gistfile1.php

<?php

add_filter( 'wp_stream_record_array', 'bhww_filter_wp_stream_record_array', 10, 1 );

function bhww_filter_wp_stream_record_array( $recordarr ) {
	if ( ! isset( $recordarr[0] ) )
		return array();

	// BackupBuddy (iThemes) entries
	if ( 'settings' === $recordarr[0]['connector'] && isset( $recordarr[0]['stream_meta']['option'] ) && 'ithemes-updater-cache' === $recordarr[0]['stream_meta']['option']
	)
		return array();

	// WP Help entries
	if ( 'wp-help' === $recordarr[0]['context'] && isset( $recordarr[0]['stream_meta']['singular_name'] ) && 'help document' === $recordarr[0]['stream_meta']['singular_name']
	)
		return array();

	// All other entries
	return $recordarr;
}