代写CSC 411/2515 Introduction to Machine Learning

CSC 411/2515

CSC 411/2515

Introduction to Machine Learning

Overview

In this assignment, you will rst derive the learning rule for mixture of Gaussians models and

convolutional neural networks (CNN), and then experiment with these models on a subset

of the Toronto Faces Dataset (TFD) 1

. Some code that partially implements a regular neural

network, a convolutional neural network, and a mixture of Gaussians model is available on

the course website (in python).

We subsample 3374, 419 and 385 grayscale images from TFD as the training, validation and

testing set respectively. Each image is of size 48 48 and contains a face that has been

extracted from a variety of sources. The faces have been rotated, scaled and aligned to make

the task easier. The faces have been labeled by experts and research assistants based on their

expression. These expressions fall into one of seven categories: 1-Anger, 2-Disgust, 3-Fear,

4-Happy, 5-Sad, 6-Surprise, 7-Neutral. We show one example face per class in Figure 1.

Figure 1: Example faces. From left to right, the the corresponding class is from 1 to 7.

1 EM for Mixture of Gaussians (10 pts)

We begin with a Gaussian mixture model:

代写CSC 411/2515 Introduction to Machine Learning

Consider a special case of a Gaussian mixture model in which the covariance matrix k of

each component is constrained to have a common value . In other words k = , for all

k. Derive the EM equations for maximizing the likelihood function under such a model.

1http://aclab.ca/users/josh/TFD.html2 Convolutional Neural Networks (10 pts)

Let x 2 RNHWC be N images, and f 2 RIJCK be the convolutional lters. H;W

are the height and width of the image; I; J are the height and width of the lters; C is the

depth of the image (a.k.a. channels); K is the number of lters.

Padding is an operation that adds zeros to the edges of an image to form a larger image.

Formally, the padding operator pad is dened as:

代写CSC 411/2515 Introduction to Machine Learning