Related papers: GOGMA: Globally-Optimal Gaussian Mixture Alignment
Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning,…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
Constructing precise global maps is a key task in robotics and is required for localization, surveying, monitoring, or constructing digital twins. To build accurate maps, data from mobile 3D LiDAR sensors is often used. Mapping requires…
This paper introduces LiGSM, a novel LiDAR-enhanced 3D Gaussian Splatting (3DGS) mapping framework that improves the accuracy and robustness of 3D scene mapping by integrating LiDAR data. LiGSM constructs joint loss from images and LiDAR…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
This study proposes a new Gaussian Mixture Filter (GMF) to improve the estimation performance for the autonomous robotic radio signal source search and localization problem in unknown environments. The proposed filter is first tested with a…
This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This…
In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications such as GANs. Large-scale edge-based collection of training data in these applications calls for…
We prove the existence of an algorithm $A$ for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every sequence $\sigma$ of $n$ points and for every algorithm $A'$ in a certain class…
Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…
Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However,…
Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation ($\boldsymbol{\theta}$) and correspondence ($\mathbf{P}$) estimation has…
The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be…
Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…
In this paper, we present SeGMan, a hybrid motion planning framework that integrates sampling-based and optimization-based techniques with a guided forward search to address complex, constrained sequential manipulation challenges, such as…
Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only…
A global navigation satellite system (GNSS) is a sensor that can acquire 3D position and velocity in an earth-fixed coordinate system and is widely used for outdoor position estimation of robots and vehicles. Various GNSS/inertial…
We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the…