# Comparing Chain Outputs

Suppose you have two different prompts (or LLMs). How do you know which will generate "better" results?

One automated way to predict the preferred configuration is to use a `PairwiseStringEvaluator`

like the `PairwiseStringEvalChain`

^{[1]}. This chain prompts an LLM to select which output is preferred, given a specific input.

For this evaluation, we will need 3 things:

- An evaluator
- A dataset of inputs
- 2 (or more) LLMs, Chains, or Agents to compare

Then we will aggregate the results to determine the preferred model.

### Step 1. Create the Evaluator

In this example, you will use gpt-4 to select which output is preferred.

`%pip install --upgrade --quiet langchain langchain-openai`

`from langchain.evaluation import load_evaluator`

eval_chain = load_evaluator("pairwise_string")

#### API Reference:

### Step 2. Select Dataset

If you already have real usage data for your LLM, you can use a representative sample. More examples provide more reliable results. We will use some example queries someone might have about how to use langchain here.

`from langchain.evaluation.loading import load_dataset`

dataset = load_dataset("langchain-howto-queries")

#### API Reference:

`Found cached dataset parquet (/Users/wfh/.cache/huggingface/datasets/LangChainDatasets___parquet/LangChainDatasets--langchain-howto-queries-bbb748bbee7e77aa/0.0.0/14a00e99c0d15a23649d0db8944380ac81082d4b021f398733dd84f3a6c569a7)`

` 0%| | 0/1 [00:00<?, ?it/s]`

### Step 3. Define Models to Compare

We will be comparing two agents in this case.

`from langchain.agents import AgentType, Tool, initialize_agent`

from langchain_community.utilities import SerpAPIWrapper

from langchain_openai import ChatOpenAI

# Initialize the language model

# You can add your own OpenAI API key by adding openai_api_key="<your_api_key>"

llm = ChatOpenAI(temperature=0, model="gpt-3.5-turbo-0613")

# Initialize the SerpAPIWrapper for search functionality

# Replace <your_api_key> in openai_api_key="<your_api_key>" with your actual SerpAPI key.

search = SerpAPIWrapper()

# Define a list of tools offered by the agent

tools = [

Tool(

name="Search",

func=search.run,

coroutine=search.arun,

description="Useful when you need to answer questions about current events. You should ask targeted questions.",

),

]

#### API Reference:

`functions_agent = initialize_agent(`

tools, llm, agent=AgentType.OPENAI_MULTI_FUNCTIONS, verbose=False

)

conversations_agent = initialize_agent(

tools, llm, agent=AgentType.CHAT_ZERO_SHOT_REACT_DESCRIPTION, verbose=False

)

### Step 4. Generate Responses

We will generate outputs for each of the models before evaluating them.

`import asyncio`

from tqdm.notebook import tqdm

results = []

agents = [functions_agent, conversations_agent]

concurrency_level = 6 # How many concurrent agents to run. May need to decrease if OpenAI is rate limiting.

# We will only run the first 20 examples of this dataset to speed things up

# This will lead to larger confidence intervals downstream.

batch = []

for example in tqdm(dataset[:20]):

batch.extend([agent.acall(example["inputs"]) for agent in agents])

if len(batch) >= concurrency_level:

batch_results = await asyncio.gather(*batch, return_exceptions=True)

results.extend(list(zip(*[iter(batch_results)] * 2)))

batch = []

if batch:

batch_results = await asyncio.gather(*batch, return_exceptions=True)

results.extend(list(zip(*[iter(batch_results)] * 2)))

` 0%| | 0/20 [00:00<?, ?it/s]`

## Step 5. Evaluate Pairs

Now it's time to evaluate the results. For each agent response, run the evaluation chain to select which output is preferred (or return a tie).

Randomly select the input order to reduce the likelihood that one model will be preferred just because it is presented first.

