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Indian Statistical Institute

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Representative Papers

MK-SGC-SC: Multiple Kernel Guided Sparse Graph Construction in Spectral Clustering for Unsupervised Speaker Diarization

Jan 24, 2026

This work addresses the challenges of lacking labeled data and reliance on pretraining in unsupervised speaker diarization by proposing a multi-kernel fusion–based similarity measure. It systematically integrates polynomial kernels with first-order arc-cosine kernels for the first time to construct a sparse affinity graph that emphasizes local structural properties, followed by spectral clustering for speaker segmentation and clustering. The method requires no supervision or pretrained models and achieves state-of-the-art unsupervised performance on major benchmarks including DIHARD-III, AMI, and VoxConverse, significantly advancing the practical applicability of unsupervised speaker diarization.

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Estimation of Piecewise Continuous Regression Function in Finite Dimension using Oblique-axis Regression Tree with Applications in Image Denoising

Mar 20, 2025Statistica sinica

This paper addresses high-precision estimation of piecewise continuous regression functions with complex jump-location curves (JLCs) under fixed finite-dimensional designs. We propose a recursive space-partitioning method based on oblique random trees (ORTs), where local averaging is applied at leaf nodes—marking the first use of ORTs for modeling non-axis-aligned, multi-directional JLCs. Unlike conventional decision trees, which are limited to piecewise constant or smooth functions, our approach significantly enhances preservation of intricate edge structures. Theoretical analysis establishes consistency and convergence rates. Image denoising experiments demonstrate that the method effectively suppresses noise while faithfully retaining jump discontinuities along arbitrary orientations. The core contribution is a novel ORT-based modeling paradigm specifically designed for JLCs, achieving both statistical accuracy and geometric fidelity in representing discontinuous boundaries.

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On Fourier analysis of sparse Boolean functions over certain Abelian groups

Jun 26, 2024International Symposium on Mathematical Foundations of Computer Science

This work investigates the structural properties of Fourier-sparse Boolean functions over general finite abelian groups $mathbb{Z}_{p_1}^{n_1} imes cdots imes mathbb{Z}_{p_t}^{n_t}$ and their applications to property testing. Addressing odd prime-power-order groups, we first extend Granularity theory to this broader class. We refute the existence of a universal $O(1/s)$ lower bound on the smallest non-zero Fourier coefficient, constructing explicit counterexamples showing that in $mathbb{Z}_p^n$ ($p>2$), this coefficient can be as small as $1/omega(n)$. We establish a tight lower bound of $1/(m^2 s)^{lceil varphi(m)/2 ceil}$, where $m = mathrm{lcm}(p_1,dots,p_t)$. Leveraging this, we design an efficient property tester with query complexity $mathrm{poly}((ms)^{varphi(m)}, 1/varepsilon)$. Furthermore, we prove an $Omega(sqrt{s})$ lower bound on adaptive queries, demonstrating inherent limitations for testing Fourier sparsity in this setting.

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