BIOINF 585: Machine Learning for Systems Biology & Clinical Informatics
|
|
- Robert Warren
- 6 years ago
- Views:
Transcription
1 BIOINF 585: Machine Learning for Systems Biology & Clinical Informatics Lecture 12: Ensemble Learning I Jie Wang Department of Computational Medicine & Bioinformatics University of Michigan 1
2 Outline Bias and Variance Bagging Application of Bagging to CART (Classfication & Regression Tree) 2
3 Bias and Variance The reducible error of a model can be decomposed into two parts. Error due to Bias Error due to Variance Good references include Scott Fortmann-Roe s blog: Lecture 8 of the free online course: Introductory Machine Learning (a bit technical)
4 The Error Due to Bias The error due to bias refers to the difference between the expected (or average) prediction of the model and the true value that we are trying to predict. Suppose that there are infinitely many marbles in the bin. How can we estimate the fraction of red marbles in the bin? We use the fraction of red marbles in the sample to estimate the fraction of red marbles in the bin. Figure is from 4
5 The Error Due to Bias Is the fraction of red marbles computed from the sample a good approximation to its real value? unlucky It is unfair to say a model is bad if it performs poorly on one sample. We average the performance on many samples. μ 1 μ n The error due to bias is 0 n μ = 1 n i=1 μ i 5
6 The Error Due to Bias Low bias means the model fits the data well Linear regression applied to linear data SVM applied to linearly separable data with large margin Caution: can be overfitting High bias means poor approximation to the data Linear regression to nonlinear data KNN with very large k 6
7 The Error due to Variance The error due to variance refers to the variance of a model prediction for a given data point. x Data 1 g D1 g D1 x Data 2 g D2 g D2 x error due to variance = Var g D x fixed Data n g Dn g Dn x Random variable 7
8 The Error due to Variance Low variance means the prediction of the model is stable Linear regression applied to nonlinear data Model independent with the data Caution: can be under-fitting High variance means the prediction of the model is unstable High degree polynomial KNN with k = 1 8
9 Graphical illustration of bias and variance (figure is from Scott Fortmann-Roe s blog) 9
10 Bias/Variance Tradeoff E D g D x g x 2 = E D g D x g x 2 + ED g D x E D g D x 2 The true model (usually unknown) bias 2 variance We usually have low bias, high variance (the model is too complex) low variance, high bias (the model is too simple) Duda, Pattern Classification Tradeoff: Bias 2 vs variance 10
11 Bias/Variance Tradeoff Hastie, Tibshirani, Friedman Elements of Statistical Learning 11
12 Tips to reduce errors High bias Try to get new features High variance Try to get more training samples Try subset of features 12
13 Reduce Variance without increasing Bias Averaging reduces variance Var N i=1 N Xi = Var X N X i are identical and independent distributed (i.i.d.) random variables The training data is given. How can we find more data? 13
14 Bagging Breiman, 1996 Derived from bootstrap (Efron, 1993) Create classifiers using training sets that are bootstrapped (drawn with replacement) Average results for each case
15 What is Bagging? bootstrap aggregating Basic idea of bootstrap Suppose we have a model fit to a set of training data. The training set is Z = z 1, z 2,, z N where z i = x i, y i. The basic idea is to randomly draw datasets with replacement from the training data. Each sample set is the same size as the original training set. This is done B times and we will have B bootstrap datasets. We refit the model to each of the bootstrap datasets, and examines the behavior over the B replications. Question: what would happen if you draw datasets without replacement?
16 Review on Bootstrap Bootstrap can be used to assess the accuracy of a parameter estimate or prediction In Bagging, we use it to improve the estimation or prediction itself. For each bootstrap sample set Z b, b = 1,2,, B, we fit our model, giving prediction f b x, the bagging estimate is f bag x = 1 B b=1 B f b x. The average over the prediction reduces variance (not bias).
