# IEEE Proof. Web Version. PROGRESSIVE speaker adaptation has been considered

Save this PDF as:

Size: px
Start display at page:

## Transcription

11 YIN et al.: A JOINT FACTOR ANALYSIS APPROACH TO PROGRESSIVE MODEL ADAPTATION IN TEXT-INDEPENDENT SPEAKER VERIFICATION 11 APPENDIX A POSTERIOR CALCULATION OF THE LATENT VARIABLES AND In the joint factor analysis model, a -dimensional supervector can be decomposed as where and is the speaker-dependent supervector given by is the channel-dependent supervector given by (10) (11) (12) We are given the prior distribution of,, the prior distribution of,, and the diagonal matrix used to capture the uncertainty in the utterance that is independent of and. In this appendix, we summarize the calculations needed to jointly evaluate the posterior distribution of the hidden variables and. The theorem is presented in [8]. For each mixture component, let be the total number of acoustic observation vectors in the training utterance for the given mixture component, which is given by (13) and set to be the sum which extends over all acoustic observations aligned with the given mixture component, which is given by (14) where refers to the a posteriori probability of occupying mixture component in the GMM-based universal background model at time. Let be the diagonal matrix whose diagonal blocks are (for ) where is the identity matrix. Let be the 1 vector obtained by concatenating (for ). Set (15) This can be used to compute the log likelihood function described in the Appendix B. Theorem: If then the posterior distribution of is Gaussian of the same form as the posterior distribution described in Proposition 1 of [6]. Specifically, if is the identity matrix and and are the matrices defined by Web Version (16) (17) then the posterior distribution of has covariance matrix and mean. Thus, calculating the posterior distribution of is essentially a matter of inverting the matrix. A straightforward calculation shows that can be written as So, where with can be calculated by using the identity APPENDIX B LOG LIKELIHOOD FUNCTION USED TO MAKE SPEAKER VERIFICATION DECISIONS (18) Some notation is required before describing the test likelihood function used in the joint factor analysis-based speaker verification system. We are given the speaker-independent hyperparameter set. Let be the th diagonal covariance matrix in, where. Recall that captures the speaker-independent and channel-independent uncertainty, which is fixed in the test likelihood function for any target speaker. Let,, and be the zero-order, first-order, and second-order sufficient statistics for the given mixture component, which are obtained from the test utterance as described in (13) (15). Use the same definition described in Appendix A for the notations and. In addition, let be the diagonal matrix whose diagonal blocks are (for ). Given the distribution of supervector, either the prior distribution or the posterior distribution, the expectations of the firstand second-order moments of around, and, are given by Finally, let and let be an upper triangular matrix such that (19) (20) (21)

### Automatic Cross-Biometric Footstep Database Labelling using Speaker Recognition

Automatic Cross-Biometric Footstep Database Labelling using Speaker Recognition Ruben Vera-Rodriguez 1, John S.D. Mason 1 and Nicholas W.D. Evans 1,2 1 Speech and Image Research Group, Swansea University,

### AS indicated by the growing number of participants in

1960 IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING, VOL. 15, NO. 7, SEPTEMBER 2007 State-of-the-Art Performance in Text-Independent Speaker Verification Through Open-Source Software Benoît

### ARMORVOX IMPOSTORMAPS HOW TO BUILD AN EFFECTIVE VOICE BIOMETRIC SOLUTION IN THREE EASY STEPS

ARMORVOX IMPOSTORMAPS HOW TO BUILD AN EFFECTIVE VOICE BIOMETRIC SOLUTION IN THREE EASY STEPS ImpostorMaps is a methodology developed by Auraya and available from Auraya resellers worldwide to configure,

### (57) (58) (59) (60) (61)

Module 4 : Solving Linear Algebraic Equations Section 5 : Iterative Solution Techniques 5 Iterative Solution Techniques By this approach, we start with some initial guess solution, say for solution and

### Training Universal Background Models for Speaker Recognition

Odyssey 2010 The Speaer and Language Recognition Worshop 28 June 1 July 2010, Brno, Czech Republic Training Universal Bacground Models for Speaer Recognition Mohamed Kamal Omar and Jason Pelecanos IBM

### The effect of mismatched recording conditions on human and automatic speaker recognition in forensic applications

Forensic Science International 146S (2004) S95 S99 www.elsevier.com/locate/forsciint The effect of mismatched recording conditions on human and automatic speaker recognition in forensic applications A.

