Identifying Variables Eval (openai#1488)

@JunShern will review this

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## Eval details 📑

### Eval name

Identifying variables

### Eval description

This eval tests how well models can determine what should be treated as
the independent, dependent, and control variables for an experiment that
tests a particular hypothesis, given some observational context.

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evals/elsuite/identifying_variables/.gitattributes

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+images/*.png filter=lfs diff=lfs merge=lfs -text

evals/elsuite/identifying_variables/README.md

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+# Identifying Variables
+
+This eval tests how well models can determine what should be treated as the
+independent, dependent, and control variables for an experiment that tests a
+particular hypothesis, given some observational context.
+
+## Usage
+
+Run with:
+
+```bash
+oaieval <solver> identifying_variables
+```
+
+We have found that `generation/cot/gpt-4-1106-preview` works well on this eval. For more examples of tested solvers, see [`./scripts/run_experiments.sh`](./scripts/run_experiments.sh).
+
+## Evaluation Process
+
+The evaluation process is as follows for a given sample from our dataset:
+
+1. The `TASK_DESCRIPTION` prompt is shown to the solver.
+2. The sample is passed through a _renderer_ that processes the samples and
+ renders an observation of the interactions of variables, which is placed in
+ the `SAMPLE_MESSAGE` prompt template.
+3. The solver answers in the form: `[@ANSWER valid_hyp: <true/false>; independent: <var>; dependent: <var>; control: <vars>]`. The answer is parsed and evaluated by the eval. If the answer cannot be parsed, we mark this as a violation and the sample is treated as incorrect.
+
+## Prompts
+
+We refer readers to the [`./prompts.py`](./prompts.py) file for the
+`TASK_DESCRIPTION` and `SAMPLE_MESSAGE` prompts used in the eval.
+
+## Metrics
+
+<!-- prettier-ignore-start -->
+| **Metric** | **Notes** |
+|---|---|
+| `ctrl_nDCG` | A modified version of the [normalized discounted cumulative gains (nDCG)](https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Normalized_DCG) metric, which rewards listing the correct control variables first and penalizes naming irrelevant variables. |
+| `ctrl_recall` | Number of variables correctly marked as control variables / total number of variables to control according to the gold label |
+| `ctrl_recall` | Number of variables incorrectly marked as control variables / total number of variables not to control according to the gold label |
+| `hyp_valid_acc` | Target hypothesis plausibility validation accuracy (correct/incorrect) |
+| `ind_acc` | Independent variable determination accuracy (correct/incorrect) |
+| `dep_acc` | Dependent variable determination accuracy (correct/incorrect) |
+| `violation_rate` | Number of samples with violations (model failed to answer in correct format) / total number of samples |
+<!-- prettier-ignore-end -->
+
+## Variants
+
+We support variations on the eval along two dimensions, `renderer` and `dataset`:
+
+```bash
+oaieval <solver> identifying_variables.<renderer>.<dataset>
+```
+
+The eval defaults to `identifying_variables.language-corrset.balanced-ctrl`.
+
+### Dataset
+
+We provide 4 dataset variants:
+
+| `dataset` | Notes |
+| --- | --- |
+| `balanced-ctrl` | 500 samples balanced across number of control variables (from 0 to 8). |
+| `balanced-ctrl-large` | As `balanced-ctrl`, but with 5,000 samples. |
+| `balanced-hypotheses` | 500 samples balanced across target hypotheses being implausible/plausible. |
+| `balanced-hypotheses-large` | As `balanced-hypotheses`, but with 5,000 samples. |
+
+### Renderers
+
+We have 6 different renderers, implemented in [`./renderers/`](./renderers/).
+
+The default renderer is `language-corrset`. Here is an example render from this type:
+```
+The following is a description of the observations made about a set of variables.
+
+In general, there were cases where some variables changed in tandem with each other, while others did not.
+For example, changes in x_5075 were observed to reflect changes in x_3314 and viceversa.
+Changes in x_9549 were not observed to reflect any changes in previously mentioned variables.
+Changes in x_1808 were not observed to reflect any changes in previously mentioned variables.
+Likewise, changes in x_9726 were observed to reflect changes in x_1808 and viceversa.
+```
+
+### Show Tree