17 Bagging Example (Opitz, 1999) Original Training set Training set Training set Training set
18 Bagging ML f 1 ML f 2 f ML f T
19 Examples in Tree-based methods Tree-based methods Partition the feature space into a set of rectangles, and usually fit a constant in each one. The figure is from Wei-Yin Loh (2011) Classfication and regression trees. WIREs Data Mining and Knowledge Discovery 1:14-23.
20 Why Bagging in CART CART = Classification and Regression Tree To construct the tree, usually MSE or Misclassification error is minimized over the training sample. Tree based methods have very high variance. It is unstable because of the hierarchical structure. Bagging can average many trees to reduce the variance.
21 Example I: Tree-based Regression
22 Example II: Classification Tree Training Sample Results from one CART Bagged Tree Decision Boundary
23 Results from Breiman 96
24 Tips of Using Bagging Bagging is useful when the base-learner is unstable. A base-learner is unstable if a small perturbation in the training data leads to large change in the model. Neural networks, KNN with small k, and decision tree are unstable. KNN and naive Bayes classifier are stable. Bagging is not intended for reducing bias. 24
25 References Breiman 96, Bagging Predictors, Machine Learning, 26, Leblanc M. and Tibshirani, R., 96, Combining estimates in regression and classfication, J. of Amer. Stat. Assoc. 91: Textbook: The elements of Statistical Learning
CSC 411 Lecture 4: Ensembles I
CSC 411 Lecture 4: Ensembles I Roger Grosse, Amir-massoud Farahmand, and Juan Carrasquilla University of Toronto UofT CSC 411: 04-Ensembles I 1 / 22 Overview We ve seen two particular classification algorithms:
Naïve Bayes for text classification
Road Map Basic concepts Decision tree induction Evaluation of classifiers Rule induction Classification using association rules Naïve Bayesian classification Naïve Bayes for text classification Support
RESAMPLING METHODS. Chapter 05
1 RESAMPLING METHODS Chapter 05 2 Outline Cross Validation The Validation Set Approach Leave-One-Out Cross Validation K-fold Cross Validation Bias-Variance Trade-off for k-fold Cross Validation Cross Validation
Ensemble Learning. Another approach is to leverage the algorithms we have via ensemble methods
Ensemble Learning Ensemble Learning So far we have seen learning algorithms that take a training set and output a classifier What if we want more accuracy than current algorithms afford? Develop new learning
Network Traffic Measurements and Analysis
DEIB - Politecnico di Milano Fall, 2017 Sources Hastie, Tibshirani, Friedman: The Elements of Statistical Learning James, Witten, Hastie, Tibshirani: An Introduction to Statistical Learning Andrew Ng:
Random Forest A. Fornaser
Random Forest A. Fornaser alberto.fornaser@unitn.it Sources Lecture 15: decision trees, information theory and random forests, Dr. Richard E. Turner Trees and Random Forests, Adele Cutler, Utah State University
STA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 12 Combining
Model combination. Resampling techniques p.1/34
Model combination The winner-takes-all approach is intuitively the approach which should work the best. However recent results in machine learning show that the performance of the final model can be improved
Trimmed bagging a DEPARTMENT OF DECISION SCIENCES AND INFORMATION MANAGEMENT (KBI) Christophe Croux, Kristel Joossens and Aurélie Lemmens
Faculty of Economics and Applied Economics Trimmed bagging a Christophe Croux, Kristel Joossens and Aurélie Lemmens DEPARTMENT OF DECISION SCIENCES AND INFORMATION MANAGEMENT (KBI) KBI 0721 Trimmed Bagging
Lecture #11: The Perceptron
Lecture #11: The Perceptron Mat Kallada STAT2450 - Introduction to Data Mining Outline for Today Welcome back! Assignment 3 The Perceptron Learning Method Perceptron Learning Rule Assignment 3 Will be
Nonparametric Methods Recap
Nonparametric Methods Recap Aarti Singh Machine Learning 10-701/15-781 Oct 4, 2010 Nonparametric Methods Kernel Density estimate (also Histogram) Weighted frequency Classification - K-NN Classifier Majority
