数据科学编程作业代写 ST340代写

ST340 Programming for Data Science

Assignment 3

数据科学编程作业代写 Instructions Work in groups Specify your student number and name on your assignment. You need submit only one copy for each group.

Instructions

Work in groups
Specify your student number and name on your assignment. You need submit only one copy for each group.
Any programming should be in R. Your report should be created using R markdown. Submit a single knitted pdf document which includes any code you have written (together with the rmd file)
This assignment is worth 17% of your overall mark

Q1 Gradient descent 数据科学编程作业代写

Here is a function that does gradient descent with a fixed number of iterations to find local minima:

gradient.descent <- function(f, gradf, x0, iterations=1000, eta=0.2) {
  x<-x0
  for (i in 1:iterations) {
    cat(i,"/",iterations,": ",x," ",f(x),"\n")
    x<-x-eta*gradf(x)
  }
  x
}

Example:

f <-function(x) { sum(xˆ2) }
gradf<-function(x) { 2*x }
gradient.descent(f,gradf,c(10,20),10,0.2)

(a) Write a short function that uses gradient.descent to find a local maximum. (For the purpose of this question, gradient.descent is a “black box”. Don’t worry about the printed output, just the return value matters.)

i.e.

gradient.ascent <- function(f, df, x0, iterations=1000, eta=0.2) {
# ... use gradient.descent(...) here ...
}
f <-function(x) { (1+xˆ2)ˆ(-1) }
gradf<-function(x) { -2*x*(1+xˆ2)ˆ(-2) }
gradient.ascent(f,gradf,3,40,0.5)

(b) Consider the function f : R² → R given by

f <- function(x) (x[1]-1)ˆ2 + 100*(x[1]ˆ2-x[2])ˆ2

i) Give a short mathematical proof that f has a unique minimum.

ii) Write a function gradf to calculate ∇f, i.e.

gradf <- function(x) { # ... use x[1] and x[2] ... }

iii) Starting from the point x0=c(3,4), try to find the minimum using gradient descent.

gradient.descent(f,gradf,c(3,4), ... , ...)

(c) Write a function to do gradient descent with momentum. Starting from the point x0=c(3,4), use your function to find the minimum of the function from part (b).

Q2 Support vector machines 数据科学编程作业代写

Run the following code to load the tiny MNIST dataset:

load("mnist.tiny.RData")
train.X=train.X/255
test.X=test.X/255

and then show some digits:

library(grid)
grid.raster(array(aperm(array(train.X[1:50,],c(5,10,28,28)),c(4,1,3,2)),c(140,280)),
              interpolate=FALSE)

(a) Use three-fold cross validation on the training set to compare SVMs with linear kernels, polynomial kernels and RBF kernels, i.e.

library(e1071)
svm(train.X,train.labels,type="C classification",kernel="linear",cross=3)$tot.accuracy
svm(train.X,train.labels,type="C-classification",kernel="poly",
  degree=2,coef=1,cross=3)$tot.accuracy

etc. (The flag warning=FALSE is helpful here. What is the suppressed warning message warning you about?)

(b) For the RBF kernels, write a grid search function that takes two lists, log.C.range and log.gamma.range, and for each pair (lc,lg) of entries in the pair of lists attempts cross-validation with parameters cost = exp(lc) and gamma=exp(lg). Once you have found the model with the best cross-validation error, train it on the full tiny’ training set and then test it on thetiny’ test set.

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ST340 Programming for Data Science

Assignment 3

Instructions

Q1 Gradient descent 数据科学编程作业代写

Q2 Support vector machines 数据科学编程作业代写

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