ActiveRecord.php

<?php

class ActiveRecord extends CActiveRecord
{
    /**
     * Updates cross-table for MANY_MANY relations, no AR class for cross-table needed.
     * This method will delete all existing cross-table records not present in relatedIdList, then populate cross-table with new relations from relatedIdList in one transaction.
     * @param string $relationName relation name to be updated (as given in CActiveRecord::relations())
     * @param array $relatedIdList list of related ids OR list of related ARs
     * @param string $idKey PK accessor for related entity (used only if list of ARs passed in relatedIdList). Defaults to `id`, which is ok for almost every AR.
     * @throws CDbException
     */
    public function setRelated($relationName, array $relatedIdList, $idKey = 'id'){
        // getting relation options
        $crossTableTempInfo = explode('(', $this->relations()[$relationName][2]);
        $crossTableMeta['table_name'] = trim($crossTableTempInfo[0], "() \t\n\r\0\x0B");
        $crossTableMeta['key_1'] = trim(explode(',', $crossTableTempInfo[1])[0], "() \t\n\r\0\x0B");
        $crossTableMeta['key_2'] = trim(explode(',', $crossTableTempInfo[1])[1], "() \t\n\r\0\x0B");

        // filtering out ids
        $flat = [];
        foreach ( $relatedIdList as $currentRelated ){
            if ( is_object($currentRelated) ){
                $flat[] = $currentRelated->$idKey;
            } else {
                $flat[] = $currentRelated;
            }
        }

        $related = [];
        foreach ( $this->$relationName as $currentRelated ){
            $related[] = $currentRelated->$idKey;
        }

        // relations to connect
        $connect = array_diff($flat, $related);
        // relations to disconnect
        $disconnect = array_diff($related, $flat);

        $transaction = $this->dbConnection->beginTransaction();

        // connecting
        if ( !empty($connect) ){
            $params = [];
            foreach ( $connect as $key => $value ){
                $params[':rel_con_v_'.(string)$key] = $value;
            }
            $query = 'INSERT INTO '
                . $crossTableMeta['table_name']
                . ' ('
                . $crossTableMeta['key_2']
                . ', '
                . $crossTableMeta['key_1']
                . ') VALUES (' . implode(', :rel_pk), (', array_keys($params))
                . ', :rel_pk)';
            /** @var CDbCommand $connectRelatedCommand */
            $connectRelatedCommand = Yii::app()->db->createCommand($query);
            $connectRelatedCommand->bindValues($params + [':rel_pk' => $this->primaryKey]);
            $connectRelatedCommand->execute();
        }

        // disconnecting
        if ( !empty($disconnect) ){
            $criteria = new CDbCriteria();
            $criteria->addInCondition($crossTableMeta['key_2'], $disconnect);
            $criteria->addCondition($crossTableMeta['key_1'] . '=:rel_pk');
            /** @var CDbCommand $clearRelatedCommand */
            $clearRelatedCommand = Yii::app()->db->createCommand('DELETE FROM ' . $crossTableMeta['table_name'] . ' WHERE ' . $criteria->condition);
            $clearRelatedCommand->bindValues($criteria->params + [':rel_pk' => $this->primaryKey]);
            $clearRelatedCommand->execute();
        }

        $transaction->commit();
    }
}

Given

class Mail extends ActiveRecord
{
        //...
    public function relations()
    {
        return array(
            'categories' => array(self::MANY_MANY, 'Category', 'mail_to_category(mail, category)'),
            'regions' => array(self::MANY_MANY, 'Region', 'mail_to_region(mail, region)'),
        );
    }

used for checkbox groups:

            if ( isset($_POST['category']) ){
                $mail->setRelated('categories', array_keys($_POST['category']));
            }