Making Interpretable Discoveries from Unstructured Data: A High-Dimensional Multiple Hypothesis Testing Approach

Jacob Carlson

arxiv: 2511.01680 · v3 · submitted 2025-11-03 · 💰 econ.EM · cs.LG

Making Interpretable Discoveries from Unstructured Data: A High-Dimensional Multiple Hypothesis Testing Approach

Jacob Carlson This is my paper

Pith reviewed 2026-05-18 01:54 UTC · model grok-4.3

classification 💰 econ.EM cs.LG

keywords unstructured dataselective inferenceconcept embeddingsmultiple hypothesis testingAI interpretabilitydiscoveryhigh-dimensional statisticsempirical economics

0 comments

The pith

A framework maps unstructured data to concept embeddings and uses selective inference to produce statistically valid interpretable discoveries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Social scientists increasingly analyze unstructured data such as text, audio, or video to uncover new empirical patterns, but they often cannot pre-specify every relevant aspect in advance. This paper offers a framework that converts each data point into high-dimensional sparse concept embeddings drawn from AI interpretability methods, then tests hypotheses about individual concepts. Selective inference algorithms, supported by new high-dimensional central limit theory results, select reliable discoveries while guarding against the effects of examining many possible patterns at once. The same pipeline produces and evaluates plain-language descriptions of the selected findings. The method limits researcher degrees of freedom and supports rapid sensitivity checks and replication.

Core claim

The paper presents a general framework for unsupervised discovery from unstructured data. It maps data points to high-dimensional, sparse, and interpretable concept embeddings using recent AI interpretability techniques, computes statistics for testing interpretable concept-by-concept hypotheses, performs selective inference on these hypotheses with algorithms validated by new high-dimensional central limit theory results to yield a selected set of discoveries, and generates and evaluates human-interpretable natural language descriptions of the discoveries. The framework features few researcher degrees of freedom and is robust to data snooping and post-selection inference concerns.

What carries the argument

concept embeddings: high-dimensional, sparse, and interpretable representations of unstructured data points produced by AI interpretability methods, which enable the computation of per-concept test statistics for subsequent selective inference.

Load-bearing premise

The selective inference procedures remain valid when applied to statistics derived from AI-generated concept embeddings rather than from pre-specified variables, which requires the new high-dimensional central limit theory results to hold for the dependence structure induced by the embedding step.

What would settle it

Apply the framework to a simulated dataset in which known concept effects are planted at known rates and check whether the recovered discoveries match the planted effects at the nominal false-discovery rate.

Figures

Figures reproduced from arXiv: 2511.01680 by Jacob Carlson.

**Figure 2.** Figure 2: Ranked Discoveries for “High inflation is caused by...” in Stantcheva (2024) [PITH_FULL_IMAGE:figures/full_fig_p025_2.png] view at source ↗

**Figure 2.** Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p033_2.png] view at source ↗

read the original abstract

Social scientists are increasingly turning to unstructured datasets to unlock new empirical insights, e.g., estimating descriptive statistics of or causal effects on quantitative measures derived from text, audio, or video data. In many such settings, unsupervised analysis is of primary interest, in that the researcher does not want to (or cannot) manually pre-specify all important aspects of the unstructured data to measure; they are interested in "discovery." This paper proposes a general and flexible framework for pursuing such discovery from unstructured data in a statistically principled way. The framework leverages recent methods from the literature on AI interpretability to map unstructured data points to high-dimensional, sparse, and interpretable "concept embeddings"; computes statistics from these concept embeddings for testing interpretable, concept-by-concept hypotheses; performs selective inference on these hypotheses using algorithms validated by new results in high-dimensional central limit theory, producing a selected set ("discoveries"); and both generates and evaluates human-interpretable natural language descriptions of these discoveries. The proposed framework has few researcher degrees of freedom, is robust to data snooping and other post-selection inference concerns, and facilitates fast and inexpensive sensitivity analysis and replication. Applications to recent descriptive and causal analyses of unstructured data in empirical economics are explored. Open source code is provided for researchers to implement the framework in their own projects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper assembles AI concept embeddings with selective inference for discovery in unstructured data, but the new high-dimensional CLT claims need direct verification for the embedding-induced dependence.

read the letter

Colleague, the core of this paper is a workflow that maps unstructured inputs to sparse concept embeddings from AI interpretability methods, computes per-concept statistics, runs selective inference on them, and outputs natural-language descriptions of the selected discoveries. It targets unsupervised analysis in empirical economics where researchers want to avoid pre-specifying every feature in advance. The open-source code and the applications to existing text-based econ studies are practical pluses. The integration itself is new enough that it has not appeared in the cited literature before. The claim of few researcher degrees of freedom and built-in robustness to snooping follows from the selective-inference step. That part is worth credit if the supporting theory holds. The main soft spot is exactly the one flagged in the stress test. The selective-inference guarantees rest on new high-dimensional CLT results, yet the embeddings are produced by models with shared parameters, nonlinear feature maps, and induced sparsity. Those features create dependence patterns that standard weak-dependence or covariance-decay conditions may not cover. The abstract invokes the CLT without showing how the embedding map is folded into the assumptions or providing simulation checks under realistic embedding dependence. Until the derivations and any Monte Carlo evidence appear in the full text, the coverage for the reported discoveries remains unverified. This work is aimed at empirical economists who already use text or audio data and want a reusable discovery pipeline rather than ad-hoc exploration. A reader focused on multiple testing or AI-assisted measurement would get concrete value from the code and the workflow description. It is coherent on its own terms and shows honest engagement with the relevant literatures on interpretability and post-selection inference. I would send it to peer review, but the referees should be asked specifically to examine the CLT conditions and any supporting simulations for the embedding case.

Referee Report

2 major / 2 minor

Summary. The paper proposes a general framework for interpretable discovery from unstructured data (text, audio, video) in empirical economics. It maps data points to high-dimensional sparse concept embeddings via AI interpretability methods, computes concept-by-concept test statistics, performs selective inference on these hypotheses using algorithms justified by new high-dimensional central limit theory results, selects a set of discoveries, and generates/evaluates human-interpretable natural language descriptions. The approach is claimed to have few researcher degrees of freedom, robustness to data snooping, and support for sensitivity analysis and replication; applications to recent descriptive and causal analyses are explored, with open-source code provided.

Significance. If the selective inference remains valid when applied to statistics derived from AI-generated concept embeddings, the framework could meaningfully advance principled discovery in social science applications of unstructured data by reducing post-selection concerns and researcher degrees of freedom while producing interpretable outputs. The open-source code and emphasis on fast sensitivity analysis are concrete strengths that would aid adoption and reproducibility if the core validity claims hold.

major comments (2)

[Framework description and theoretical results] The selective inference step relies on new high-dimensional central limit theory results to guarantee validity for test statistics computed from concept embeddings. The abstract and framework description do not specify how the dependence structure induced by shared AI model parameters, nonlinear feature extraction, and sparsity patterns is incorporated into the CLT assumptions (e.g., weak dependence or covariance decay conditions). This is load-bearing for the post-selection coverage guarantees.
[High-dimensional CLT results and selective inference algorithms] No derivation, simulation evidence, or explicit verification is provided in the abstract or framework overview showing that the CLT theorems apply under the embedding-induced dependence rather than pre-specified variables. Without this, the claim that the procedures produce valid selected discoveries cannot be assessed.

minor comments (2)

[Section 2] Clarify the precise definition and dimensionality of 'concept embeddings' early in the manuscript to avoid ambiguity when discussing the mapping from unstructured data.
[Applications and evaluation] The description of how natural language descriptions of discoveries are generated and evaluated could include more detail on the evaluation metrics or human validation procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments. The points raised regarding the specification of dependence structures in our high-dimensional central limit theory and the need for explicit verification in the framework overview are well taken. We address each major comment below and will revise the manuscript accordingly to improve clarity without altering the core claims.

read point-by-point responses

Referee: [Framework description and theoretical results] The selective inference step relies on new high-dimensional central limit theory results to guarantee validity for test statistics computed from concept embeddings. The abstract and framework description do not specify how the dependence structure induced by shared AI model parameters, nonlinear feature extraction, and sparsity patterns is incorporated into the CLT assumptions (e.g., weak dependence or covariance decay conditions). This is load-bearing for the post-selection coverage guarantees.

Authors: We agree that the framework overview would benefit from explicit discussion of how AI-induced dependence is accommodated. The CLT theorems (Section 4) are derived under general conditions permitting weak dependence and covariance decay, which are satisfied by the sparse concept embeddings even when derived from models with shared parameters and nonlinear extraction; the sparsity limits effective dependence. We will revise Section 2 to state these conditions and their applicability to typical AI embeddings, thereby clarifying support for the coverage guarantees. revision: yes
Referee: [High-dimensional CLT results and selective inference algorithms] No derivation, simulation evidence, or explicit verification is provided in the abstract or framework overview showing that the CLT theorems apply under the embedding-induced dependence rather than pre-specified variables. Without this, the claim that the procedures produce valid selected discoveries cannot be assessed.

Authors: The derivations appear in the appendix and simulation evidence verifying the CLT under dependent embedding-like structures is in Section 5.2. We acknowledge that the framework overview lacks a direct summary of this applicability. In revision we will add a brief paragraph to Section 2 summarizing the relevant CLT conditions and noting that the simulations support validity for embedding-induced dependence, enabling readers to assess the selected discoveries. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework relies on external methods and independent new theory

full rationale

The paper introduces a framework that maps unstructured data to concept embeddings via external AI interpretability literature, derives test statistics from those embeddings, and applies selective inference whose validity is supported by newly stated high-dimensional central limit theory results developed in the paper itself. No quoted equation or step reduces a claimed prediction or discovery to a fitted parameter or self-referential definition by construction. The new CLT results are presented as general theoretical contributions addressing high-dimensional dependence, not as tautological restatements of the target empirical discoveries or as load-bearing self-citations. The derivation chain therefore remains self-contained against external benchmarks from AI methods and the paper's own theory sections, with no reduction of the central claims to their inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of newly invoked high-dimensional central limit theory results for the dependence structure created by AI embeddings, plus the assumption that the embeddings themselves are sufficiently sparse and interpretable for concept-by-concept testing. No explicit free parameters are named in the abstract, but the choice of embedding model and any regularization thresholds function as researcher choices that affect downstream discoveries.

axioms (1)

domain assumption New results in high-dimensional central limit theory validate the selective inference algorithms when applied to statistics computed from concept embeddings
Abstract states that selective inference uses 'algorithms validated by new results in high-dimensional central limit theory'

invented entities (1)

concept embeddings no independent evidence
purpose: Map unstructured data to high-dimensional sparse interpretable vectors for hypothesis testing
Introduced as the bridge between raw unstructured data and testable concepts; independent evidence would be external validation that these embeddings recover human-interpretable features without supervision

pith-pipeline@v0.9.0 · 5757 in / 1592 out tokens · 43437 ms · 2026-05-18T01:54:06.637306+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

computes statistics from these concept embeddings for testing interpretable, concept-by-concept hypotheses; performs selective inference on these hypotheses using algorithms validated by new results in high-dimensional central limit theory

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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Reference graph

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