(5/5)

# use the given discrete data y with a discrete Dirac means

INSTRUCTIONS TO CANDIDATES

Figure 1 shows a visualization of eq. (3) for the setting of image denoising, where noise is added to a specific instance Y = y. Moreover, the process of denoising a noisy image X = x can be described by the posterior

P(YX = x).

(4) Since we don't know the complete distribution over the target space p(y) we need to make some assumptions given our finite training dataset y = {y1,..., YN}. We want to compare two options to estimate our prior distribution p(y), see also Figure 2:

1. use the given discrete data y with a discrete Dirac means

use kernel density estimation (KDE), a non-parametric approach for density estimation with a kernel k and a bandwidth

where any kernel function k can be used, however, a smooth kernel, such as the Gauss kernel is desirable to avoid discontinuities in the estimated probability density function and yields the following=density estimation with KDE

Figure 2: Given a finite numer of 2D samples (red markers) we can either use the data itself (Dirac measure) or a kernel density estimation (KDE). Note that the latter allows for a smooth prior distribution and for h→0 it approaches the Dirac measure.

Having a model for the likelihood and the prior distribution, we now have two possibilities to use the posterior eq. (4) for making predictions, as shown in the lecture notes and slides. The first possibility is the so called conditional mean, also know as regression function, and is given by

(5/5)

## Related Questions

##### . Introgramming & Unix Fall 2018, CRN 44882, Oakland University Homework Assignment 6 - Using Arrays and Functions in C

DescriptionIn this final assignment, the students will demonstrate their ability to apply two ma

##### . The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is an

Path finding involves finding a path from A to B. Typically we want the path to have certain properties,such as being the shortest or to avoid going t

##### . Develop a program to emulate a purchase transaction at a retail store. This program will have two classes, a LineItem class and a Transaction class. The LineItem class will represent an individual

Develop a program to emulate a purchase transaction at a retail store. Thisprogram will have two classes, a LineItem class and a Transaction class. Th

##### . SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 1 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

##### . Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

Hire Me

Hire Me