UVA CS 4501: Machine Learning. Lecture 10: K-nearest-neighbor Classifier / Bias-Variance Tradeoff. Dr. Yanjun Qi. University of Virginia
UVA CS 4501: Machine Learning Lecture 10: K-nearest-neighbor Classifier / Bias-Variance Tradeoff Dr. Yanjun Qi University of Virginia Department of Computer Science 1 Where are we? è Five major secfons
CSC411 Fall 2014 Machine Learning & Data Mining. Ensemble Methods. Slides by Rich Zemel
CSC411 Fall 2014 Machine Learning & Data Mining Ensemble Methods Slides by Rich Zemel Ensemble methods Typical application: classi.ication Ensemble of classi.iers is a set of classi.iers whose individual
CS273 Midterm Exam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014
CS273 Midterm Eam Introduction to Machine Learning: Winter 2015 Tuesday February 10th, 2014 Your name: Your UCINetID (e.g., myname@uci.edu): Your seat (row and number): Total time is 80 minutes. READ THE
Support Vector Machines + Classification for IR
Support Vector Machines + Classification for IR Pierre Lison University of Oslo, Dep. of Informatics INF3800: Søketeknologi April 30, 2014 Outline of the lecture Recap of last week Support Vector Machines
Model Assessment and Selection. Reference: The Elements of Statistical Learning, by T. Hastie, R. Tibshirani, J. Friedman, Springer
Model Assessment and Selection Reference: The Elements of Statistical Learning, by T. Hastie, R. Tibshirani, J. Friedman, Springer 1 Model Training data Testing data Model Testing error rate Training error
Tree-based methods for classification and regression
Tree-based methods for classification and regression Ryan Tibshirani Data Mining: 36-462/36-662 April 11 2013 Optional reading: ISL 8.1, ESL 9.2 1 Tree-based methods Tree-based based methods for predicting
DS Machine Learning and Data Mining I. Alina Oprea Associate Professor, CCIS Northeastern University
DS 4400 Machine Learning and Data Mining I Alina Oprea Associate Professor, CCIS Northeastern University January 24 2019 Logistics HW 1 is due on Friday 01/25 Project proposal: due Feb 21 1 page description
Machine Learning in Biology
Università degli studi di Padova Machine Learning in Biology Luca Silvestrin (Dottorando, XXIII ciclo) Supervised learning Contents Class-conditional probability density Linear and quadratic discriminant
Stat 342 Exam 3 Fall 2014
Stat 34 Exam 3 Fall 04 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed There are questions on the following 6 pages. Do as many of them as you can
Data Mining Lecture 8: Decision Trees
Data Mining Lecture 8: Decision Trees Jo Houghton ECS Southampton March 8, 2019 1 / 30 Decision Trees - Introduction A decision tree is like a flow chart. E. g. I need to buy a new car Can I afford it?
Bias-Variance Analysis of Ensemble Learning
Bias-Variance Analysis of Ensemble Learning Thomas G. Dietterich Department of Computer Science Oregon State University Corvallis, Oregon 97331 http://www.cs.orst.edu/~tgd Outline Bias-Variance Decomposition
Machine Learning. Chao Lan
Machine Learning Chao Lan Machine Learning Prediction Models Regression Model - linear regression (least square, ridge regression, Lasso) Classification Model - naive Bayes, logistic regression, Gaussian
Kernels + K-Means Introduction to Machine Learning. Matt Gormley Lecture 29 April 25, 2018
10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Kernels + K-Means Matt Gormley Lecture 29 April 25, 2018 1 Reminders Homework 8:
Probabilistic Approaches
Probabilistic Approaches Chirayu Wongchokprasitti, PhD University of Pittsburgh Center for Causal Discovery Department of Biomedical Informatics chw20@pitt.edu http://www.pitt.edu/~chw20 Overview Independence
A Systematic Overview of Data Mining Algorithms
A Systematic Overview of Data Mining Algorithms 1 Data Mining Algorithm A well-defined procedure that takes data as input and produces output as models or patterns well-defined: precisely encoded as a
Cross-validation. Cross-validation is a resampling method.
