About

Bhaswar B. Bhattacharya is an Associate Professor of Statistics and Data Science at the University of Pennsylvania's Wharton School, with a secondary appointment in Mathematics. He completed his Ph.D. in Statistics at Stanford University in 2016, earned a Master of Statistics from the Indian Statistical Institute in 2011, and a Bachelor of Statistics from the same institute in 2009. His research interests encompass nonparametric statistics, distribution-free inference, networks analysis, graphical models, statistical learning, combinatorial probability, discrete and computational geometry. Bhattacharya has contributed to various fields through his research, which includes optimizing vaccination site locations to control zoonotic epidemics, growth rates of geometric structures, inference in instrumental variable models, fluctuations in graphon-based random graphs, and motif estimation in subgraph sampling. He has received notable awards such as the NSF Career Award, the Alfred P. Sloan Research Fellowship, and the Probability Dissertation Award from Stanford University.

Research topics

• Computer Science
• Medicine
• Virology
• Data Mining
• Environmental health
• Algorithm
• Computer network
• Statistics
• Mathematics
• Biology

Selected publications

• On the Number of Almost Empty Monochromatic Triangles

  ArXiv.org · 2026-01-26

  articleOpen access1st authorCorresponding

  In this paper, we consider the problem of counting almost empty monochromatic triangles in colored planar point sets, that is, triangles whose vertices are all assigned the same color and that contain only a few interior points. Specifically, we show that any $c$-coloring of a set of $n$ points in the plane in general position (that is, no three on a line) contains $Ω(n^2)$ monochromatic triangles with at most $c-1$ interior points and $Ω(n^{\frac{4}{3}})$ monochromatic triangles with at most $c-2$ interior points, for any fixed $c \geq 2$. The latter, in particular, generalizes the result of Pach and Tóth (2013) on the number of monochromatic empty triangles in 2-colored point sets, to the setting of multiple colors and monochromatic triangles with a few interior points. We also derive the limiting value of the expected number of triangles with $s$ interior points in random point sets, for any integer $s \geq 0$. As a result, we obtain the expected number of monochromatic triangles with at most $s$ interior points in random colorings of random point sets.

  PublisherOA PDF

• A Ball Divergence-Based Measure for Conditional Independence Testing With a Local Wild Bootstrap

  Biometrika · 2026-04-08

  article

  Abstract In this paper we introduce a new measure of conditional dependence between two random vectors X and Y given another random vector Z using the ball divergence. Our measure characterizes conditional independence and does not require any moment assumptions. We propose an estimator of the measure using a kernel-averaging technique and derive its asymptotic distribution. Using this estimator, we construct a test for conditional independence based on a novel local wild bootstrap algorithm. Specifically, we design a double-bandwidth-based wild bootstrap algorithm that asymptotically controls the Type I error rate and gives a consistent test against a general class of alternatives. We illustrate the advantage of our method, both in terms of Type I error and power, in a range of simulation settings and also in a real-data example. A consequence of our theoretical results is a general framework for studying the asymptotic properties of a two-sample conditional V -statistic, which is of independent interest.

  PublisherDOI

• On the Number of Almost Empty Monochromatic Triangles

  Open MIND · 2026-01-26

  preprint1st authorCorresponding

  In this paper, we consider the problem of counting almost empty monochromatic triangles in colored planar point sets, that is, triangles whose vertices are all assigned the same color and that contain only a few interior points. Specifically, we show that any $c$-coloring of a set of $n$ points in the plane in general position (that is, no three on a line) contains $Ω(n^2)$ monochromatic triangles with at most $c-1$ interior points and $Ω(n^{\frac{4}{3}})$ monochromatic triangles with at most $c-2$ interior points, for any fixed $c \geq 2$. The latter, in particular, generalizes the result of Pach and Tóth (2013) on the number of monochromatic empty triangles in 2-colored point sets, to the setting of multiple colors and monochromatic triangles with a few interior points. We also derive the limiting value of the expected number of triangles with $s$ interior points in random point sets, for any integer $s \geq 0$. As a result, we obtain the expected number of monochromatic triangles with at most $s$ interior points in random colorings of random point sets.

  DOI

• Phase transitions of the maximum likelihood estimators in the p-spin Curie-Weiss model

  Bernoulli · 2025-02-11 · 3 citations

  articleSenior author
  PublisherDOI

• Multiplexons: Limits of Multiplex Networks

  ArXiv.org · 2025-10-08

  preprintOpen accessSenior author

  In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to the widespread coexistence of diverse interactions in social, industrial, and biological domains. This motivates the development of a rigorous and readily applicable framework for studying properties of large multiplex networks. In this article, we provide a self-contained introduction to the limit theory of dense multiplex networks, analogous to the theory of graphons (limit theory of dense graphs). As applications, we derive limiting analogues of commonly used multiplex features, such as degree distributions and clustering coefficients. We also present a range of illustrative examples, including correlated versions of Erdős-Rényi and inhomogeneous random graph models and dynamic networks. Finally, we discuss how multiplex networks fit within the broader framework of decorated graphs, and how the convergence results can be recovered from the limit theory of decorated graphs. Several future directions are outlined for further developing the multiplex limit theory.