+
+We provide an additional variant of the eval where the decision tree implementing
+the reasoning for scoring a perfect score is shown to the model. This variant
+can be run by passing the `show_tree=True` flag to eval, e.g.
+
+```bash
+oaieval <solver> identifying_variables --extra_eval_params show_tree=True
+```
+
+## Custom Solvers
+
+We implement two custom programmatic solvers to serve as baselines.
+
+1. `identifying_variables/random`: a solver that randomly selects whether the
+ hypothesis is plausible with probability 0.5, and if so randomly samples the
+ independent, dependent and control variables. We view this baseline as
+ equivalent to randomly guessing.
+2. `identifying_variables/noctrl`: this is a solver that always outputs an empty
+ list for the variables to control, essentially eliminating any chance of
+ false positives. This can provide stronger performance than the random
+ baseline, since it avoids any penalization for returning incorrect variables,
+ and can even achieve a perfect score on samples that indeed do not have any
+ variables to control
+
+We refer to [`./solvers.py`](./solvers.py) for the implementation of these
+solvers.
+
+## Token Usage Estimates
+
+We estimated per-run token usage on the default dataset size (500 samples)
+for the least and most token-intensive configurations for each model type
+(respectively, direct models on `identifying_variables.corrset` with
+`show_tree=False`; and CoT models on `identifying_variables.language-tabular`
+with `show_tree=True`).
+
+<!-- prettier-ignore-start -->
+| | **input tokens/run** | **output tokens/run** | **total tokens/run** |
+|---|---|---|---|
+| **GPT-4-base HHH (corrset, no tree)** | 1,200,000 | 250,000 | 1,450,000 |
+| **GPT-4-base CoT HHH (language-tabular, with tree)** | 1,500,000 | 240,000 | 1,740,000 |
+| **GPT-3.5-turbo Direct (corrset, no tree)** | 430,000 | 88,000 | 518,000 |
+| **GPT-3.5-turbo CoT (language-tabular, with tree)** | 780,000 | 14,000 | 794,000 |
+| **GPT-4-1106-preview Direct (corrset, no tree)** | 430,000 | 53,000 | 483,000 |
+| **GPT-4-1106-preview CoT (language-tabular, with tree)** | 860,000 | 14,000 | 874,000 |
+<!-- prettier-ignore-end -->
+
+These estimates were taken using the `balanced-hypotheses` dataset but should
+roughly apply to the `-balanced-ctrl` datasets. For `-large` datasets (5000
+samples), multiply the above numbers by 10.
+
+## Future modifications
+
+- Revisit the definition of the headline `ctrl_nDCG` metric
+- Devise additional auxiliary metrics to paint a more complete picture
+- What if we show the decision trees described in natural language rather than
+ pseudocode?
+- How can we extend this eval to multi-variable dependencies?
+
+## Version History
+
+- v0: Initial version released
+
+## Contribution Statement
+
+Eval design, implementation, and results evaluation and writeup were primarily
+conducted by Giulio Starace. James Aung was of enormous assistance in report
+writing, and additionally provided general feedback and project management
+throughout the eval. Oliver Jaffe and Jan Betley were responsible for code
+reviews throughout the implementation process, along with fine-grained feedback
+on the project in general. Additional guidance was provided by (alphabetically
+by last-name) Steven Adler and Chan Jun Shern, who helped with brainstorming,
+gave research input and report revisions.
+
+## Appendix
+
+### Perfect output decision trees
+
+The following decision trees are used to determine the perfect output (aka "gold
+label") for a given sample.
+
+---
+
+<img src="images/control_var_tree.png" width="700">
+
+**Figure A1**: Decision tree for determining whether a given variable should be
+controlled.
+
+---
+
+<img src="images/valid_hyp_tree.png" width="312">
+
+**Figure A2**: Decision tree for determining a hypothesis is valid and if so
+what the independent and dependent variables are.
+
+---

evals/elsuite/identifying_variables/constants.py

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+# variables that have at least this amount of sparsity are considered to be unobserved
+SPARSITY_FOR_UNOBS = 0.8
+# num of variables in a given sample
+MIN_VARS = 2
+MAX_VARS = 10
+# num of hypotheses in a given sample
+MIN_HYPS = 1
+MAX_HYPS = 3
+# sparse var rate: percentage of variables to sparsify
+MIN_SPARSE_VAR_RATE = 0
+MAX_SPARSE_VAR_RATE = 1
+# sparsity: percentage of NaNs in a sparsified variable
+MIN_SPARSITY = 0.2
+MAX_SPARSITY = 1
+
+# specific to tabular renderers ------------
+
+# num of observations
+NUM_OBS = 20