### Example: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.

Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C

### ABC System description for NIST SRE 2010

ABC System description for NIST SRE 2010 May 6, 2010 1 Introduction The ABC submission is a collaboration between: Agnitio Labs, South Africa Brno University of Technology, Czech Republic CRIM, Canada

### Generating Gaussian Mixture Models by Model Selection For Speech Recognition

Generating Gaussian Mixture Models by Model Selection For Speech Recognition Kai Yu F06 10-701 Final Project Report kaiy@andrew.cmu.edu Abstract While all modern speech recognition systems use Gaussian

### Secure-Access System via Fixed and Mobile Telephone Networks using Voice Biometrics

Secure-Access System via Fixed and Mobile Telephone Networks using Voice Biometrics Anastasis Kounoudes 1, Anixi Antonakoudi 1, Vasilis Kekatos 2 1 The Philips College, Computing and Information Systems

### Measuring Performance in a Biometrics Based Multi-Factor Authentication Dialog. A Nuance Education Paper

Measuring Performance in a Biometrics Based Multi-Factor Authentication Dialog A Nuance Education Paper 2009 Definition of Multi-Factor Authentication Dialog Many automated authentication applications

### Study on the Effects of Intrinsic Variation using i-vectors in Text-Independent Speaker Verification

Study on the Effects of Intrinsic Variation using i-vectors in Text-Independent Speaker Verification Sheng Chen, Mingxing Xu, Emlyn Pratt Department of Computer Science and Technology Tsinghua University,

### On sequence kernels for SVM classification of sets of vectors: application to speaker verification

On sequence kernels for SVM classification of sets of vectors: application to speaker verification Major part of the Ph.D. work of In collaboration with Jérôme Louradour Francis Bach (ARMINES) within E-TEAM

### Lecture 10: Sequential Data Models

CSC2515 Fall 2007 Introduction to Machine Learning Lecture 10: Sequential Data Models 1 Example: sequential data Until now, considered data to be i.i.d. Turn attention to sequential data Time-series: stock

### Introduction to General and Generalized Linear Models

Introduction to General and Generalized Linear Models General Linear Models - part I Henrik Madsen Poul Thyregod Informatics and Mathematical Modelling Technical University of Denmark DK-2800 Kgs. Lyngby

### EFFECTS OF BACKGROUND DATA DURATION ON SPEAKER VERIFICATION PERFORMANCE

Uludağ Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, Cilt 18, Sayı 1, 2013 ARAŞTIRMA EFFECTS OF BACKGROUND DATA DURATION ON SPEAKER VERIFICATION PERFORMANCE Cemal HANİLÇİ * Figen ERTAŞ * Abstract:

### Blind Deconvolution of Corrupted Barcode Signals

Blind Deconvolution of Corrupted Barcode Signals Everardo Uribe and Yifan Zhang Advisors: Ernie Esser and Yifei Lou Interdisciplinary Computational and Applied Mathematics Program University of California,

### Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree of PhD of Engineering in Informatics

INTERNATIONAL BLACK SEA UNIVERSITY COMPUTER TECHNOLOGIES AND ENGINEERING FACULTY ELABORATION OF AN ALGORITHM OF DETECTING TESTS DIMENSIONALITY Mehtap Ergüven Abstract of Ph.D. Dissertation for the degree

### Developing an Isolated Word Recognition System in MATLAB

MATLAB Digest Developing an Isolated Word Recognition System in MATLAB By Daryl Ning Speech-recognition technology is embedded in voice-activated routing systems at customer call centres, voice dialling

### Test of Hypotheses. Since the Neyman-Pearson approach involves two statistical hypotheses, one has to decide which one

