Dynamic angular synchronization under smoothness constraints
Authors: Ernesto Araya, Mihai Cucuringu, Hemant Tyagi
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We complement our theoretical results with experiments on synthetic data. ... Section 4 contains numerical experiments on synthetic data and Section 5 contains concluding remarks. |
| Researcher Affiliation | Academia | Ernesto Araya EMAIL Department of Mathematics Ludwig-Maximilians-Universit at M unchen Geschwister-Scholl-Platz 1, Munich, 80539, Germany Mihai Cucuringu EMAIL Department of Mathematics University of California Los Angeles 520 Portola Plaza, Los Angeles, CA 90095, USA Department of Statistics & Oxford-Man Institute of Quantitative Finance University of Oxford 24-29 St Giles , Oxford OX1 3LB, United Kingdom Hemant Tyagi EMAIL Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore |
| Pseudocode | Yes | Algorithm 1 Global TRS for Dynamic Synchronization (GTRS-Dyn Sync) ... Algorithm 2 Local TRS + Global Smoothing for Dynamic Synchronization (LTRS-GS-Dyn Sync) ... Algorithm 3 Global Matrix Denoising + Local TRS for Dynamic Synchronization (GMD-LTRS-Dyn Sync) ... Algorithm 4 Global Matrix Denoising + Local Spectral method for Dynamic Synchronization (GMD-LSPEC-Dyn Sync) ... Algorithm 5 Projected Power Method for Dynamic Synchronization (PPM-Dyn Sync) |
| Open Source Code | Yes | The code is available at https://github.com/Ernesto Araya V/dynamic_synch. |
| Open Datasets | No | We complement our theoretical results with experiments on synthetic data. ... For specified values of n, T and smoothness ST , we generate a smooth signal g Cn T , with g 1(k) = 1 for each block k, as follows. Define τ := min 1 + TST , T , define Pτ ,n 1 as in (11). Generate a Gaussian u N(0, I(n 1)T ) and compute T Pτ ,n 1u Pτ ,n 1u 2 . Then denoting g := exp(ι(0.5π)u ) which is computed entry-wise, we form g by prepending each block of g with 1. It is a simple exercise to verify that g (almost surely) satisfies the smoothness condition in Assumption 2 for the specified ST , up to a constant. |
| Dataset Splits | No | In a single MC run, we randomly generate the ground-truth for a specified smoothness ST (as described earlier), then generate the noisy pairwise data (as per specified noise model), and then compute the RMSE for each algorithm for the regularization parameters selected by the aforementioned data-fidelity rule. |
| Hardware Specification | No | No specific hardware details (like GPU/CPU models, memory amounts, or processor types) are mentioned in the paper's experimental setup or results sections. |
| Software Dependencies | No | The paper does not explicitly provide specific software dependencies with version numbers (e.g., Python version, library versions like PyTorch, TensorFlow, scikit-learn, or specific solvers). |
| Experiment Setup | Yes | Experiment setup. The following remarks are in order. 1. For specified values of n, T and smoothness ST , we generate a smooth signal g Cn T , with g 1(k) = 1 for each block k, as follows. ... 2. For an estimate bg Cn T of the ground truth truth g Cn T , we will measure the Root Mean Square Error (RMSE) defined as 1 n T bg g 2. ... 3. In order to choose the appropriate value of the regularization parameters for the algorithms (λ for GTRS-Dyn Syncand τ for LTRS-GS-Dyn Sync, GMD-LTRS-Dyn Sync), we consider a data-driven grid-search based heuristic. In particular, define a discretization of [0, T], where (i) the first T +1 elements of the grid are the numbers 0, 1, . . . , T ; (ii) the next five elements are equi-spaced numbers in the interval [ T , T 2/3 ]; (iii) the last five elements are equi-spaced numbers in the interval [ T 2/3 , T]. For each value on the grid, call it β, we set τ = min {β + 1, T} and λ = β λscale for a fixed choice of the scaling parameter λscale > 0. For the corresponding output bg of each algorithm, we compute a data-fidelity value using the input pairwise data, as for the data-fidelity term in (16) (with g therein replaced by bg). Then we select the optimal β (thus optimal τ and λ) for each algorithm as follows. (a) For GTRS-Dyn Sync, the optimal β is the value that leads to the largest datafidelity. (b) For LTRS-GS-Dyn Syncand GMD-LTRS-Dyn Sync, the optimal β is chosen to be the value that leads to the maximum change in the slope of the data-fidelity (w.r.t β). |