Alex Shvets

Alex Shvets

Part I of this series (arXiv:2602.09029) develops a sharp Gaussian (LAN/GDP) limit theory for neighboring shuffle experiments when the local randomizer is fixed and has full support bounded away from zero. The present paper characterizes the first universality-breaking frontier: critical sequences of increasingly concentrated local randomizers for which classical Lindeberg conditions fail and the shuffle score exhibits rare macroscopic jumps. For shuffled binary randomized response with local privacy $\varepsilon_0 = \varepsilon_0(n)$, we prove experiment-level convergence (in Le Cam distance) to explicit shift limit experiments: a Poisson-shift limit for the canonical neighboring pair when $\exp(\varepsilon_0(n))/n \to c^2$, and a Skellam-shift limit for proportional compositions $k/n \to π\in (0,1)$ in the same scaling, including an explicit disappearance of the two-sided $δ$-floor away from boundary compositions. For general finite alphabets, we introduce a sparse-error critical regime and prove a multivariate compound-Poisson / independent Poisson vector limit for the centered released histogram, yielding a multivariate Poisson-shift experiment and an explicit limiting $(\varepsilon, δ)$ curve as a multivariate Poisson series. Together with Part I, these results yield a three-regime picture (Gaussian/GDP, critical Poisson/Skellam/compound-Poisson, and super-critical no privacy) under convergent macroscopic scalings.

Alex Shvets

Part I of this series (arXiv:2602.09029) establishes a sharp Gaussian (LAN/GDP) limit theory for neighboring shuffle experiments in the fixed full-support regime. Part II (arXiv:2603.10073) identifies the first universality-breaking frontier: critical Poisson, Skellam, and multivariate compound-Poisson regimes. The present paper completes the finite-alphabet weak-limit theory by identifying the dominant-block quotient geometry that governs neighboring shuffle experiments. We treat dominant blocks of arbitrary finite size, allow overlap between the dominant output sets under the two neighboring hypotheses, and show that the limiting experiment decomposes according to this geometry: projecting onto the sum of the dominant tangent spaces yields a Gaussian factor, while quotienting by those same tangent spaces isolates a compound-Poisson jump field in the rare block. We also identify the regimes in which this quotient description determines the full privacy-curve, as well as the obstruction that appears when projected jump limits alone do not suffice. Two further sections sharpen the rate picture and the boundary interface: we show that the O(n^{-1/2}) rate for the full hybrid experiment is sharp in general, identify a compatibility condition restoring the O(n^{-1}) rate, and prove a boundary Berry--Esseen theorem giving O(c) Le Cam proximity between the critical Poisson-shift and Gaussian shift experiments as c tends to 0. Together with Parts I--II, this yields a three-regime universality picture and a precise finite-alphabet Levy--Khintchine layer for shuffle privacy.

Alex Shvets

We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact likelihood-ratio identities for shuffled histograms and a complete conditional-expectation linearization theorem with explicit typical-set remainders. We then derive sharp Jensen-Shannon divergence expansions, identifying the universal leading constant I_pi/(8n) for proportional compositions and emphasizing the correct fixed-composition covariance Sigma_pi=(1-pi)Sigma_0+pi*Sigma_1. Next we establish equivalence to Gaussian Differential Privacy with Berry-Esseen bounds and obtain the full limiting (epsilon,delta) privacy curve. Finally, for unbundled multi-message shuffling we give an exact degree-m likelihood ratio, asymptotic GDP formulas, and a strict bundled-versus-unbundled comparison. Further results include Local Asymptotic Normality with quantitative Le Cam equivalence, exact finite-n privacy curves, a boundary Berry-Esseen theorem for randomized response, and a frequency-estimation application.

Alex Shvets

We study neighboring shuffle experiments for epsilon_0-LDP channels along growing alphabets d -> infinity, and optimal mechanism design for frequency estimation under a canonical pairwise chi-squared budget. On the privacy side, we prove an exact compression theorem: the shuffled histogram experiment depends only on the pushforward law of the pairwise likelihood ratio. We establish a sharp universal bound chi^2 <= (e^{epsilon_0}-1)^2/e^{epsilon_0}, construct explicit obstruction families for which the shuffled privacy curve equals binary randomized response for all d, and prove a sharp diluting/persistent dichotomy. On the estimation side, we prove a universal lower bound of order (d-1)/(n chi_*(W)) via Cramer-Rao and Assouad arguments, and show that symmetrization to equivariant channels is WLOG. On the design side, we show calibrated GRR is not optimal. The optimal mechanism is an augmented GRR: fraction p of users applies aggressive GRR with lambda_* = sqrt(d-1), the rest sends a null symbol. This thinning principle is specific to shuffle and has no local-DP counterpart. For low budget 0 < C <= C_*(d), augmented GRR is optimal among all permutation-equivariant channels. GRR is also the unique optimizer within the subset-selection family.

Alex Shvets

We develop a geometric framework for anonymous shuffle experiments based on an anchored affine likelihood-ratio law: a mean-zero measure on the regular simplex polytope. Every finite-output d-ary channel corresponds, up to refinements, to a unique anchored law, and conversely. On privacy: among all epsilon_0-LDP channels, binary randomized response universally extremizes all convex f-divergences and hockey-stick profiles after shuffling. A rigidity converse shows that saturation of both directed envelopes at finite n forces the binary endpoint law. On design: under the pairwise chi_* budget, we prove exact trace-cap and two-orbit frontier theorems. Every frontier point is realized by a mixture of at most two orbit laws. In the low-budget regime, augmented randomized response is minimax-optimal to the sharp constant over all channels and estimators. Under the raw LDP cap, the problem reduces to subset-selection with explicit optimal subset size. The arguments are self-contained and independent of the author's trilogy.

Max Allan, Alex Shvets, Thomas Kurmann et al.

In mainstream computer vision and machine learning, public datasets such as ImageNet, COCO and KITTI have helped drive enormous improvements by enabling researchers to understand the strengths and limitations of different algorithms via performance comparison. However, this type of approach has had limited translation to problems in robotic assisted surgery as this field has never established the same level of common datasets and benchmarking methods. In 2015 a sub-challenge was introduced at the EndoVis workshop where a set of robotic images were provided with automatically generated annotations from robot forward kinematics. However, there were issues with this dataset due to the limited background variation, lack of complex motion and inaccuracies in the annotation. In this work we present the results of the 2017 challenge on robotic instrument segmentation which involved 10 teams participating in binary, parts and type based segmentation of articulated da Vinci robotic instruments.