pints is 100. Shw all
More information