Cross-validation Cross-validation is a resampling method. It refits a model of interest to samples formed from the training set, in order to obtain additional information about the fitted model. For example,
Classification/Regression Trees and Random Forests
Classification/Regression Trees and Random Forests Fabio G. Cozman - fgcozman@usp.br November 6, 2018 Classification tree Consider binary class variable Y and features X 1,..., X n. Decide Ŷ after a series
UVA CS 6316/4501 Fall 2016 Machine Learning. Lecture 15: K-nearest-neighbor Classifier / Bias-Variance Tradeoff. Dr. Yanjun Qi. University of Virginia
UVA CS 6316/4501 Fall 2016 Machine Learning Lecture 15: K-nearest-neighbor Classifier / Bias-Variance Tradeoff Dr. Yanjun Qi University of Virginia Department of Computer Science 11/9/16 1 Rough Plan HW5
CS 229 Midterm Review
CS 229 Midterm Review Course Staff Fall 2018 11/2/2018 Outline Today: SVMs Kernels Tree Ensembles EM Algorithm / Mixture Models [ Focus on building intuition, less so on solving specific problems. Ask
Statistics 202: Statistical Aspects of Data Mining
Statistics 202: Statistical Aspects of Data Mining Professor Rajan Patel Lecture 9 = More of Chapter 5 Agenda: 1) Lecture over more of Chapter 5 1 Introduction to Data Mining by Tan, Steinbach, Kumar Chapter
CS570: Introduction to Data Mining
CS570: Introduction to Data Mining Classification Advanced Reading: Chapter 8 & 9 Han, Chapters 4 & 5 Tan Anca Doloc-Mihu, Ph.D. Slides courtesy of Li Xiong, Ph.D., 2011 Han, Kamber & Pei. Data Mining.
Nonparametric Classification Methods
Nonparametric Classification Methods We now examine some modern, computationally intensive methods for regression and classification. Recall that the LDA approach constructs a line (or plane or hyperplane)
Overview. Non-Parametrics Models Definitions KNN. Ensemble Methods Definitions, Examples Random Forests. Clustering. k-means Clustering 2 / 8
Tutorial 3 1 / 8 Overview Non-Parametrics Models Definitions KNN Ensemble Methods Definitions, Examples Random Forests Clustering Definitions, Examples k-means Clustering 2 / 8 Non-Parametrics Models Definitions
Information Management course
Università degli Studi di Milano Master Degree in Computer Science Information Management course Teacher: Alberto Ceselli Lecture 20: 10/12/2015 Data Mining: Concepts and Techniques (3 rd ed.) Chapter
MIT Samberg Center Cambridge, MA, USA. May 30 th June 2 nd, by C. Rea, R.S. Granetz MIT Plasma Science and Fusion Center, Cambridge, MA, USA
Exploratory Machine Learning studies for disruption prediction on DIII-D by C. Rea, R.S. Granetz MIT Plasma Science and Fusion Center, Cambridge, MA, USA Presented at the 2 nd IAEA Technical Meeting on
Big Data Methods. Chapter 5: Machine learning. Big Data Methods, Chapter 5, Slide 1
Big Data Methods Chapter 5: Machine learning Big Data Methods, Chapter 5, Slide 1 5.1 Introduction to machine learning What is machine learning? Concerned with the study and development of algorithms that
Stat 602X Exam 2 Spring 2011
Stat 60X Exam Spring 0 I have neither given nor received unauthorized assistance on this exam. Name Signed Date Name Printed . Below is a small p classification training set (for classes) displayed in
Module 4. Non-linear machine learning econometrics: Support Vector Machine
Module 4. Non-linear machine learning econometrics: Support Vector Machine THE CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE COMMISSION Introduction When the assumption of linearity
Chapter 5. Tree-based Methods
Chapter 5. Tree-based Methods Wei Pan Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455 Email: weip@biostat.umn.edu PubH 7475/8475 c Wei Pan Regression
Notes and Announcements
Notes and Announcements Midterm exam: Oct 20, Wednesday, In Class Late Homeworks Turn in hardcopies to Michelle. DO NOT ask Michelle for extensions. Note down the date and time of submission. If submitting
Lecture 20: Bagging, Random Forests, Boosting
