arXiv subjects

Prasanjit Dubey

Publications and source records attributed to Prasanjit Dubey.

9 recordsLinked to original sources

arXiv2026

Report resolution in federated multiple testing under family-wise error control

Several institutions test one family of hypotheses under family-wise error control but cannot pool their data, so each site releases, for each hypothesis, only a report of its own p-value. The report's resolution is the number of values it can take. We quantify the power lost to such reports relative to the most powerful centralized procedure (the oracle), with reports and combining rule chosen optimally. A report from which the p-value can be recovered loses no power, so the loss is due to compression, not decentralization. Under the stated regularity and power-objective conditions, every finite resolution loses power, and the optimal loss decays as the inverse square of the resolution: equal-width intervals attain this order, and no partition into as many cells improves it. In two-site Beta examples, optimized one-bit reports are nearly lossless for a single hypothesis but lose several times as much power for two. At level 0.05 with two Beta(1, 2) hypotheses, optimally combined three-bit equal-width reports retain 99.2% of oracle power. We give the power-optimal combining rule for given reports, and a rule using only their exactly known null distribution, valid under arbitrary dependence across hypotheses.

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arXiv2026

Optimal multiple testing under family-wise error control: elementary symmetric polynomials and a scalable algorithm

Family-wise error rate control is essential when even one false rejection is costly, but distribution-free procedures do not exploit information in a specified alternative model. Existing dual theory characterises the maximum-average-power procedure under strong family-wise error control, but its optimal multipliers had been computed only up to $K = 3$. Under an exchangeable product model of independent $p$-values with a common non-increasing density under the alternative, we develop a general-$K$ statistical methodology that removes this computational barrier. An elementary-symmetric-polynomial representation yields global monotonicity of every constraint function and converts the coupled multiplier problem into monotone coordinate-wise searches. The resulting algorithm, symmetric-polynomial optimal testing (SPOT), uses bisection coordinate descent and has polynomial per-sweep cost in $K$ and the Monte Carlo size. Under stated conditions, its exact population objective values converge to the optimum and every limit point is optimal, without contraction or strong-convexity assumptions. Additional local regularity gives linear convergence of the exact population iterates, and an achieved $O_p(N^{-1/2})$ residual gives $\sqrt{N}$-consistent Monte Carlo output. In a truncated-normal scaling experiment, the relative average-power gain over Hommel's method increases from 15% at $K = 3$ to 83% at $K = 12$. Applications with up to 21 hypotheses demonstrate SPOT's practical reach.

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arXiv2026

Matching Rates and Optimal Allocation for Federated Probe-Logit Distillation under Heterogeneous Bandwidth Budgets

In federated language modeling, $K$ nodes each hold $n$ samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over $V$ tokens can be estimated when each node may upload at most $B$ bits per query in a public probe set. In federated probe-logit distillation (FPLD), each node transmits a scalar-quantized logit vector on the probe set, and an aggregator distills a global parametric student. Prior work (Dubey and Huo, 2026) establishes a high-probability KL rate $O(d/(Kn) + ρ\sqrt{V \log V / m} + K^{-1} \cdot 2^{-2B/V})$ plus optimization slack, with the bandwidth term in its trace-sharpened form. Whether this bandwidth-term rate is tight, and how the upper bound generalizes to heterogeneous per-node bandwidths, are left open. We close both gaps. First, the dithered FPLD construction has a matching single-round lower bound $Ω(K^{-1} \cdot 2^{-2B/V})$ under non-degeneracy, pinning the bandwidth-axis rate at $Θ(K^{-1} \cdot 2^{-2B/V})$. $T$-round sequential refinement with nested/scaled residual quantizers achieves $O(K^{-1} \cdot 2^{-2TB/V})$; vanilla FPLD's $T$-independent bandwidth term is suboptimal for every $T > 1$. Second, we establish a heterogeneous-bandwidth upper bound for per-node budgets $B_i$, paired with a closed-form optimal allocation $B_i^* = B_{\mathrm{tot}}/K + (V/2) \log_2(w_i / \bar{w}_g)$, a log-tilted water-filling rule that is the per-node analogue of reverse water-filling for distortion-rate optimization. A plug-in adaptive variant estimates the weights from a short warm-up phase and attains $1 + O(\sqrt{\log(K/δ)/(m T_0)})$ relative suboptimality. Synthetic n-gram simulations confirm that empirical KL is bracketed by the upper and lower bounds and that the optimal allocation strictly dominates uniform and inverse-weighted baselines under heterogeneous clipping.

