MAST90083 Computational Statistics & Data Mining Linear Regression Tutorial & Practical 4: Model Selection Question 1 In this question we are interested in deriving an algorithm for solving Lasso. Given the model y = Xβ + � where y ∈ Rn, X ∈ Rn×p and � ∈ Rn ∼ N (0, σ2In). Let β̂ be […]
Microsoft PowerPoint – L2 2021 Outline • Discussion on first week’s lab • Encoding, numbers, floating‐point (details) • Lab walk through • Memory (unlikely time – probably just back‐up slides) Let’s talk about labs • My point of view: • Lots of groups interacted well • Cameras on • Active chat • Discord worked well for those who used it • Progress was slower than in‐person labs • Codeshare really helps demonstrators to interact with students • Work‐through (answers) later in lecture An ideal setup Let’s talk about labs • My point of view: • T12 until R09 ran about the same. Groups are set‐up, should be smoother next week • Issues exist – we’re trying to learn about them so we can try to address them Let’s talk about labs •
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MAST90083 Computational Statistics & Data Mining EM Algorithm Tutorial & Practical 8: EM Algorithm Question 1 Consider a mixture distribution of the form p (y) = K∑ k=1 pkp (y|k) where the elements of y could be discrete or continuous or a combination of these. Denote the mean and the covariance of p (y|k) by
MAST90083 Computational Statistics & Data Mining EM Algorithm Tutorial and Practical 8: Solutions Question 1 1. The mean of p(y) is given by E(y) = ∫ yp (y) dy = ∫ y K∑ k=1 pkp (y|k) dy = K∑ k=1 pk ∫ yp (y|k) dy = K∑ k=1 pkµk 2. The covariance of y is
CM0304 Graphics I Graphics Hardware I.1 Graphics Systems CMT107 Visual Computing Copyright By PowCoder代写 加微信 powcoder III.1 Object Representation Xianfang Sun School of Computer Science & Informatics Cardiff University ➢Constructive solid geometry ➢Boundary representation ➢Mesh representation • Rendering meshes with OpenGL ➢Volumetric representation: voxels 15:14 2CMT107 Visual Computing Example Models and Scenes 15:14 3CMT107 Visual
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Mandatory: Approximate Data Structures Philip Bille Inge Li Gørtz Eva Rotenberg 1 Exercise Consider the following 4 points in R: w = 0, x = 10, y = 20, z = 30. Consider the metric given by distance between the points, eg. d(z, x) = 30− 10 = 20. In this exercise, you will analyse
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Approximate Distance Oracles Mikkel Thorup AT&T Labs – Research 180 Park Avenue Florham Park, NJ 07932, USA .com Uri Zwick � School of Computer Science Tel Aviv University Tel Aviv 69978, Israel .ac.il ABSTRACT LetG = (V;E) be an undirected weighted graph with jV j = n and jEj = m. Let k � 1
Java Concurrency Deadlock, Reader-Writer problem and Condition synchronization Michelle Kuttel Serial versus concurrent Sequential correctness is mostly concerned with safety properties: ensuing that a program transforms each before-state to the correct after-state. Concurrent correctness is also concerned with safety, but the problem is much, much harder: safety must be ensured despite the vast number of
Robust decomposition of cell type mixtures in spatial transcriptomics Robust decomposition of cell type mixtures in spatial transcriptomics Dylan M. Cable1,2,3, Evan Murray2, Luli S. Zou2,3,4, Aleksandrina Goeva2, Evan Z. Macosko2,5, Fei Chen2,*, and Rafael A. Irizarry3,4,* 1 Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA, 02139 2Broad Institute of Harvard and MIT,
#generate data set.seed(123) n=100; y=rnorm(n,2,1) Copyright By PowCoder代写 加微信 powcoder #true posterior distribution for theta posterior=function(theta,data){ n=length(data) thetam=((0/100)+(n*mean(data)/1))/((1/100)+n/1) thetasd=sqrt(1/((1/100)+n/1)) post=dnorm(theta,mean=thetam,sd=thetasd) return(post) #unnormalised posterior unposterior=function(theta,data){ likelihood=prod(dnorm(data,theta,1)) prior=dnorm(theta,0,10) unpost=likelihood*prior return(unpost) #proposal distribution g=function(theta,m,s){ g=dnorm(theta,mean=m,sd=s) #auxiliar function to determine the optimal value of M; need to find maximum of unnormalised posterior/g aux=function(theta,data){ likelihood=prod(dnorm(data,theta,1)) prior=dnorm(theta,0,10) post=likelihood*prior g=dnorm(theta,mean=mean(data),sd=sd(data)) aux=post/g return(aux)
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