arXiv subjects

Abhay Parekh

Publications and source records attributed to Abhay Parekh.

7 recordsLinked to original sources

arXiv2026

Bayesian Wind Tunnels for Model Selection

Prior work has shown that transformers can perform exact Bayesian filtering within a fixed hypothesis class. Can they also perform Bayesian model selection -- identifying the correct hypothesis class from data? We introduce model-selection Bayesian wind tunnels: controlled environments where ground-truth posteriors over hypothesis classes are available in closed form. Using fixed-point-free involutions -- whose defining property f(f(x))=x is purely relational -- a 2.8M-parameter transformer achieves 0.01-bit entropy agreement with the Bayesian optimum (3 seeds), with both integer tokens and opaque symbols whose meanings change every episode. This extends to non-nested comparisons: involutions vs. 3-cycles (where neither class is a subset of the other) achieve class-posterior MAE under 0.001, demonstrating genuine model selection beyond simplicity/subset bias. We then identify a sharp perceptual access condition: when the discriminative statistic requires arithmetic -- modular addition (rotations) or multiplication (f(x)=cx mod p) -- model selection succeeds with integer tokens but fails completely with opaque symbols, and this boundary persists under 112x scaling (2.8M to 316M parameters). A stationarity control confirms the operative factor: opaque tokens with a fixed relabeling succeed (0.009-bit MAE), showing that stable semantics, not integer identity, enable circuit compilation. Header subtask diagnostics localize the failure to the composition of header inversion with arithmetic rather than header parsing itself. Probing frontier LLMs on the same tasks shows qualitative Bayesian behavior but a large calibration gap (~55x), measured through lossy probes and therefore directional rather than exact.

cs.LG↗

arXiv2022

The Square Root Agreement Rule for Incentivizing Truthful Feedback on Online Platforms

A major challenge in obtaining evaluations of products or services on e-commerce platforms is eliciting informative responses in the absence of verifiability. This paper proposes the Square Root Agreement Rule (SRA): a simple reward mechanism that incentivizes truthful responses to objective evaluations on such platforms. In this mechanism, an agent gets a reward for an evaluation only if her answer matches that of her peer, where this reward is inversely proportional to a popularity index of the answer. This index is defined to be the square root of the empirical frequency at which any two agents performing the same evaluation agree on the particular answer across evaluations of similar entities operating on the platform. Rarely agreed-upon answers thus earn a higher reward than answers for which agreements are relatively more common. We show that in the many tasks regime, the truthful equilibrium under SRA is strictly payoff-dominant across large classes of natural equilibria that could arise in these settings, thus increasing the likelihood of its adoption. While there exist other mechanisms achieving such guarantees, they either impose additional assumptions on the response distribution that are not generally satisfied for objective evaluations or they incentivize truthful behavior only if each agent performs a prohibitively large number of evaluations and commits to using the same strategy for each evaluation. SRA is the first known incentive mechanism satisfying such guarantees without imposing any such requirements. Moreover, our empirical findings demonstrate the robustness of the incentive properties of SRA in the presence of mild subjectivity or observational biases in the responses. These properties make SRA uniquely attractive for administering reward-based incentive schemes (e.g., rebates, discounts, reputation scores, etc.) on online platforms.

cs.GT↗

arXiv2019

Matching Observations to Distributions: Efficient Estimation via Sparsified Hungarian Algorithm

Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood estimator (MLE) for this problem can be computed using weighted bipartite matching, even when $n$, the number of observations per distribution, exceeds one. This is achieved by instantiating $n$ duplicates of each distribution node. However, in the regime where the number of observations per distribution is much larger than the number of distributions, the Hungarian matching algorithm for computing the weighted bipartite matching requires $\mathcal O(n^3)$ time. We introduce a novel randomized matching algorithm that reduces the runtime to $\tilde{\mathcal O}(n^2)$ by sparsifying the original graph, returning the exact MLE with high probability. Next, we give statistical justification for using the MLE by bounding the excess risk of the MLE, where the loss is defined as the negative log-likelihood. We test these bounds for the case of isotropic Gaussians with equal covariances and whose means are separated by a distance $η$, and find (1) that $\gg \log k$ separation suffices to drive the proportion of mismatches of the MLE to 0, and (2) that the expected fraction of mismatched observations goes to zero at rate $\mathcal O({(\log k)}^2/η^2)$.

cs.DS↗

arXiv2015

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared via its Laplacian spectrum. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre-factors.

cs.LG↗

arXiv2014

When is it Better to Compare than to Score?

When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We provide empirical evidence based on experiments on Amazon Mechanical Turk that in a variety of tasks, (pairwise-comparative) ordinal measurements have lower per sample noise and are typically faster to elicit than cardinal ones. Ordinal measurements however typically provide less information. We then consider the popular Thurstone and Bradley-Terry-Luce (BTL) models for ordinal measurements and characterize the minimax error rates for estimating the unknown quantity. We compare these minimax error rates to those under cardinal measurement models and quantify for what noise levels ordinal measurements are better. Finally, we revisit the data collected from our experiments and show that fitting these models confirms this prediction: for tasks where the noise in ordinal measurements is sufficiently low, the ordinal approach results in smaller errors in the estimation.

stat.ML↗

arXiv2010

An Adaptive Multi-channel P2P Video-on-Demand System using Plug-and-Play Helpers

We present a multi-channel P2P Video-on-Demand (VoD) system using "plug-and-play" helpers. Helpers are heterogenous "micro-servers" with limited storage, bandwidth and number of users they can serve simultaneously. Our proposed system has the following salient features: (1) it minimizes the server load; (2) it is distributed, and requires little or no maintenance overhead and which can easily adapt to system dynamics; and (3) it is adaptable to varying supply and demand patterns across multiple video channels irrespective of video popularity. Our proposed solution jointly optimizes over helper-user topology, video storage allocation and bandwidth allocation. The combinatorial nature of the problem and the system demand for distributed algorithms makes the problem uniquely challenging. By utilizing Lagrangian decomposition and Markov chain approximation based arguments, we address this challenge by designing two distributed algorithms running in tandem: a primal-dual storage and bandwidth allocation algorithm and a "soft-worst-neighbor-choking" topology-building algorithm. Our scheme provably converges to a near-optimal solution, and is easy to implement in practice. Simulation results validate that the proposed scheme achieves minimum sever load under highly heterogeneous combinations of supply and demand patterns, and is robust to system dynamics of user/helper churn, user/helper asynchrony, and random delays in the network.

cs.NI↗

arXiv2008

The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference Channels

Recently, Etkin, Tse, and Wang found the capacity region of the two-user Gaussian interference channel to within one bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the many-to-one and one-to-many Gaussian interference channels to within a constant number of bits. The result makes use of a deterministic model to provide insight into the Gaussian channel. The deterministic model makes explicit the dimension of signal scale. A central theme emerges: the use of lattice codes for alignment of interfering signals on the signal scale.

cs.IT↗