arXiv subjects

Shrutimoy Das

Publications and source records attributed to Shrutimoy Das.

6 recordsLinked to original sources

arXiv2026

Individual Fairness in Hierarchical Clustering

Hierarchical clustering produces ultrametric representations that impose strong global geometric constraints and may distort local similarities in ways that disproportionately affect individual data points. We study hierarchical clustering under an individual fairness requirement that bounds relative distortion within local $k$-nearest neighborhoods. We formulate this requirement as a feasibility problem over dominated ultrametrics and characterize the minimal multiplicative slack required for feasibility. We identify a sharp local threshold, prove stability under bounded perturbations, establish monotonicity in $k$, and show an intrinsic $Θ(\log n)$ separation between local and global realizability. Experiments on synthetic and real world datasets support our theoretical results.

cs.LG↗

arXiv2025

Local Fragments, Global Gains: Subgraph Counting using Graph Neural Networks

Subgraph counting is a fundamental task for analyzing structural patterns in graph-structured data, with important applications in domains such as computational biology and social network analysis, where recurring motifs reveal functional and organizational properties. In this paper, we propose localized versions of the Weisfeiler-Leman (WL) algorithms to improve both expressivity and computational efficiency for this task. We introduce Local $k$-WL, which we prove to be more expressive than $k$-WL and at most as expressive as $(k+1)$-WL, and provide a characterization of patterns whose subgraph and induced subgraph counts are invariant under Local $k$-WL equivalence. To enhance scalability, we present two variants -- Layer $k$-WL and Recursive $k$-WL -- that achieve greater time and space efficiency compared to applying $k$-WL on the entire graph. Additionally, we propose a novel fragmentation technique that decomposes complex subgraphs into simpler subpatterns, enabling the exact count of all induced subgraphs of size at most $4$ using only $1$-WL, with extensions possible for larger patterns when $k>1$. Building on these ideas, we develop a three-stage differentiable learning framework that combines subpattern counts to compute counts of more complex motifs, bridging combinatorial algorithm design with machine learning approaches. We also compare the expressive power of Local $k$-WL with existing GNN hierarchies and demonstrate that, under bounded time complexity, our methods are more expressive than prior approaches.

cs.LG↗

arXiv2025

Private Sketches for Linear Regression

Linear regression is frequently applied in a variety of domains, some of which might contain sensitive information. This necessitates that the application of these methods does not reveal private information. Differentially private (DP) linear regression methods, developed for this purpose, compute private estimates of the solution. These techniques typically involve computing a noisy version of the solution vector. Instead, we propose releasing private sketches of the datasets, which can then be used to compute an approximate solution to the regression problem. This is motivated by the \emph{sketch-and-solve} paradigm, where the regression problem is solved on a smaller sketch of the dataset instead of on the original problem space. The solution obtained on the sketch can also be shown to have good approximation guarantees to the original problem. Various sketching methods have been developed for improving the computational efficiency of linear regression problems under this paradigm. We adopt this paradigm for the purpose of releasing private sketches of the data. We construct differentially private sketches for the problems of least squares regression, as well as least absolute deviations regression. We show that the privacy constraints lead to sketched versions of regularized regression. We compute the bounds on the regularization parameter required for guaranteeing privacy. The availability of these private sketches facilitates the application of commonly available solvers for regression, without the risk of privacy leakage.

cs.LG↗

arXiv2025

Local Search-based Individually Fair Clustering with Outliers

In this paper, we present a local search-based algorithm for individually fair clustering in the presence of outliers. We consider the individual fairness definition proposed in Jung et al., which requires that each of the $n$ points in the dataset must have one of the $k$ centers within its $n/k$ nearest neighbors. However, if the dataset is known to contain outliers, the set of fair centers obtained under this definition might be suboptimal for non-outlier points. In order to address this issue, we propose a method that discards a set of points marked as outliers and computes the set of fair centers for the remaining non-outlier points. Our method utilizes a randomized variant of local search, which makes it scalable to large datasets. We also provide an approximation guarantee of our method as well as a bound on the number of outliers discarded. Additionally, we demonstrate our claims experimentally on a set of real-world datasets.

cs.DS↗

arXiv2025

Review of Extreme Multilabel Classification

Extreme multi-label classification or XMLC, is an active area of interest in machine learning. Compared to traditional multi-label classification, here the number of labels is extremely large, hence, the name extreme multi-label classification. Using classical one-versus-all classification does not scale in this case due to large number of labels; the same is true for any other classifier. Embedding labels and features into a lower-dimensional space is a common first step in many XMLC methods. Moreover, other issues include existence of head and tail labels, where tail labels are those that occur in a relatively small number of samples. The existence of tail labels creates issues during embedding. This area has invited application of wide range of approaches ranging from bit compression motivated from compressed sensing, tree based embeddings, deep learning based latent space embedding including using attention weights, linear algebra based embeddings such as SVD, clustering, hashing, to name a few. The community has come up with a useful set of metrics to identify correctly the prediction for head or tail labels.

cs.LG↗

arXiv2024

Linear Programming based Approximation to Individually Fair k-Clustering with Outliers

Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm for datasets that contain outliers. That is, given $n$ points and $k$ centers, we want that for each point which is not an outlier, there must be a center within the $\frac{n}{k}$ nearest neighbours of the given point. While a few of the recent works have looked into individually fair clustering, this is the first work that explores this problem in the presence of outliers for $k$-means clustering. For this purpose, we define and solve a linear program (LP) that helps us identify the outliers. We exclude these outliers from the dataset and apply a rounding algorithm that computes the $k$ centers, such that the fairness constraint of the remaining points is satisfied. We also provide theoretical guarantees that our method leads to a guaranteed approximation of the fair radius as well as the clustering cost. We also demonstrate our techniques empirically on real-world datasets.

cs.LG↗