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Tata Institute of Fundamental Research

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Research library98linked papers
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Selected work

Representative Papers

Simultaneous Coverage and Efficiency Guarantee in Online Conformal Prediction

Jul 29, 2026

This work addresses a critical limitation of existing online conformal prediction methods, which under distribution shift only control signed coverage error and thus risk persistent one-sided miscoverage while lacking effective constraints on prediction set size. The paper proposes a unified online learning framework that simultaneously guarantees absolute coverage validity and prediction efficiency across three settings: adversarial, stochastic, and covariate-dependent shifts. Its core contributions include the first joint control of non-canceling coverage bias and efficiency; the design of a sliding-window quantile tracker combined with a partitioned ACI algorithm; and matching minimax lower bounds establishing rate optimality. The method provides distribution-free, convexity-free theoretical guarantees, achieves optimal convergence rates in the stochastic setting, and ensures simultaneous coverage and efficiency relative to dynamic oracle thresholds under covariate-dependent shifts.

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Deterministic Algorithms for Low Individual Degree Factors of Sparse Polynomials

Jun 25, 2026

This work addresses the problem of efficiently and deterministically enumerating all factors of bounded individual degree in sparse polynomials. For an $n$-variate, $s$-sparse polynomial with individual degrees at most $d$, the paper presents the first deterministic quasi-polynomial time algorithm that works over arbitrary fields and accommodates unbounded total degree. The approach combines interpolation, divisibility testing, and algebraic complexity techniques to construct constant-depth arithmetic circuits capturing all such factors, achieving a running time of $\mathrm{poly}(n, s^d)$. For general sparse polynomials, the algorithm runs in time $\mathrm{poly}(D^{d \log s}, s^{d^2 \log n})$, where $D$ bounds the total degree. These results generalize prior work and yield new upper bounds on the number of low individual-degree factors.

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Recent publications

Latest Papers

Simultaneous Coverage and Efficiency Guarantee in Online Conformal Prediction

Jul 29, 2026

This work addresses a critical limitation of existing online conformal prediction methods, which under distribution shift only control signed coverage error and thus risk persistent one-sided miscoverage while lacking effective constraints on prediction set size. The paper proposes a unified online learning framework that simultaneously guarantees absolute coverage validity and prediction efficiency across three settings: adversarial, stochastic, and covariate-dependent shifts. Its core contributions include the first joint control of non-canceling coverage bias and efficiency; the design of a sliding-window quantile tracker combined with a partitioned ACI algorithm; and matching minimax lower bounds establishing rate optimality. The method provides distribution-free, convexity-free theoretical guarantees, achieves optimal convergence rates in the stochastic setting, and ensures simultaneous coverage and efficiency relative to dynamic oracle thresholds under covariate-dependent shifts.

0 citationsRead paper

Deterministic Algorithms for Low Individual Degree Factors of Sparse Polynomials

Jun 25, 2026

This work addresses the problem of efficiently and deterministically enumerating all factors of bounded individual degree in sparse polynomials. For an $n$-variate, $s$-sparse polynomial with individual degrees at most $d$, the paper presents the first deterministic quasi-polynomial time algorithm that works over arbitrary fields and accommodates unbounded total degree. The approach combines interpolation, divisibility testing, and algebraic complexity techniques to construct constant-depth arithmetic circuits capturing all such factors, achieving a running time of $\mathrm{poly}(n, s^d)$. For general sparse polynomials, the algorithm runs in time $\mathrm{poly}(D^{d \log s}, s^{d^2 \log n})$, where $D$ bounds the total degree. These results generalize prior work and yield new upper bounds on the number of low individual-degree factors.

0 citationsRead paper