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Debasish Chatterjee

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TMLR Journal 2026 Journal Article

On a Gradient Approach to Chebyshev Center Problems with Applications to Function Learning

Abhinav Raghuvanshi
Mayank Baranwal
Debasish Chatterjee

We introduce $\textsf{gradOL}$, the first gradient-based optimization framework for solving Chebyshev center problems, a fundamental challenge in optimal function learning and geometric optimization. $\textsf{gradOL}$ hinges on reformulating the semi-infinite problem as a finitary max-min optimization, making it amenable to gradient-based techniques. By leveraging automatic differentiation for precise numerical gradient computation, $\textsf{gradOL}$ ensures numerical stability and scalability, making it suitable for large-scale settings. Under strong convexity of the ambient norm, $\textsf{gradOL}$ provably recovers optimal Chebyshev centers while directly computing the associated radius. This addresses a key bottleneck in constructing stable optimal interpolants. Empirically, $\textsf{gradOL}$ achieves significant improvements in accuracy and efficiency on 34 benchmark Chebyshev center problems from a benchmark \textsf{CSIP} library. Moreover, we extend $\textsf{gradOL}$ to general convex semi-infinite programming (CSIP), attaining up to $4000\times$ speedups over the state-of-the-art \textsf{sipampl} solver tested on the indicated \textsf{CSIP} library containing 67 benchmark problems. Furthermore, we provide the first theoretical foundation for applying gradient-based methods to Chebyshev center problems, bridging rigorous analysis with practical algorithms. $\textsf{gradOL}$ thus offers a unified solution framework for Chebyshev centers and broader CSIPs.

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NeurIPS Conference 2025 Conference Paper

A Computationally Viable Numerical Gradient-based Technique for Optimal Covering Problems

Gokul Rajaraman
Debasish Chatterjee

The problem of optimally covering a given compact subset of $\mathbb{R}^N$ with a preassigned number $n$ of Euclidean metric balls has a long-standing history and it is well-recognized to be computationally hard. This article establishes a numerically viable algorithm for obtaining optimal covers of compact sets via two key contributions. The first is a foundational result establishing Lipschitz continuity of the marginal function of a certain parametric non-convex maximization problem in the optimal covering problem, and it provides the substrate for numerical gradient algorithms to be employed in this context. The second is an adaptation of a stochastically smoothed numerical gradient-based (zeroth-order) algorithm for a non-convex minimization problem, that, equipped with randomized restarts, spurs global convergence to an optimal cover. Several numerical experiments with complicated nonconvex compact sets demonstrate the excellent performance of our techniques.

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JBHI Journal 2024 Journal Article

Topological Gait Analysis: A New Framework and Its Application to the Study of Human Gait

Shreyam Mishra
Debasish Chatterjee
Neeta Kanekar

Objective: This study introduces a physiologically driven topological gait analysis (TGA) framework to gain insights into pathological gait. Methods: A publicly available gait dataset consisting of four groups: healthy adults, people with Parkinson's disease (PD), Huntington's disease (HD), and amyotrophic lateral sclerosis (ALS) was used. The topological properties of the configuration space of three gait parameters were studied by approximating the underlying distribution through a Gaussian kernel-based density estimation technique. Thereafter, sublevel sets of the density estimate were analyzed using cubical persistence homology. Results: Three new features were constructed: 1. Probability density estimates (PDEs) that characterize the distribution of gait parameters over their configuration space. Healthy adults exhibited a unimodal distribution, while people with neurodegenerative disorders displayed a multi-modal distribution. 2. Persistence entropy plots that summarize changes in the PDEs and characterize the uncertainty in the underlying distribution. Gait of healthy adults was concentrated at higher entropy values as opposed to neurodegenerative gait. 3. A number $\alpha _{s}$ that captures disease severity trends. Conclusions: Topological features in PD and HD indicate a ‘bias’ to a certain set of gait configurations. This lack of exploration may reflect poor planning of the underlying topology, resulting in outward manifestations of impaired gait. The lower variegations in PDEs in ALS compared to PD and HD suggest that the planning of the topology of gait may occur at higher levels of the neural architecture. Significance: TGA offers characterization of gait at a hitherto uncharted level, potentially serving neuromotor markers for early diagnosis and personalized rehabilitation protocols.

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JMLR Journal 2022 Journal Article

Novel Min-Max Reformulations of Linear Inverse Problems

Mohammed Rayyan Sheriff
Debasish Chatterjee

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refer to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a variety of settings with applications ranging from medical image processing, recommender systems, etc. We propose a slightly generalized version of the error constrained linear inverse problem and obtain a novel and equivalent convex-concave min-max reformulation by providing an exposition to its convex geometry. Saddle points of the min-max problem are completely characterized in terms of a solution to the LIP, and vice versa. Applying simple saddle point seeking ascend-descent type algorithms to solve the min-max problems provides novel and simple algorithms to find a solution to the LIP. Moreover, the reformulation of an LIP as the min-max problem provided in this article is crucial in developing methods to solve the dictionary learning problem with almost sure recovery constraints. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2017 Journal Article

Optimal Dictionary for Least Squares Representation

Mohammed Rayyan Sheriff
Debasish Chatterjee

Dictionaries are collections of vectors used for the representation of a class of vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., $\ell_0$-optimal representations. Here we consider the problem of finding optimal dictionaries with which representations of a given class of vectors is optimal in an $\ell_2$-sense: optimality of representation is defined as attaining the minimal average $\ell_2$-norm of the coefficients used to represent the vectors in the given class. With the help of recent results on rank-1 decompositions of symmetric positive semidefinite matrices, we provide an explicit description of $\ell_2$-optimal dictionaries as well as their algorithmic constructions in polynomial time. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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