Lecture 20: Bagging, Random Forests, Boosting Reading: Chapter 8 STATS 202: Data mining and analysis November 13, 2017 1 / 17 Classification and Regression trees, in a nut shell Grow the tree by recursively
Regularization and model selection
CS229 Lecture notes Andrew Ng Part VI Regularization and model selection Suppose we are trying select among several different models for a learning problem. For instance, we might be using a polynomial
Machine Learning (CS 567)
Machine Learning (CS 567) Time: T-Th 5:00pm - 6:20pm Location: GFS 118 Instructor: Sofus A. Macskassy (macskass@usc.edu) Office: SAL 216 Office hours: by appointment Teaching assistant: Cheol Han (cheolhan@usc.edu)
INTRO TO RANDOM FOREST BY ANTHONY ANH QUOC DOAN
INTRO TO RANDOM FOREST BY ANTHONY ANH QUOC DOAN MOTIVATION FOR RANDOM FOREST Random forest is a great statistical learning model. It works well with small to medium data. Unlike Neural Network which requires
Supervised Learning for Image Segmentation
Supervised Learning for Image Segmentation Raphael Meier 06.10.2016 Raphael Meier MIA 2016 06.10.2016 1 / 52 References A. Ng, Machine Learning lecture, Stanford University. A. Criminisi, J. Shotton, E.
Overfitting. Machine Learning CSE546 Carlos Guestrin University of Washington. October 2, Bias-Variance Tradeoff
Overfitting Machine Learning CSE546 Carlos Guestrin University of Washington October 2, 2013 1 Bias-Variance Tradeoff Choice of hypothesis class introduces learning bias More complex class less bias More
Instance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University February 19 th, 2007 2005-2007 Carlos Guestrin 1 Why not just use Linear Regression? 2005-2007 Carlos Guestrin
Mondrian Forests: Efficient Online Random Forests
Mondrian Forests: Efficient Online Random Forests Balaji Lakshminarayanan (Gatsby Unit, UCL) Daniel M. Roy (Cambridge Toronto) Yee Whye Teh (Oxford) September 4, 2014 1 Outline Background and Motivation
Lecture #17: Autoencoders and Random Forests with R. Mat Kallada Introduction to Data Mining with R
Lecture #17: Autoencoders and Random Forests with R Mat Kallada Introduction to Data Mining with R Assignment 4 Posted last Sunday Due next Monday! Autoencoders in R Firstly, what is an autoencoder? Autoencoders
CSE 446 Bias-Variance & Naïve Bayes
CSE 446 Bias-Variance & Naïve Bayes Administrative Homework 1 due next week on Friday Good to finish early Homework 2 is out on Monday Check the course calendar Start early (midterm is right before Homework
8. Tree-based approaches
Foundations of Machine Learning École Centrale Paris Fall 2015 8. Tree-based approaches Chloé-Agathe Azencott Centre for Computational Biology, Mines ParisTech chloe agathe.azencott@mines paristech.fr
Random Forest Classification and Attribute Selection Program rfc3d
Random Forest Classification and Attribute Selection Program rfc3d Overview Random Forest (RF) is a supervised classification algorithm using multiple decision trees. Program rfc3d uses training data generated
COMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18. Lecture 6: k-nn Cross-validation Regularization
COMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18 Lecture 6: k-nn Cross-validation Regularization LEARNING METHODS Lazy vs eager learning Eager learning generalizes training data before
IOM 530: Intro. to Statistical Learning 1 RESAMPLING METHODS. Chapter 05
IOM 530: Intro. to Statistical Learning 1 RESAMPLING METHODS Chapter 05 IOM 530: Intro. to Statistical Learning 2 Outline Cross Validation The Validation Set Approach Leave-One-Out Cross Validation K-fold
Ensemble Methods: Bagging
Ensemble Methods: Bagging Instructor: Jessica Wu Harvey Mudd College The instructor gratefully acknowledges Eric Eaton (UPenn), Jenna Wiens (UMich), Tommi Jaakola (MIT), David Kauchak (Pomona), David Sontag
Applying Supervised Learning