`import random`

def predict_preferences(dataset, results) -> list:

preferences = []

for example, (res_a, res_b) in zip(dataset, results):

input_ = example["inputs"]

# Flip a coin to reduce persistent position bias

if random.random() < 0.5:

pred_a, pred_b = res_a, res_b

a, b = "a", "b"

else:

pred_a, pred_b = res_b, res_a

a, b = "b", "a"

eval_res = eval_chain.evaluate_string_pairs(

prediction=pred_a["output"] if isinstance(pred_a, dict) else str(pred_a),

prediction_b=pred_b["output"] if isinstance(pred_b, dict) else str(pred_b),

input=input_,

)

if eval_res["value"] == "A":

preferences.append(a)

elif eval_res["value"] == "B":

preferences.append(b)

else:

preferences.append(None) # No preference

return preferences

`preferences = predict_preferences(dataset, results)`

**Print out the ratio of preferences.**

`from collections import Counter`

name_map = {

"a": "OpenAI Functions Agent",

"b": "Structured Chat Agent",

}

counts = Counter(preferences)

pref_ratios = {k: v / len(preferences) for k, v in counts.items()}

for k, v in pref_ratios.items():

print(f"{name_map.get(k)}: {v:.2%}")

`OpenAI Functions Agent: 95.00%`

None: 5.00%

### Estimate Confidence Intervals

The results seem pretty clear, but if you want to have a better sense of how confident we are, that model "A" (the OpenAI Functions Agent) is the preferred model, we can calculate confidence intervals.

Below, use the Wilson score to estimate the confidence interval.

`from math import sqrt`

def wilson_score_interval(

preferences: list, which: str = "a", z: float = 1.96

) -> tuple:

"""Estimate the confidence interval using the Wilson score.

See: https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval

for more details, including when to use it and when it should not be used.

"""

total_preferences = preferences.count("a") + preferences.count("b")

n_s = preferences.count(which)

if total_preferences == 0:

return (0, 0)

p_hat = n_s / total_preferences

denominator = 1 + (z**2) / total_preferences

adjustment = (z / denominator) * sqrt(

p_hat * (1 - p_hat) / total_preferences

+ (z**2) / (4 * total_preferences * total_preferences)

)

center = (p_hat + (z**2) / (2 * total_preferences)) / denominator

lower_bound = min(max(center - adjustment, 0.0), 1.0)

upper_bound = min(max(center + adjustment, 0.0), 1.0)

return (lower_bound, upper_bound)

`for which_, name in name_map.items():`

low, high = wilson_score_interval(preferences, which=which_)

print(

f'The "{name}" would be preferred between {low:.2%} and {high:.2%} percent of the time (with 95% confidence).'

)

`The "OpenAI Functions Agent" would be preferred between 83.18% and 100.00% percent of the time (with 95% confidence).`

The "Structured Chat Agent" would be preferred between 0.00% and 16.82% percent of the time (with 95% confidence).

**Print out the p-value.**

`from scipy import stats`

preferred_model = max(pref_ratios, key=pref_ratios.get)

successes = preferences.count(preferred_model)

n = len(preferences) - preferences.count(None)

p_value = stats.binom_test(successes, n, p=0.5, alternative="two-sided")

print(

f"""The p-value is {p_value:.5f}. If the null hypothesis is true (i.e., if the selected eval chain actually has no preference between the models),

then there is a {p_value:.5%} chance of observing the {name_map.get(preferred_model)} be preferred at least {successes}

times out of {n} trials."""

)

`The p-value is 0.00000. If the null hypothesis is true (i.e., if the selected eval chain actually has no preference between the models),`

then there is a 0.00038% chance of observing the OpenAI Functions Agent be preferred at least 19

times out of 19 trials.

``````output

/var/folders/gf/6rnp_mbx5914kx7qmmh7xzmw0000gn/T/ipykernel_15978/384907688.py:6: DeprecationWarning: 'binom_test' is deprecated in favour of 'binomtest' from version 1.7.0 and will be removed in Scipy 1.12.0.

p_value = stats.binom_test(successes, n, p=0.5, alternative="two-sided")