  PublisherOA PDFDOI

• Pitman efficiency lower bounds for multivariate distribution-free tests based on optimal transport

  Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2025-11-07 · 1 citations

  article

  Abstract The Wilcoxon rank sum test is one of the most popular distribution-free two-sample tests for univariate data. Among the important reasons for their popularity are the striking results of Hodges–Lehmann and Chernoff–Savage, where the authors show that the asymptotic (Pitman) relative efficiency of Wilcoxon’s test compared to Student’s t-test, never falls below 0.864 (with identity score) and 1 (with Gaussian score), respectively. Motivated by these results, we propose and study a large family of exactly distribution-free multivariate rank-based two-sample tests by leveraging the theory of optimal transport. First, we propose distribution-free analogues of the Hotelling T2 test and show that they satisfy Hodges–Lehmann and Chernoff–Savage-type efficiency lower bounds over natural sub-families of multivariate distributions—making them the first multivariate, nonparametric, finite-sample distribution-free tests that provably achieve such efficiency lower bounds. Next, we propose exactly distribution-free versions of the celebrated kernel maximum mean discrepancy test. In addition to being distribution-free in finite-samples, these tests are universally consistent under no moment assumptions and have nontrivial Pitman efficiency. To the best of our knowledge, these are the first class of tests to have this trifecta of properties.

  PublisherDOI

• Growth rates of the number of empty triangles and simplices

  Computational Geometry · 2025-04-17

  article1st authorCorresponding
  PublisherDOI

• Thresholds and Fluctuations of Submultiplexes in Random Multiplex Networks

  ArXiv.org · 2025-11-15

  preprintOpen access1st authorCorresponding

  In a multiplex network a common set of nodes is connected through different types of interactions, each represented as a separate graph (layer) within the network. In this paper, we study the asymptotic properties of submultiplexes, the counterparts of subgraphs (motifs) in single-layer networks, in the correlated Erdős-Rényi multiplex model. This is a random multiplex model with two layers, where the graphs in each layer marginally follow the classical (single-layer) Erdős-Rényi model, while the edges across layers are correlated. We derive the precise threshold condition for the emergence of a fixed submultiplex $\boldsymbol{H}$ in a random multiplex sampled from the correlated Erdős-Rényi model. Specifically, we show that the satisfiability region, the regime where the random multiplex contains infinitely many copies of $\boldsymbol{H}$, forms a polyhedral subset of $\mathbb{R}^3$. Furthermore, within this region the count of $\boldsymbol{H}$ is asymptotically normal, with an explicit convergence rate in the Wasserstein distance. We also establish various Poisson approximation results for the count of $\boldsymbol{H}$ on the boundary of the threshold, which depends on a notion of balance of submultiplexes. Collectively, these results provide an asymptotic theory for small submultiplexes in the correlated multiplex model, analogous to the classical theory of small subgraphs in random graphs.

  PublisherOA PDFDOI

• Asymptotic Normality of Subgraph Counts in Sparse Inhomogeneous Random Graphs

  ArXiv.org · 2025-12-15

  preprintOpen accessSenior author

  In this paper, we derive the asymptotic distribution of the number of copies of a fixed graph $H$ in a random graph $G_n$ sampled from a sparse graphon model. Specifically, we provide a refined analysis that separates the contributions of edge randomness and vertex-label randomness, allowing us to identify distinct sparsity regimes in which each component dominates or both contribute jointly to the fluctuations. As a result, we establish asymptotic normality for the count of any fixed graph $H$ in $G_n$ across the entire range of sparsity (above the containment threshold for $H$ in $G_n$). These results provide a complete description of subgraph count fluctuations in sparse inhomogeneous networks, closing several gaps in the existing literature that were limited to specific motifs or suboptimal sparsity assumptions.

  PublisherOA PDFDOI

• Almost Empty Monochromatic Polygons in Planar Point Sets

  Lecture notes in computer science · 2025-01-01

  book-chapter1st authorCorresponding
  PublisherDOI

Recent grants

• CAREER: Geometric and Combinatorial Methods for Distribution-Free Inference and Dependent Network Data

  NSF · $400k · 2021–2027

Frequent coauthors

• Sumit Mukherjee

  25 shared

• Somabha Mukherjee

  23 shared

• Sandip Das

  Indian Statistical Institute

  22 shared

• Shirshendu Ganguly

  University of California, Berkeley

  14 shared

• Aritra Banik

  12 shared

• Dylan S. Small

  12 shared

• Qingyuan Zhao

  9 shared

• Susmita Sur‐Kolay

  Indian Statistical Institute

  9 shared

Awards & honors

• NSF Career Award, 2021-2026
• Alfred P. Sloan Research Fellowship, 2021
• Probability Dissertation Award, Department of Statistics, St…
• Sabyasachi Roy Memorial Gold Medal for the best master's the…