arXiv subjects

Buddha Dev Das

Publications and source records attributed to Buddha Dev Das.

4 recordsLinked to original sources

arXiv2026

From Decision to Random Certificates: Exponential Separation for Edge Estimation with Independent Set Queries

We study the problem of estimating the number of edges in an undirected, unweighted graph using sublinear query access. We consider a query model that preserves the structure of Independent Set (IS) queries, but augments their output with a random certificate: given a vertex subset, the oracle returns a uniformly random edge from the induced subgraph if one exists, and returns null otherwise. Using this access, we give a randomized algorithm that outputs a $(1 \pm \varepsilon)$-approximation to the number of edges with constant success probability using $\widetilde{O}(\log^{2} m)$ queries. This implies an exponential separation from both standard IS queries and global random edge-sampling models: estimating the number of edges using standard IS queries require $\widetilde{\Theta}\!\left(\min\left\{\sqrt{m},\, \frac{n}{\sqrt{m}}\right\}\right)$ queries, while direct random edge-sample access requires $\widetilde{\Theta}(\sqrt{m})$ samples. Beyond separation in query complexity, our algorithm is output-sensitive: its query complexity is polylogarithmic in the number of edges in the graph. This aligns with the classical objective in group testing, where one seeks algorithms that are both worst-case optimal and instance-adaptive. Conceptually, our model connects group testing, the decision-versus-counting dichotomy, graph property testing, and the "power of a random certificate", and can be viewed as a structured form of conditional sampling of edges in graphs.

cs.DS↗

arXiv2025

Optimal non-adaptive algorithm for edge estimation

We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph, our method requires only $\widetilde{O}(\sqrt{n})$ queries, achieving sublinear query complexity. The algorithm independently samples a set of vertices and queries their degrees, and also independently samples a set of edges, using the answers to these queries to estimate the total number of edges in the graph. We further prove a matching lower bound, establishing the optimality of our algorithm and resolving the non-adaptive query complexity of this problem with respect to degree and random-edge queries.

cs.DS↗

arXiv2025

Dimension Agnostic Testing of Survey Data Credibility through the Lens of Regression

Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional distributions, which typically requires a number of samples that grows exponentially with the dimension. However, depending on the model used for data analysis, the conclusions drawn from the data may remain consistent across different underlying distributions. In this context, we propose a task-based approach to assess the credibility of sampled surveys. Specifically, we introduce a model-specific distance metric to quantify this notion of credibility. We also design an algorithm to verify the credibility of survey data in the context of regression models. Notably, the sample complexity of our algorithm is independent of the data dimension. This efficiency stems from the fact that the algorithm focuses on verifying the credibility of the survey data rather than reconstructing the underlying regression model. Furthermore, we show that if one attempts to verify credibility by reconstructing the regression model, the sample complexity scales linearly with the dimensionality of the data. We prove the theoretical correctness of our algorithm and numerically demonstrate our algorithm's performance.

cs.LG↗

arXiv2024

Testing Credibility of Public and Private Surveys through the Lens of Regression

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

cs.LG↗