Dimir House Guard says, "Sacrifice a creature. Regenerate Dimir House Guard."
Can the creature that you sacrifice be Dimir House Guard? Of does the fact that the sacrifice is the cost of the ability mean that, when the ability takes effect, Dimir House Guard is no longer in play, so there isn't a valid target for the ability?
You can sacrifice any creature you control to pay for Dimir House Guard's second ability, including Dimir House Guard itself (review C.R. 701.17a). (The ability will get to resolve even if Dimir House Guard isn't on the battlefield [see also C.R. 113.7a]; however, the ability won't have any useful effect anymore if Dimir House Guard is no longer on the battlefield.)
Note that that ability doesn't target anything (it lacks the word "target", for example) (C.R. 115.1c, 115.10, 115.10a), and note also that the ability contains a colon that separates the cost (here "Sacrifice a creature") from the effect ("Regenerate Dimir House Guard") (C.R. 602.1, 602.1a).
Dimir House Guard says, "Sacrifice a creature. Regenerate Dimir House Guard."
Can the creature that you sacrifice be Dimir House Guard? Of does the fact that the sacrifice is the cost of the ability mean that, when the ability takes effect, Dimir House Guard is no longer in play, so there isn't a valid target for the ability?
Your question appears to imply some common misconceptions about Regeneration.
Let it be clear:
1-Regeneration cannot bring a creature back from the Graveyard; Regeneration is intended to help a creature BEFORE it ever leaves the Battlefield.
2-Regeneration does not provide any help against Sacrifice; Regeneartion helps against Destruction, which Sacrifice is not.
3-Regeneration does not help against -x/-x effects; Regeneration works against Damage and/or effects that say 'Destroy', and nothing else.
Can the creature that you sacrifice be Dimir House Guard? Of does the fact that the sacrifice is the cost of the ability mean that, when the ability takes effect, Dimir House Guard is no longer in play, so there isn't a valid target for the ability?
Note that that ability doesn't target anything (it lacks the word "target", for example) (C.R. 115.1c, 115.10, 115.10a), and note also that the ability contains a colon that separates the cost (here "Sacrifice a creature") from the effect ("Regenerate Dimir House Guard") (C.R. 602.1, 602.1a).
EDIT (Nov. 15): Correctness edit.
EDIT (Nov. 10, 2022): Edited.
Let it be clear:
1-Regeneration cannot bring a creature back from the Graveyard; Regeneration is intended to help a creature BEFORE it ever leaves the Battlefield.
2-Regeneration does not provide any help against Sacrifice; Regeneartion helps against Destruction, which Sacrifice is not.
3-Regeneration does not help against -x/-x effects; Regeneration works against Damage and/or effects that say 'Destroy', and nothing else.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules