Problem Set 2: Computational Inference: 2014
Surajit Ray
1. Let X1 , X2 , . . . be a sequence of independent, identically distributed [i.i.d.] random variables with
common distribution function F (t) = P (X1 t). The empirical distribution function (EDF) o
Lab 3: Computational Inference: 2014
Lab 3 will be devoted towards nding Bootstrap CI using the US Crime dataset. We will use
both parametric and non-parametric bootstrap.
1
Parametric Bootstrap Condence Interval
Load the UScrime data in the MASS package.
Lab 2: Computational Inference: 2014
In the rst half we will perform PCR and PLSR on the prostate data that we used in the
rst Lab. The second half will be devoted towards nding Bootstrap CI and calculating Bias
and Variance.
1
Partial least squares and P
Linear Regression refresher
Ridge Regression
LASSO
1.5 LARS
Computational Inference
Unit01: Regularized Regression
Surajit Ray
School of Mathematics and Statistics
University of Glasgow
October 21, 2014
-1-
Partial Least Squares
Linear Regression refreshe
Problem Set 1: Computational Inference: 2014
1. Show that the ridge regression estimate can be obtained by ordinary least squares regression on an augmented data set.
Hint: Suppose X and y are centered. Let (X, y ) be the augmented data from (X, y),
i.e.
Wednesday, 8th May 2013
2.00pm 3.30pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI. AND B.SC.
(SCIENCE)
Statistics 4H/M Computational Inference
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used
in examinations. No calcul
Monday, 12th May 2014
2.00pm 3.30pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI. AND B.SC.
(SCIENCE)
Statistics 4H/M Computational Inference
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used
in examinations. No calculat
Lab 1: Computational Inference: 2012
Surajit Ray
October 9, 2014
The purpose of this Lab is to apply linear regression on a real data set. We will consider several
ways of improving prediction accuracy: feature selection, ridge regression, lasso, (partial
Problem Set 4: Computational Inference: 2014
Surajit Ray
November 27, 2014
1. Why do we need multiple starting values when initialising an EM Algorithm ?
Answer
If the likelihood have multiple modes there is no guarantee that the EM Algorithm will converg
Problem Set 4: Computational Inference: 2014
Surajit Ray
November 26, 2014
1. Why do we need multiple starting values when initialising an EM Algorithm ?
2. Prove Jensens Inequality (Needed for showing the the EM iterative steps always increases the likel
Problem Set 2: Computational Inference: 2014
Surajit Ray
1. Let X1 , X2 , . . . be a sequence of independent, identically distributed [i.i.d.] random variables with
common distribution function F (t) = P (X1 t). The empirical distribution function (EDF) o
Problem Set 3: Computational Inference: 2014
Surajit Ray
1. Here are heights (inches) of professional female basketball players who are centers and forwards.
We wonder if the players in two positions dier in average height.
Forwards:
69
72
71
71
66
68
67
Lab 4: Computational Inference: 2014
This Lab focuses on performing Bootstrap hypothesis testing and generating random variates
1
Bootstrap hypothesis testing for equality of distribution (Solved
Example)
Suppose x1 , . . . , xn and y1 , . . . , yn are sa
Problem Set 3: Computational Inference: 2014
Surajit Ray
1. Here are heights (inches) of professional female basketball players who are centers and forwards.
We wonder if the players in two positions dier in average height.
Forwards:
69
72
71
71
66
68
67
Problem Set 1: Computational Inference: 2014
1. Show that the ridge regression estimate can be obtained by ordinary least squares regression on an augmented data set.
Hint: Suppose X and y are centered. Let (X, y ) be the augmented data from (X, y),
i.e.
Wednesday, 8th May 2013
2.00pm 3.30pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI. AND B.SC.
(SCIENCE)
Statistics 4H/M Computational Inference
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used
in examinations. No calcul
COMPUTATATIONAL INFERENCE (2014)
Course instructor: Surajit Ray
Email: [email protected]
Office: Mathematics building 229
Aims
This course introduces methods of computational inference, with an emphasis
on practical issues
Monday, 12th May 2014
2.00pm 3.30pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI. AND B.SC.
(SCIENCE)
Statistics 4H/M Computational Inference
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used
in examinations. No calculat