Applying Supervised Learning When to Consider Supervised Learning A supervised learning algorithm takes a known set of input data (the training set) and known responses to the data (output), and trains
Preface to the Second Edition. Preface to the First Edition. 1 Introduction 1
Preface to the Second Edition Preface to the First Edition vii xi 1 Introduction 1 2 Overview of Supervised Learning 9 2.1 Introduction... 9 2.2 Variable Types and Terminology... 9 2.3 Two Simple Approaches
CSE 417T: Introduction to Machine Learning. Lecture 22: The Kernel Trick. Henry Chai 11/15/18
CSE 417T: Introduction to Machine Learning Lecture 22: The Kernel Trick Henry Chai 11/15/18 Linearly Inseparable Data What can we do if the data is not linearly separable? Accept some non-zero in-sample
CSE 6242/CX Ensemble Methods. Or, Model Combination. Based on lecture by Parikshit Ram
CSE 6242/CX 4242 Ensemble Methods Or, Model Combination Based on lecture by Parikshit Ram Numerous Possible Classifiers! Classifier Training time Cross validation Testing time Accuracy knn classifier None
Multi-label classification using rule-based classifier systems
Multi-label classification using rule-based classifier systems Shabnam Nazmi (PhD candidate) Department of electrical and computer engineering North Carolina A&T state university Advisor: Dr. A. Homaifar
Chapter 7: Numerical Prediction
Ludwig-Maximilians-Universität München Institut für Informatik Lehr- und Forschungseinheit für Datenbanksysteme Knowledge Discovery in Databases SS 2016 Chapter 7: Numerical Prediction Lecture: Prof. Dr.
Machine Learning Models for Pattern Classification. Comp 473/6731
Machine Learning Models for Pattern Classification Comp 473/6731 November 24th 2016 Prof. Neamat El Gayar Neural Networks Neural Networks Low level computational algorithms Learn by example (no required
Predictive Analytics: Demystifying Current and Emerging Methodologies. Tom Kolde, FCAS, MAAA Linda Brobeck, FCAS, MAAA
Predictive Analytics: Demystifying Current and Emerging Methodologies Tom Kolde, FCAS, MAAA Linda Brobeck, FCAS, MAAA May 18, 2017 About the Presenters Tom Kolde, FCAS, MAAA Consulting Actuary Chicago,
What is machine learning?
Machine learning, pattern recognition and statistical data modelling Lecture 12. The last lecture Coryn Bailer-Jones 1 What is machine learning? Data description and interpretation finding simpler relationship
Bagging and Random Forests
STAT 5474 Intro to Data Mining Bagging and Random Forests Xiaogang Su, Ph.D. Department of Mathematical Sciences University of Texas at El Paso (UTEP) xsu@utep.edu April 24, 2018 Contents 1 Introduction
Content-based image and video analysis. Machine learning
Content-based image and video analysis Machine learning for multimedia retrieval 04.05.2009 What is machine learning? Some problems are very hard to solve by writing a computer program by hand Almost all
A Systematic Overview of Data Mining Algorithms. Sargur Srihari University at Buffalo The State University of New York
A Systematic Overview of Data Mining Algorithms Sargur Srihari University at Buffalo The State University of New York 1 Topics Data Mining Algorithm Definition Example of CART Classification Iris, Wine
An introduction to random forests
An introduction to random forests Eric Debreuve / Team Morpheme Institutions: University Nice Sophia Antipolis / CNRS / Inria Labs: I3S / Inria CRI SA-M / ibv Outline Machine learning Decision tree Random
Lecture 27: Review. Reading: All chapters in ISLR. STATS 202: Data mining and analysis. December 6, 2017
Lecture 27: Review Reading: All chapters in ISLR. STATS 202: Data mining and analysis December 6, 2017 1 / 16 Final exam: Announcements Tuesday, December 12, 8:30-11:30 am, in the following rooms: Last
Oliver Dürr. Statistisches Data Mining (StDM) Woche 12. Institut für Datenanalyse und Prozessdesign Zürcher Hochschule für Angewandte Wissenschaften
Statistisches Data Mining (StDM) Woche 12 Oliver Dürr Institut für Datenanalyse und Prozessdesign Zürcher Hochschule für Angewandte Wissenschaften oliver.duerr@zhaw.ch Winterthur, 6 Dezember 2016 1 Multitasking
