代写CSC 411/2515 Introduction to Machine Learning

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  • 代写CSC 411/2515 Introduction to Machine Learning
    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 de ned as:
    代写CSC 411/2515 Introduction to Machine Learning