Test of Hypotheses Hypothesis, Test Statistic, and Rejection Region Imagine that you play a repeated Bernoulli game: you win \$1 if head and lose \$1 if tail. After 10 plays, you lost \$2 in net (4 heads

### Statistical Inference

Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

### Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 15 Version 8, August 5, 2014 1 Abstract This paper discusses alternatives

### Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

### PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical

### SPEAKER IDENTIFICATION FROM YOUTUBE OBTAINED DATA

SPEAKER IDENTIFICATION FROM YOUTUBE OBTAINED DATA Nitesh Kumar Chaudhary 1 and Shraddha Srivastav 2 1 Department of Electronics & Communication Engineering, LNMIIT, Jaipur, India 2 Bharti School Of Telecommunication,

### Optimal Replacement of Underground Distribution Cables

1 Optimal Replacement of Underground Distribution Cables Jeremy A. Bloom, Member, IEEE, Charles Feinstein, and Peter Morris Abstract This paper presents a general decision model that enables utilities

### UNDERSTANDING THE TWO-WAY ANOVA

UNDERSTANDING THE e have seen how the one-way ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables

### CS229 Project Final Report. Sign Language Gesture Recognition with Unsupervised Feature Learning

CS229 Project Final Report Sign Language Gesture Recognition with Unsupervised Feature Learning Justin K. Chen, Debabrata Sengupta, Rukmani Ravi Sundaram 1. Introduction The problem we are investigating

### SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING

AAS 07-228 SPECIAL PERTURBATIONS UNCORRELATED TRACK PROCESSING INTRODUCTION James G. Miller * Two historical uncorrelated track (UCT) processing approaches have been employed using general perturbations

### Least Squares Estimation

Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

### Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model

Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written

### Guido Sciavicco. 11 Novembre 2015

classical and new techniques Università degli Studi di Ferrara 11 Novembre 2015 in collaboration with dr. Enrico Marzano, CIO Gap srl Active Contact System Project 1/27 Contents What is? Embedded Wrapper

### Linear Dependence Tests

Linear Dependence Tests The book omits a few key tests for checking the linear dependence of vectors. These short notes discuss these tests, as well as the reasoning behind them. Our first test checks

### CROP CLASSIFICATION WITH HYPERSPECTRAL DATA OF THE HYMAP SENSOR USING DIFFERENT FEATURE EXTRACTION TECHNIQUES

Proceedings of the 2 nd Workshop of the EARSeL SIG on Land Use and Land Cover CROP CLASSIFICATION WITH HYPERSPECTRAL DATA OF THE HYMAP SENSOR USING DIFFERENT FEATURE EXTRACTION TECHNIQUES Sebastian Mader

### How to Conduct a Hypothesis Test

How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some

### STA 4273H: Statistical Machine Learning

STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 6 Three Approaches to Classification Construct

### IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181 The Global Kernel k-means Algorithm for Clustering in Feature Space Grigorios F. Tzortzis and Aristidis C. Likas, Senior Member, IEEE

### Predict the Popularity of YouTube Videos Using Early View Data

000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050

### 1816 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7, JULY 2006. Principal Components Null Space Analysis for Image and Video Classification

1816 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7, JULY 2006 Principal Components Null Space Analysis for Image and Video Classification Namrata Vaswani, Member, IEEE, and Rama Chellappa, Fellow,

### Social Media Mining. Data Mining Essentials

Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers

### Basics of Statistical Machine Learning

CS761 Spring 2013 Advanced Machine Learning Basics of Statistical Machine Learning Lecturer: Xiaojin Zhu jerryzhu@cs.wisc.edu Modern machine learning is rooted in statistics. You will find many familiar

### ELICITING a representative probability distribution from

146 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 53, NO. 1, FEBRUARY 2006 Entropy Methods for Joint Distributions in Decision Analysis Ali E. Abbas, Member, IEEE Abstract A fundamental step in decision

### Introduction to Statistical Machine Learning

CHAPTER Introduction to Statistical Machine Learning We start with a gentle introduction to statistical machine learning. Readers familiar with machine learning may wish to skip directly to Section 2,

