| _version_ | 1866901753659654144 |
|---|---|
| author | De Palma, Fabrizio |
| author_facet | De Palma, Fabrizio |
| contents | <p>We study the problem of structural regime identification under finite observational scale and finite computational budget. We consider a stochastic or deterministic process observed through a representation map at a given scale, generating an observable sequence. We introduce the notion of a <strong>novelty curve</strong>, defined as the number of distinct observations encountered up to a given time, and show that its finite-sample behavior encodes structural information about the underlying regime.</p> <p>Our main result establishes a non-asymptotic equivalence between finite-budget identifiability and observational separability. In particular, we derive:</p> <ul> <li> <p>a sufficient condition for regime identification expressed through a <strong>critical identification time</strong> depending on structural latency, effective integration cost, and the maximal novelty gap between regimes;</p> </li> <li> <p>a <strong>matching lower bound</strong> showing that without positive separability, no test can outperform random guessing;</p> </li> <li> <p>the existence of a <strong>maximal identifiable observational scale</strong> under finite budget constraints;</p> </li> <li> <p>and a <strong>structural allocation principle</strong> determining the optimal resolution compatible with identifiability.</p> </li> </ul> <p>The analysis reveals a phenomenon of resolution-induced collapse: increasing observational granularity may destroy identifiability when computational resources are fixed. Identification limits therefore arise not only from computational complexity, but from structural properties of observable novelty growth.</p> <p>We provide explicit regime constructions illustrating latency-dominated, estimation-dominated, and separation-dominated domains. A companion <strong>software artifact</strong> is provided separately and linked via DOI, enabling empirical estimation of the structural quantities introduced in the paper.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18736073 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Finite-Budget Structural Identifiability under Bounded Observation De Palma, Fabrizio structural identifiability finite-budget inference bounded observation novelty growth non-asymptotic analysis hypothesis testing observational scale identifiability limits statistical separation structural collapse <p>We study the problem of structural regime identification under finite observational scale and finite computational budget. We consider a stochastic or deterministic process observed through a representation map at a given scale, generating an observable sequence. We introduce the notion of a <strong>novelty curve</strong>, defined as the number of distinct observations encountered up to a given time, and show that its finite-sample behavior encodes structural information about the underlying regime.</p> <p>Our main result establishes a non-asymptotic equivalence between finite-budget identifiability and observational separability. In particular, we derive:</p> <ul> <li> <p>a sufficient condition for regime identification expressed through a <strong>critical identification time</strong> depending on structural latency, effective integration cost, and the maximal novelty gap between regimes;</p> </li> <li> <p>a <strong>matching lower bound</strong> showing that without positive separability, no test can outperform random guessing;</p> </li> <li> <p>the existence of a <strong>maximal identifiable observational scale</strong> under finite budget constraints;</p> </li> <li> <p>and a <strong>structural allocation principle</strong> determining the optimal resolution compatible with identifiability.</p> </li> </ul> <p>The analysis reveals a phenomenon of resolution-induced collapse: increasing observational granularity may destroy identifiability when computational resources are fixed. Identification limits therefore arise not only from computational complexity, but from structural properties of observable novelty growth.</p> <p>We provide explicit regime constructions illustrating latency-dominated, estimation-dominated, and separation-dominated domains. A companion <strong>software artifact</strong> is provided separately and linked via DOI, enabling empirical estimation of the structural quantities introduced in the paper.</p> |
| title | Finite-Budget Structural Identifiability under Bounded Observation |
| topic | structural identifiability finite-budget inference bounded observation novelty growth non-asymptotic analysis hypothesis testing observational scale identifiability limits statistical separation structural collapse |
| url | https://doi.org/10.5281/zenodo.18736073 |