CAMCOS Report Day. December 9 th, 2015 San Jose State University Project Theme: Classification
CAMCOS Report Day December 9 th, 2015 San Jose State University Project Theme: Classification On Classification: An Empirical Study of Existing Algorithms based on two Kaggle Competitions Team 1 Team 2
Lecture 25: Review I
Lecture 25: Review I Reading: Up to chapter 5 in ISLR. STATS 202: Data mining and analysis Jonathan Taylor 1 / 18 Unsupervised learning In unsupervised learning, all the variables are on equal standing,
Cross-validation and the Bootstrap
Cross-validation and the Bootstrap In the section we discuss two resampling methods: cross-validation and the bootstrap. These methods refit a model of interest to samples formed from the training set,
Overview Citation. ML Introduction. Overview Schedule. ML Intro Dataset. Introduction to Semi-Supervised Learning Review 10/4/2010
INFORMATICS SEMINAR SEPT. 27 & OCT. 4, 2010 Introduction to Semi-Supervised Learning Review 2 Overview Citation X. Zhu and A.B. Goldberg, Introduction to Semi- Supervised Learning, Morgan & Claypool Publishers,
Classification. Slide sources:
Classification Slide sources: Gideon Dror, Academic College of TA Yaffo Nathan Ifill, Leicester MA4102 Data Mining and Neural Networks Andrew Moore, CMU : http://www.cs.cmu.edu/~awm/tutorials 1 Outline
Comparison of different preprocessing techniques and feature selection algorithms in cancer datasets
Comparison of different preprocessing techniques and feature selection algorithms in cancer datasets Konstantinos Sechidis School of Computer Science University of Manchester sechidik@cs.man.ac.uk Abstract
Bias-Variance Decomposition Error Estimators
Bias-Variance Decomposition Error Estimators Cross-Validation Bias-Variance tradeoff Intuition Model too simple does not fit the data well a biased solution. Model too comple small changes to the data,
Evaluation Measures. Sebastian Pölsterl. April 28, Computer Aided Medical Procedures Technische Universität München
Evaluation Measures Sebastian Pölsterl Computer Aided Medical Procedures Technische Universität München April 28, 2015 Outline 1 Classification 1. Confusion Matrix 2. Receiver operating characteristics
Bias-Variance Decomposition Error Estimators Cross-Validation
Bias-Variance Decomposition Error Estimators Cross-Validation Bias-Variance tradeoff Intuition Model too simple does not fit the data well a biased solution. Model too comple small changes to the data,
Combining Models to Improve Classifier Accuracy and Robustness
Combining Models to Improve Classifier Accuracy and Robustness Dean W. Abbott Abbott Consulting P.O. Box 22536 San Diego, CA 92192-2536 USA Email: dean@abbott-consulting.com Abstract Recent years have
Lecture 9: Support Vector Machines
Lecture 9: Support Vector Machines William Webber (william@williamwebber.com) COMP90042, 2014, Semester 1, Lecture 8 What we ll learn in this lecture Support Vector Machines (SVMs) a highly robust and
Bias - variance tradeoff of soft decision trees
Bias - variance tradeoff of soft decision trees Cristina Olaru University of Liège Montefiore Institute B28 B4000, Liège, Belgium olaru@montefiore.ulg.ac.be Louis Wehenkel University of Liège Montefiore
Introduction to Classification & Regression Trees
Introduction to Classification & Regression Trees ISLR Chapter 8 vember 8, 2017 Classification and Regression Trees Carseat data from ISLR package Classification and Regression Trees Carseat data from
Classification and Regression Trees
Classification and Regression Trees Matthew S. Shotwell, Ph.D. Department of Biostatistics Vanderbilt University School of Medicine Nashville, TN, USA March 16, 2018 Introduction trees partition feature
Estimating Data Center Thermal Correlation Indices from Historical Data
