[#1] Add leaderboard based on Elo rating

Changes:
- Added leaderboards for Summarization and Translation categories.
- Implemented Elo rating for each rating.
- Ref: https://colab.research.google.com/drive/1RAWb22-PFNI-X1gPVzc927SGUdfr6nsR?usp=sharing#scrollTo=QLGc6DwxyvQc

Screenshot: https://screen.yanolja.in/j7inrSXCtFtnJije.png

app.py

@@ -13,6 +13,8 @@ import firebase_admin
 from firebase_admin import firestore
 import gradio as gr
 
+from leaderboard import build_leaderboard
+
 db_app = firebase_admin.initialize_app()
 db = firestore.client()
 
@@ -214,6 +216,8 @@ with gr.Blocks() as app:
   submit.click(user, prompt, states + model_names,
                queue=False).then(bot, states, states + responses)
 
+  build_leaderboard(db)
+
 if __name__ == "__main__":
   # We need to enable queue to use generators.
   app.queue()

leaderboard.py

@@ -0,0 +1,78 @@
+"""
+It provides a leaderboard component.
+"""
+
+from collections import defaultdict
+import enum
+import math
+
+import gradio as gr
+import pandas as pd
+
+
+class LeaderboardTab(enum.Enum):
+  SUMMARIZATION = "Summarization"
+  TRANSLATION = "Translation"
+
+
+# Ref: https://colab.research.google.com/drive/1RAWb22-PFNI-X1gPVzc927SGUdfr6nsR?usp=sharing#scrollTo=QLGc6DwxyvQc pylint: disable=line-too-long
+def compute_elo(battles, k=4, scale=400, base=10, initial_rating=1000):
+  rating = defaultdict(lambda: initial_rating)
+
+  for model_a, model_b, winner in battles[["model_a", "model_b",
+                                           "winner"]].itertuples(index=False):
+    rating_a = rating[model_a]
+    rating_b = rating[model_b]
+
+    expected_score_a = 1 / (1 + base**((rating_b - rating_a) / scale))
+    expected_score_b = 1 / (1 + base**((rating_a - rating_b) / scale))
+
+    scored_point_a = 0.5 if winner == "tie" else int(winner == "model_a")
+
+    rating[model_a] += k * (scored_point_a - expected_score_a)
+    rating[model_b] += k * (1 - scored_point_a - expected_score_b)
+
+  return rating
+
+
+def get_docs(tab, db):
+  if tab.label == LeaderboardTab.SUMMARIZATION.value:
+    return db.collection("arena-summarizations").order_by("timestamp").stream()
+
+  if tab.label == LeaderboardTab.TRANSLATION.value:
+    return db.collection("arena-translations").order_by("timestamp").stream()
+
+
+# TODO(#8): Update the value periodically.
+def load_elo_ratings(tab, db):
+  docs = get_docs(tab, db)
+
+  battles = []
+  for doc in docs:
+    data = doc.to_dict()
+    battles.append({
+        "model_a": data["model_a"],
+        "model_b": data["model_b"],
+        "winner": data["winner"]
+    })
+
+  battles = pd.DataFrame(battles)
+  ratings = compute_elo(battles)
+
+  sorted_ratings = sorted(ratings.items(), key=lambda x: x[1], reverse=True)
+  return [[i + 1, model, math.floor(rating + 0.5)]
+          for i, (model, rating) in enumerate(sorted_ratings)]
+
+
+def build_leaderboard(db):
+  with gr.Tabs():
+    with gr.Tab(LeaderboardTab.SUMMARIZATION.value) as summarization_tab:
+      gr.Dataframe(headers=["Rank", "Model", "Elo rating"],
+                   datatype=["number", "str", "number"],
+                   value=load_elo_ratings(summarization_tab, db))
+
+    # TODO(#9): Add language filter options.
+    with gr.Tab(LeaderboardTab.TRANSLATION.value) as translation_tab:
+      gr.Dataframe(headers=["Rank", "Model", "Elo rating"],
+                   datatype=["number", "str", "number"],
+                   value=load_elo_ratings(translation_tab, db))