arXiv subjects

Jeffery Opoku

Publications and source records attributed to Jeffery Opoku.

9 recordsLinked to original sources

arXiv2026

SynthGuard-ReleaseBench: Locked-Audit Evidence for Synthetic Tabular Data Releases

Synthetic tabular data are often judged by realism, privacy, or downstream-task scores. Those scores do not answer whether a proposed release is supported for a named use, population, and threat model. We introduce SynthGuard-ReleaseBench, an audit framework that locks the use, candidate panel, tolerances, and audit schedule before evaluation. It compares real-trained and synthetic-trained workflows on protected data, gives simultaneous finite-sample bounds for bounded loss gaps, requires controls, and keeps utility, empirical privacy risk, mechanism claims, and human release authority separate. Across four American Community Survey studies, five non-ACS records, two chronological diagnostics, and a sealed prototype, the benchmark retains favorable, unfavorable, and excluded outcomes. Transparent baselines pass some locked audits; compact learned models fail under the declared budgets; a health-table case is excluded because its negative control passes. A post-audit scaling arm, repeated across three generation seeds, shows the same locked criterion admitting those learned models once they are fit on enough data while still rejecting a dependence-destroying control at every size, so the criterion discriminates rather than merely rejects; the same repetition withdraws a finer single-seed ordering. The theory adds a pre-audit sample-size rule, variance-adaptive and anytime-valid certificates that tighten the bound two to ten times on the same locked evidence, a temporal certificate for time-ordered audits, and two lower bounds: ordinary bounded queries reconstruct a protected audit once the query budget reaches its size, and the panel-size correction is necessary rather than conservative. The contribution is a reproducible workflow for use-specific release evidence, not a claim that any generator is private, safe, or deployment-ready.

cs.CR↗

arXiv2026

Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data

Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable: they have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. The theory makes both parts controllable. We give an approximate coverage bound that splits the error into a spectral mismatch term and an effective-sample-size term, prove that kernel spectral weighting never increases the mismatch term relative to uniform weighting, show that a bandwidth of order N^(-1/(d+2)) balances the two terms, and establish an unconditional long-run calibration bound for the adaptive update that holds for every sample path without independence or stationarity. Simulations with recurring regimes and slowly changing frequencies, together with four real-data examples spanning monthly, weekly, and daily U.S. and European series, show when the hybrid method improves on strong adaptive baselines and when it does not, and an effective-sample-size safeguard, computable at prediction time without outcomes, detects and repairs the one observed failure.

stat.ML↗

arXiv2026

Drift-Aware Spectral Conformal Prediction for Non-Exchangeable Streaming Data

Conformal prediction provides distribution-free prediction intervals under exchangeability, but many modern data streams are neither independent nor stable. They exhibit recurring regimes, changing seasonal frequencies, abrupt shifts, and gradual drift. We propose drift-aware spectral conformal prediction (DASC), a streaming uncertainty quantification framework for structured non-exchangeable data subject to distributional drift. DASC forms conformal prediction intervals using calibration residuals weighted by local spectral similarity, while a transport-based drift score monitors whether the current test distribution has moved away from past calibration regimes. When drift is mild, DASC borrows calibration residuals from structurally similar historical windows; when drift is severe, it contracts or reweights the calibration pool and updates the target miscoverage level online. The method also reports an effective sample size diagnostic that warns when a weighted conformal quantile is statistically fragile. We establish an approximate coverage bound that decomposes coverage loss into drift, residual mismatch, and weighted effective sample size. In synthetic experiments and five stress-test regimes, DASC maintains near-nominal coverage after drift where rolling, recency-weighted, and spectral-only conformal methods can under-cover. In real electricity and weather streams, DASC reduces average interval width by approximately 28% and 42%, respectively, relative to the best calibrated non-DASC baseline, while preserving calibrated or conservative coverage. A financial volatility example shows a more nuanced regime in which spectral-only calibration is competitive, but DASC retains near-nominal coverage and adds drift diagnostics.

stat.ME↗

arXiv2026

Signed Evidence Flow: Conflict-Aware and Stability-Calibrated Data Analysis

Modern data analysis usually gives a prediction without showing whether the evidence behind it is clear, conflicting, or stable. Two cases can have the same fitted confidence even when one has mostly agreeing evidence and the other has strong support and strong opposition. We propose Signed Evidence Flow (SEF), which combines a fitted prediction rule with signed feature attributions to measure support, opposition, conflict, and perturbation stability. We prove that confidence determines conflict exactly when it also determines total evidence mass, derive the remaining conditional variance, and state when conflict can improve loss prediction beyond confidence and other audit variables. We also connect conflict to geometric decision fragility. Across healthcare, Covertype, black-box, finance, and ten external data sets, conflict sometimes separates risk among predictions that already appear confident. Cross-fitted tests show added error-ranking information beyond confidence and attribution entropy on several data sets, including two large finance tasks. The direction is not universal: in some tasks, lowconflict cases are riskier. We therefore introduce ScopeGate, a held-out permutation diagnostic that checks the direction before SEF is used for review triage. SEF is consequently an audit tool rather than a universal risk score: it describes evidence structure, while an independent calibration sample determines whether that structure is useful in the target population.

stat.ML↗

arXiv2026

ToolChain-CRC: Conformal Risk Control for Agentic AI Under Retrieval and Tool-Use Drift