### UNIVERSAL SPEECH MODELS FOR SPEAKER INDEPENDENT SINGLE CHANNEL SOURCE SEPARATION

UNIVERSAL SPEECH MODELS FOR SPEAKER INDEPENDENT SINGLE CHANNEL SOURCE SEPARATION Dennis L. Sun Department of Statistics Stanford University Gautham J. Mysore Adobe Research ABSTRACT Supervised and semi-supervised

### Data a systematic approach

Pattern Discovery on Australian Medical Claims Data a systematic approach Ah Chung Tsoi Senior Member, IEEE, Shu Zhang, Markus Hagenbuchner Member, IEEE Abstract The national health insurance system in

### Biometric Authentication using Online Signatures

Biometric Authentication using Online Signatures Alisher Kholmatov and Berrin Yanikoglu alisher@su.sabanciuniv.edu, berrin@sabanciuniv.edu http://fens.sabanciuniv.edu Sabanci University, Tuzla, Istanbul,

### Statistical Machine Learning

Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classes

### More details on the inputs, functionality, and output can be found below.

Overview: The SMEEACT (Software for More Efficient, Ethical, and Affordable Clinical Trials) web interface (http://research.mdacc.tmc.edu/smeeactweb) implements a single analysis of a two-armed trial comparing

### CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

### Statistical Machine Learning from Data

Samy Bengio Statistical Machine Learning from Data 1 Statistical Machine Learning from Data Gaussian Mixture Models Samy Bengio IDIAP Research Institute, Martigny, Switzerland, and Ecole Polytechnique

### An introduction to Value-at-Risk Learning Curve September 2003

An introduction to Value-at-Risk Learning Curve September 2003 Value-at-Risk The introduction of Value-at-Risk (VaR) as an accepted methodology for quantifying market risk is part of the evolution of risk

### Music Mood Classification

Music Mood Classification CS 229 Project Report Jose Padial Ashish Goel Introduction The aim of the project was to develop a music mood classifier. There are many categories of mood into which songs may

### 99.37, 99.38, 99.38, 99.39, 99.39, 99.39, 99.39, 99.40, 99.41, 99.42 cm

Error Analysis and the Gaussian Distribution In experimental science theory lives or dies based on the results of experimental evidence and thus the analysis of this evidence is a critical part of the

### Linear concepts and hidden variables: An empirical study

Linear concepts and hidden variables An empirical study Adam J. Grove NEC Research Institute 4 Independence Way Princeton NJ 854 grove@research.nj.nec.com Dan Roth Department of Computer Science University

### Abstract. 1. Introduction. 1.1. Methodology

Fingerprint Recognition System Performance in the Maritime Environment Hourieh Fakourfar 1, Serge Belongie 2* 1 Department of Electrical and Computer Engineering, and 2 Department of Computer Science and

### Corrections to the First Printing

Corrections to the First Printing Chapter 2 (i) Page 48, Paragraph 1: cells/µ l should be cells/µl without the space. (ii) Page 48, Paragraph 2: Uninfected cells T i should not have the asterisk. Chapter

### Centre for Central Banking Studies

Centre for Central Banking Studies Technical Handbook No. 4 Applied Bayesian econometrics for central bankers Andrew Blake and Haroon Mumtaz CCBS Technical Handbook No. 4 Applied Bayesian econometrics

### Data, Measurements, Features

Data, Measurements, Features Middle East Technical University Dep. of Computer Engineering 2009 compiled by V. Atalay What do you think of when someone says Data? We might abstract the idea that data are

### Epipolar Geometry. Readings: See Sections 10.1 and 15.6 of Forsyth and Ponce. Right Image. Left Image. e(p ) Epipolar Lines. e(q ) q R.

Epipolar Geometry We consider two perspective images of a scene as taken from a stereo pair of cameras (or equivalently, assume the scene is rigid and imaged with a single camera from two different locations).

### Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel

IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 2, FEBRUARY 2002 359 Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel Lizhong Zheng, Student

### Notes for STA 437/1005 Methods for Multivariate Data

Notes for STA 437/1005 Methods for Multivariate Data Radford M. Neal, 26 November 2010 Random Vectors Notation: Let X be a random vector with p elements, so that X = [X 1,..., X p ], where denotes transpose.

### Introduction to latent variable models

Introduction to latent variable models lecture 1 Francesco Bartolucci Department of Economics, Finance and Statistics University of Perugia, IT bart@stat.unipg.it Outline [2/24] Latent variables and their

### Module 5 Hypotheses Tests: Comparing Two Groups

Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this

### Principal components analysis

CS229 Lecture notes Andrew Ng Part XI Principal components analysis In our discussion of factor analysis, we gave a way to model data x R n as approximately lying in some k-dimension subspace, where k

### Collision Probability Forecasting using a Monte Carlo Simulation. Matthew Duncan SpaceNav. Joshua Wysack SpaceNav

Collision Probability Forecasting using a Monte Carlo Simulation Matthew Duncan SpaceNav Joshua Wysack SpaceNav Joseph Frisbee United Space Alliance Space Situational Awareness is defined as the knowledge

### ELEC-E8104 Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems

Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems Minimum Mean Square Error (MMSE) MMSE estimation of Gaussian random vectors Linear MMSE estimator for arbitrarily distributed

### NOTES ON LINEAR TRANSFORMATIONS

NOTES ON LINEAR TRANSFORMATIONS Definition 1. Let V and W be vector spaces. A function T : V W is a linear transformation from V to W if the following two properties hold. i T v + v = T v + T v for all

### SPSS: Descriptive and Inferential Statistics. For Windows

For Windows August 2012 Table of Contents Section 1: Summarizing Data...3 1.1 Descriptive Statistics...3 Section 2: Inferential Statistics... 10 2.1 Chi-Square Test... 10 2.2 T tests... 11 2.3 Correlation...

### Unit 18 Determinants

Unit 18 Determinants Every square matrix has a number associated with it, called its determinant. In this section, we determine how to calculate this number, and also look at some of the properties of

### Two-sample inference: Continuous data

Two-sample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with two-sample inference for continuous data As

### A successful market segmentation initiative answers the following critical business questions: * How can we a. Customer Status.

MARKET SEGMENTATION The simplest and most effective way to operate an organization is to deliver one product or service that meets the needs of one type of customer. However, to the delight of many organizations

### arxiv:1506.04135v1 [cs.ir] 12 Jun 2015

Reducing offline evaluation bias of collaborative filtering algorithms Arnaud de Myttenaere 1,2, Boris Golden 1, Bénédicte Le Grand 3 & Fabrice Rossi 2 arxiv:1506.04135v1 [cs.ir] 12 Jun 2015 1 - Viadeo

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### Chapter 4: Non-Parametric Classification

Chapter 4: Non-Parametric Classification Introduction Density Estimation Parzen Windows Kn-Nearest Neighbor Density Estimation K-Nearest Neighbor (KNN) Decision Rule Gaussian Mixture Model A weighted combination

### In this chapter, you will learn to use descriptive statistics to organize, summarize, analyze, and interpret data for contract pricing.

3.0 - Chapter Introduction In this chapter, you will learn to use descriptive statistics to organize, summarize, analyze, and interpret data for contract pricing. Categories of Statistics. Statistics is

### Tagging with Hidden Markov Models

Tagging with Hidden Markov Models Michael Collins 1 Tagging Problems In many NLP problems, we would like to model pairs of sequences. Part-of-speech (POS) tagging is perhaps the earliest, and most famous,

### 9Tests of Hypotheses. for a Single Sample CHAPTER OUTLINE

9Tests of Hypotheses for a Single Sample CHAPTER OUTLINE 9-1 HYPOTHESIS TESTING 9-1.1 Statistical Hypotheses 9-1.2 Tests of Statistical Hypotheses 9-1.3 One-Sided and Two-Sided Hypotheses 9-1.4 General