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arXiv2026

Anytime-Valid Federated Conformal RAG for LLM Swarms

Federated Conformal RAG (FC-RAG) provides distribution-free coverage for a bandwidth-limited swarm of weak language models, but only at a fixed horizon. We extend it to anytime-valid sequential coverage: validity at every stopping time, preserved under predictable adaptive control (recalibration, per-node bandwidth escalation, distilled-student refresh), at no extra cost in assumptions over fixed-horizon FC-RAG. Naive composition fails because FC-RAG's marginal coverage bound makes the betting e-process a non-supermartingale on adverse calibration draws, and Ville's inequality cannot be invoked. We give Anytime-FC-RAG, a sequential extension built on a summable per-step calibration-deviation budget that converts the marginal bound into a strict conditional bound on a calibration-good event, paired with a truncated betting e-process that is a nonnegative supermartingale on the entire probability space. From these two ingredients, we obtain four guarantees: time-uniform alarm validity $\mathbb{P}(\sup_t E_t \ge 1/δ_e) \le δ_e + δ_{\mathrm{cal}}$, a Hoeffding-stitched cumulative-miscoverage envelope at the same total budget, safety under any predictable controller (recalibration, bandwidth escalation, student refresh), and training-side error propagation across an unbounded sequence of Federated Probe-Logit Distillation (FPLD) refreshes via a summable training budget. As a practical consequence, an adaptive controller that escalates retrieval bandwidth only when the e-process crosses a warning threshold matches the alarm rate of a fixed-high-bandwidth schedule at substantially lower communication cost. Experiments on a GPT-2-small + MiniLM swarm across MMLU, DBpedia, and AG News verify the predicted alarm rate, detection delay, envelope coverage, and $14$-$57\%$ bandwidth savings; the alarm fires when and only when coverage genuinely breaks.

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arXiv2026

Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage

Training a language model on data scattered across bandwidth-limited nodes that cannot be centralized is a setting that arises in clinical networks, enterprise knowledge bases, and scientific consortia. We study the regime in which data must remain distributed across nodes, and ask what statistical guarantees are in principle achievable under explicit bandwidth budgets; we aim to characterize what is provably possible, not to demonstrate a deployment-ready system. Existing theory treats either training-time consistency or inference-time calibration in isolation, and no prior work makes bandwidth a first-class statistical parameter. We analyze two protocols, Federated Probe-Logit Distillation (FPLD) for training and Federated Conformal RAG (FC-RAG) for inference, as the analytical vehicles for our results. Our first main result is an explicit high-probability KL-consistency rate for FPLD with simultaneous dependence on node count $K$, per-node sample size $n$, quantization budget $B$, probe-set size $m$, and vocabulary size $V$; bandwidth enters only through an exponentially vanishing quantization term. Our second main result is a distribution-free marginal-coverage bound for FC-RAG, whose novel retrieval-bandwidth slack $Δ_{\mathrm{RAG}} = f_{\max}\sqrt{K^{-2}\sum_i v(B_i)}$ makes per-node retrieval bandwidth a first-class statistical parameter, with arithmetic aggregation across $K$ nodes shrinking the slack as $K^{-1/2}$ in the per-node-uniform regime. A Pinsker-type corollary composes the two bounds into an end-to-end coverage guarantee. Synthetic experiments verify the predicted scaling along the bounds' parameters; small-scale experiments on a GPT-2 testbed illustrate that the qualitative bandwidth-accuracy tradeoff survives on a real language model. A deployment-scale empirical evaluation is out of scope.

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arXiv2026

BOOST: Power-Optimal Strong-FWER Testing for Block-Structured Multiplicity

Structured multiple-testing problems (gatekeeping trials, dose-finding, multi-tissue eQTL mapping, bundled-challenger A/B experiments) organize hypotheses into design-imposed blocks and demand strong family-wise error rate (FWER) control for confirmatory claims. Practitioners currently use objective-agnostic stepwise rules (Bonferroni, Holm, Hochberg, Hommel), closed-testing and graphical extensions, or hierarchical and resampling methods; none is power-optimal within the block-separable class these designs induce. We introduce BOOST (Block-Optimal Objective-driven Strong-FWER Testing), the power-optimal strong-FWER procedure for block size three, with three guarantees: (i) finite-sample strong-FWER validity at $O(K)$ cost (versus $O(K^2)$ for general closed testing) without independence assumptions, with a strict Sidak improvement under cross-block independence; (ii) power-optimal allocation across heterogeneous blocks via an equalized-marginal KKT condition, solvable by bisection in $O(B\log(1/\varepsilon))$; and (iii) a sample-split plug-in variant for unknown alternative density $g$, attaining $α$-control up to $O(B_T \mathbb E\|g-\widehat g\|_\infty)$ inflation with per-hypothesis power deficit independent of $B_T$. Simulations across independent, equicorrelated, sparse, and mis-specified regimes show 1.4-1.7$\times$ power gains over the strongest existing baseline at calibrated FWER. On two published datasets (BLUEPRINT cross-lineage cis-eQTL and Upworthy bundled-challenger A/B experiments), BOOST certifies an order of magnitude more full-block discoveries than existing baselines at controlled FWER.