Modern AI agents retrieve documents, call tools, check intermediate information, and then produce a final answer or action. This creates a risk-control problem that is not visible from the final answer alone. A final response may look acceptable even when the retrieval was weak, a tool output was wrong, or an earlier step was unsupported. We propose ToolChain-CRC, a conformal risk-control method for retrieval-augmented and tool-using agents under drift. The method treats each agent run as a full trajectory of actions, observations, and final output. It builds step-level risk scores, combines them into a trajectory risk score, calibrates an accept-or-intervene rule, and adds an anytime alarm that can stop risky runs before the final answer. We prove trajectory-level risk control under exchangeable calibration runs, give a drift-aware extension with auditable constants, and prove an anytime escalation rule through a supermartingale construction. Experiments cover synthetic tool-chain drift, RAG/tool-use stress tests, public SQuAD-derived retrieval tasks, an API-free agentic QA case study, ablations, target-risk sensitivity checks, 20-seed robustness checks, a drift-margin audit, and a live RAG/tool-use agent benchmark. Across these settings, final-answer-only calibration can miss retrieval and tool failures, while trajectory-level calibration keeps accepted-trajectory risk below the target.

stat.ML↗

arXiv2026

PromptShift-CRC: Drift-Aware Conformal Risk Control for Foundation Models Under Prompt and Domain Shift

Foundation models are now used in settings where the prompts they receive can change quickly. Users change, topics change, policies change, and the model may suddenly face a kind of request that was rare in the calibration data. This makes fixed calibration risky. Conformal prediction and conformal risk control give model-agnostic ways to control error, but they work best when the calibration data still look like the future data. This paper develops PromptShift CRC, a drift-aware conformal risk control method for foundation-model outputs under prompt and domain shift. The method embeds prompts and responses, measures how far the current prompt stream has moved from the calibration pool, gives more weight to relevant or recent calibration examples, and updates the risk level online after observed violations. It reports three practical diagnostics: realized risk error, prompt drift, and effective calibration size. We give conditions under which the method controls risk up to terms for distribution mismatch and weighted quantile uncertainty. In a synthetic prompt-shift benchmark, static conformal risk control fails sharply after drift, while PromptShift-CRC gives the best coverage among the adaptive baselines considered. We then evaluate the same calibration layer on public benchmark derived streams for question answering, toxicity, summarization factuality, and long-context hallucination risk

stat.ML↗

arXiv2026

Enumeration of modular forms for $Γ_1(N)$

This paper considers holomorphic modular forms for $Γ_1(N)$ of integral weight of the form $$f^{(N)}_{\mathbf a}(τ) =q^{s} (q^{N};q^{N})_{\infty}^{a_0}\prod_{j=1}^{\lfloor N/2 \rfloor}(q^j,q^{N-j};q^N)_\infty^{a_j}, \quad \mathbf a = (a_1, \ldots, a_{\lfloor N/2 \rfloor}),$$ for fixed $a_0=2k \in 2 \Bbb Z_{\ge 0}$. We show that the number of relevant exponent vectors $\mathbf a$ is finite and characterize them in terms of the $\mathbb{Q}$-rational cuspidal divisor class group of $X_{1}(N)$. Effective procedures are given for counting the admissible exponents by enumerating the corresponding polytopes. This leads to formulas for the number of exponent vectors in terms of quasipolynomials in $k$.

math.NT↗

arXiv2025

Ramanujan--Fine integrals for level 10

We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequence, we establish and classify an infinite number of integral evaluations such as $$ \int_0^{e^{-2π/\sqrt{10}}} q\prod_{j=1}^\infty \frac{(1-q^j)^3(1-q^{10j})^8}{(1-q^{5j})^7} \text{d} q = \frac14\left(\sqrt{10-4\sqrt{5}}-1\right). $$ We describe how the results were found and give reasons for why it is reasonable to conjecture that the list is complete for level 10.

math.NT↗

arXiv2024

Ramanujan type congruences for quotients of Klein forms

In this work, Ramanujan type congruences modulo powers of primes $p \ge 5$ are derived for a general class of products that are modular forms of level $p$. These products are constructed in terms of Klein forms and subsume generating functions for $t$-core partitions known to satisfy Ramanujan type congruences for $p=5,7,11$. The vectors of exponents corresponding to products that are modular forms for $Γ_{1}(p)$ are subsets of bounded polytopes with explicit parameterizations. This allows for the derivation of a complete list of products that are modular forms for $Γ_{1}(p)$ of weights $1\le k \le 5$ for primes $5\le p \le 19$ and whose Fourier coefficients satisfy Ramanujan type congruences for all powers of the primes. For each product satisfying a congruence, cyclic permutations of the exponents determine additional products satisfying congruences. Common forms among the exponent sets lead to products satisfying Ramanujan type congruences for a broad class of primes, including $p> 19$. Canonical bases for modular forms of level $5\le p \le 19$ are constructed by summing weight one Hecke Eisensten series of levels $5\le p \le 19$ and expressing the result as a quotient of Klein forms. Generating sets for the graded algebras of modular forms for $Γ_{1}(p)$ and $Γ(p)$ are formulated in terms of permutations of the exponent sets. A sieving process is described by decomposing the space of modular forms of weight $1$ for $Γ_{1}(p)$ as a direct sum of subspaces of modular forms for $Γ(p)$ of the form $q^{r/p}\Bbb Z[[q]]$. Since the relevant bases generate the graded algebra of modular forms for these groups, the weight one decompositions determine series dissections for modular forms of higher weight that lead to additional classes of congruences.

math.NT↗