### Discriminative Multimodal Biometric. Authentication Based on Quality Measures

Discriminative Multimodal Biometric Authentication Based on Quality Measures Julian Fierrez-Aguilar a,, Javier Ortega-Garcia a, Joaquin Gonzalez-Rodriguez a, Josef Bigun b a Escuela Politecnica Superior,

### Data reduction and descriptive statistics

Data reduction and descriptive statistics dr. Reinout Heijungs Department of Econometrics and Operations Research VU University Amsterdam August 2014 1 Introduction Economics, marketing, finance, and most

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### Language Modeling. Chapter 1. 1.1 Introduction

Chapter 1 Language Modeling (Course notes for NLP by Michael Collins, Columbia University) 1.1 Introduction In this chapter we will consider the the problem of constructing a language model from a set

### DYNAMIC RANGE IMPROVEMENT THROUGH MULTIPLE EXPOSURES. Mark A. Robertson, Sean Borman, and Robert L. Stevenson

c 1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or

### THE downlink of multiuser multiple-input multiple-output

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 7, JULY 2007 3837 Precoding for Multiple Antenna Gaussian Broadcast Channels With Successive Zero-Forcing Amir D. Dabbagh and David J. Love, Member,

### We seek a factorization of a square matrix A into the product of two matrices which yields an

LU Decompositions We seek a factorization of a square matrix A into the product of two matrices which yields an efficient method for solving the system where A is the coefficient matrix, x is our variable

### 10-810 /02-710 Computational Genomics. Clustering expression data

10-810 /02-710 Computational Genomics Clustering expression data What is Clustering? Organizing data into clusters such that there is high intra-cluster similarity low inter-cluster similarity Informally,

### Subspace Analysis and Optimization for AAM Based Face Alignment

Subspace Analysis and Optimization for AAM Based Face Alignment Ming Zhao Chun Chen College of Computer Science Zhejiang University Hangzhou, 310027, P.R.China zhaoming1999@zju.edu.cn Stan Z. Li Microsoft

### EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set

EM Clustering Approach for Multi-Dimensional Analysis of Big Data Set Amhmed A. Bhih School of Electrical and Electronic Engineering Princy Johnson School of Electrical and Electronic Engineering Martin

### Statistical Inference and t-tests

1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

### The effect of population history on the distribution of the Tajima s D statistic

The effect of population history on the distribution of the Tajima s D statistic Deena Schmidt and John Pool May 17, 2002 Abstract The Tajima s D test measures the allele frequency distribution of nucleotide

### α = u v. In other words, Orthogonal Projection

Orthogonal Projection Given any nonzero vector v, it is possible to decompose an arbitrary vector u into a component that points in the direction of v and one that points in a direction orthogonal to v

### 3.6: General Hypothesis Tests

3.6: General Hypothesis Tests The χ 2 goodness of fit tests which we introduced in the previous section were an example of a hypothesis test. In this section we now consider hypothesis tests more generally.

### Distributions: Population, Sample and Sampling Distributions

119 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics Chapter 9 Distributions: Population, Sample and Sampling Distributions In the three preceding chapters

### 4. Introduction to Statistics

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation

HAROLD CAMPING i ii iii iv v vi vii viii ix x xi xii 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

### Sample Size Determination

Sample Size Determination Population A: 10,000 Population B: 5,000 Sample 10% Sample 15% Sample size 1000 Sample size 750 The process of obtaining information from a subset (sample) of a larger group (population)

### Solutions to Math 51 First Exam January 29, 2015

Solutions to Math 5 First Exam January 29, 25. ( points) (a) Complete the following sentence: A set of vectors {v,..., v k } is defined to be linearly dependent if (2 points) there exist c,... c k R, not

### Notes on Orthogonal and Symmetric Matrices MENU, Winter 2013

Notes on Orthogonal and Symmetric Matrices MENU, Winter 201 These notes summarize the main properties and uses of orthogonal and symmetric matrices. We covered quite a bit of material regarding these topics,

### Chapter 4. Probability and Probability Distributions

Chapter 4. robability and robability Distributions Importance of Knowing robability To know whether a sample is not identical to the population from which it was selected, it is necessary to assess the