Estimating Data Center Thermal Correlation Indices from Historical Data Manish Marwah, Cullen Bash, Rongliang Zhou, Carlos Felix, Rocky Shih, Tom Christian HP Labs Palo Alto, CA 94304 Email: firstname.lastname@hp.com
Combining Models to Improve Classifier Accuracy and Robustness 1
Combining Models to Improve Classifier Accuracy and Robustness 1 Dean W. Abbott Abbott Consulting P.O. Box 22536 San Diego, CA 92192-2536 USA Email: dean@abbott-consulting.com Abstract Recent years have
Introduction to Automated Text Analysis. bit.ly/poir599
Introduction to Automated Text Analysis Pablo Barberá School of International Relations University of Southern California pablobarbera.com Lecture materials: bit.ly/poir599 Today 1. Solutions for last
Advanced and Predictive Analytics with JMP 12 PRO. JMP User Meeting 9. Juni Schwalbach
Advanced and Predictive Analytics with JMP 12 PRO JMP User Meeting 9. Juni 2016 -Schwalbach Definition Predictive Analytics encompasses a variety of statistical techniques from modeling, machine learning
Classification: Decision Trees
Classification: Decision Trees IST557 Data Mining: Techniques and Applications Jessie Li, Penn State University 1 Decision Tree Example Will a pa)ent have high-risk based on the ini)al 24-hour observa)on?
Contents. Preface to the Second Edition
Preface to the Second Edition v 1 Introduction 1 1.1 What Is Data Mining?....................... 4 1.2 Motivating Challenges....................... 5 1.3 The Origins of Data Mining....................
Text classification II CE-324: Modern Information Retrieval Sharif University of Technology
Text classification II CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2015 Some slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276, Stanford)
Machine Learning Classifiers and Boosting
Machine Learning Classifiers and Boosting Reading Ch 18.6-18.12, 20.1-20.3.2 Outline Different types of learning problems Different types of learning algorithms Supervised learning Decision trees Naïve
Model Complexity and Generalization
HT2015: SC4 Statistical Data Mining and Machine Learning Dino Sejdinovic Department of Statistics Oxford http://www.stats.ox.ac.uk/~sejdinov/sdmml.html Generalization Learning Curves Underfit Generalization
Data Mining. Lesson 9 Support Vector Machines. MSc in Computer Science University of New York Tirana Assoc. Prof. Dr.
Data Mining Lesson 9 Support Vector Machines MSc in Computer Science University of New York Tirana Assoc. Prof. Dr. Marenglen Biba Data Mining: Content Introduction to data mining and machine learning
COSC160: Detection and Classification. Jeremy Bolton, PhD Assistant Teaching Professor
COSC160: Detection and Classification Jeremy Bolton, PhD Assistant Teaching Professor Outline I. Problem I. Strategies II. Features for training III. Using spatial information? IV. Reducing dimensionality
Clustering and Classification. Basic principles of clustering. Clustering. Classification
Classification Clustering and Classification Task: assign objects to classes (groups) on the basis of measurements made on the objects Jean Yee Hwa Yang University of California, San Francisco http://www.biostat.ucsf.edu/jean/
Nonparametric Approaches to Regression
Nonparametric Approaches to Regression In traditional nonparametric regression, we assume very little about the functional form of the mean response function. In particular, we assume the model where m(xi)
Instance-based Learning CE-717: Machine Learning Sharif University of Technology. M. Soleymani Fall 2015
Instance-based Learning CE-717: Machine Learning Sharif University of Technology M. Soleymani Fall 2015 Outline Non-parametric approach Unsupervised: Non-parametric density estimation Parzen Windows K-Nearest
CS6375: Machine Learning Gautam Kunapuli. Mid-Term Review
Gautam Kunapuli Machine Learning Data is identically and independently distributed Goal is to learn a function that maps to Data is generated using an unknown function Learn a hypothesis that minimizes