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arXiv2025

Most Powerful Test with Exact Family-Wise Error Rate Control: Necessary Conditions and a Path to Fast Computing

Identifying the most powerful test in multiple hypothesis testing under strong family-wise error rate (FWER) control is a fundamental problem in statistical methodology. State-of-the-art approaches formulate this as a constrained optimisation problem, for which a dual problem with strong duality has been established in a general sense. However, a constructive method for solving the dual problem is lacking, leaving a significant computational gap. This paper fills this gap by deriving novel, necessary optimality conditions for the dual optimisation. We show that these conditions motivate an efficient coordinate-wise algorithm for computing the optimal dual solution, which, in turn, provides the most powerful test for the primal problem. We prove the linear convergence of our algorithm, i.e., the computational complexity of our proposed algorithm is proportional to the logarithm of the reciprocal of the target error. To the best of our knowledge, this is the first time such a fast and computationally efficient algorithm has been proposed for finding the most powerful test with family-wise error rate control. The method's superior power is demonstrated through simulation studies, and its practical utility is shown by identifying new, significant findings in both clinical and financial data applications.

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arXiv2025

LLmFPCA-detect: LLM-powered Multivariate Functional PCA for Anomaly Detection in Sparse Longitudinal Texts

Sparse longitudinal (SL) textual data arises when individuals generate text repeatedly over time (e.g., customer reviews, occasional social media posts, electronic medical records across visits), but the frequency and timing of observations vary across individuals. These complex textual data sets have immense potential to inform future policy and targeted recommendations. However, because SL text data lack dedicated methods and are noisy, heterogeneous, and prone to anomalies, detecting and inferring key patterns is challenging. We introduce LLmFPCA-detect, a flexible framework that pairs LLM-based text embeddings with functional data analysis to detect clusters and infer anomalies in large SL text datasets. First, LLmFPCA-detect embeds each piece of text into an application-specific numeric space using LLM prompts. Sparse multivariate functional principal component analysis (mFPCA) conducted in the numeric space forms the workhorse to recover primary population characteristics, and produces subject-level scores which, together with baseline static covariates, facilitate data segmentation, unsupervised anomaly detection and inference, and enable other downstream tasks. In particular, we leverage LLMs to perform dynamic keyword profiling guided by the data segments and anomalies discovered by LLmFPCA-detect, and we show that cluster-specific functional PC scores from LLmFPCA-detect, used as features in existing pipelines, help boost prediction performance. We support the stability of LLmFPCA-detect with experiments and evaluate it on two different applications using public datasets, Amazon customer-review trajectories, and Wikipedia talk-page comment streams, demonstrating utility across domains and outperforming state-of-the-art baselines.

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arXiv2023

Generalization Bounds for Magnitude-Based Pruning via Sparse Matrix Sketching

In this paper, we derive a novel bound on the generalization error of Magnitude-Based pruning of overparameterized neural networks. Our work builds on the bounds in Arora et al. [2018] where the error depends on one, the approximation induced by pruning, and two, the number of parameters in the pruned model, and improves upon standard norm-based generalization bounds. The pruned estimates obtained using our new Magnitude-Based compression algorithm are close to the unpruned functions with high probability, which improves the first criteria. Using Sparse Matrix Sketching, the space of the pruned matrices can be efficiently represented in the space of dense matrices of much smaller dimensions, thereby lowering the second criterion. This leads to stronger generalization bound than many state-of-the-art methods, thereby breaking new ground in the algorithm development for pruning and bounding generalization error of overparameterized models. Beyond this, we extend our results to obtain generalization bound for Iterative Pruning [Frankle and Carbin, 2018]. We empirically verify the success of this new method on ReLU-activated Feed Forward Networks on the MNIST and CIFAR10 datasets.

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