Exclude categories from list (wp_list_categories)

This…

<?php wp_list_categories('exclude=4,7&title_li='); ?>

… does not include your Walker. Why didn’t you just add that exclude the same way you added the others?

$args = array();
$args['show_last_updated'] = true;
$args['show_count'] = true;
$args['title_li'] = '';
$args['exclude'] = '4,7';
$args['walker'] = new CategoryThumbnail_Walker;

wp_list_categories($args);