Within your report you should begin each question on a newpage.You should preface your report with a single page containing, on twolines:–The module code:‘COMP0036’–The assignment title: ‘LSA Assignment1’ Computer Science1代写 Your report should be neat andlegible.You are strongly advised to use LATEX to format the report, however this is not a hard requirement, and you may submit a report formatted with the aid of another system, or even a handwritten report, provided that you have converted it to a pdf (see above).Pleaseattempt to express your answers as succinctly asPlease note that if your answer to a question or sub-question is illegible orincomprehen- sible to the marker then you will receive no marks for that question or sub-question.Computer Science1代写 Please remember to detail your working, and state clearly any assumptions which you make.Unless a question specifies otherwise, then please make use of the Notation section as a guide to the definition of objects.Computer Science1代写 Failure to adhere to any of the guidelines may result in question-specific deduction of marks. If warranted these deductions may be punitive.Computer Science1代写Notation Computer Science1代写 Inputs:x = [1, x1, x2, , xm]T ∈ Rm+1Outputs:y ∈ R for regression problemsy ∈ {0, 1} for binary classification problemsTraining Data:S = {x(i), y(i)}nInput Training Data:The design matrix, X, is defined as:Computer Science1代写 Output Training Data:Data-Generating Distribution:S is drawn i.i.d. from a data-generating distribution, DYou are given a raw training data set consisting of 50 input/output sample pairs. Each output data point is real-valued, while each input data point consists of a vector of real- valuedattributes, x = [1, x1, x2, x3, x4, x5]T .You are asked to investigate the relationship between inputs and outputs.Computer Science1代写 Your domain expertise leads you to believe that the class of cubic functions will be most appropriate for the modelling of this relationship.Computer Science1代写 (a) [7 marks]What is the problem with using the ordinary least squares approach to find such a model? Explain.[Hint: Consider the Multinomial Theorem]Computer Science1代写 (b) [3 marks]If you discarded one of the attributes in your model would this problem remain? Explain.(c) [5 marks]Briefly describe an approach that can help to remedy the problem in part (a). Explain.(d) [5 marks]You are asked to select only those features which are most important for use in your model. Explain how you would achieve this in an efficient fashion.Computer Science1代写 Recall that in linear regression in general we seek to learn a linear mapping, fw, charac- terisedby a weight vector, w ∈ Rm+1, and drawn from a function class, F:F = {fw(x) = w · x|w = [w0, w1,  , wm]   ∈ R }Now, consider a data-generating distribution described by a Gaussian additive noise model:y = w · x + s where: s ∼ N (0, α), α 0Assume that x is one dimensional, and that there is no bias term to learn, i.e. x = x ∈ R and w = w ∈ R.(a) [4 marks]Given a training set, S, find an expression for the likelihood, pD(S|w) = P[S|w] in the form: A exp (B). Characterise A and B.(b) [4 marks]Assume a prior distribution, pW (w), over w, such that each instance of w is an outcome of a Gaussian random variable, W , where:W ∼ N (0, β) where: β  0Provide a detailed characterisation of the posterior distribution over w.Computer Science1代写 (c) [4 marks]Hence succintly derive the Maximum A Posteriori (MAP) estimate of w.(d) [4 marks]Is this solution unique? Explain.(e) [4 marks]This approach should remind you of another machine learning algorithm. State the algorithm, and express the connection between the two.

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