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Graph neural networks (GNNs) with unsupervised learning can solve large-scale combinatorial optimization problems (COPs) with efficient time complexity, making them versatile for various applications. However, since this method maps the…
We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
Models trained on data composed of different groups or domains can suffer from severe performance degradation under distribution shifts. While recent methods have largely focused on optimizing the worst-group objective, this often comes at…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
Sudoku is a puzzle well-known to the scientific community with simple rules of completion, which may require a com-plex line of reasoning. This paper addresses the problem of partitioning the Sudoku image into a 1-D array, recognizing…
We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component,…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
In this paper, we investigate the trade-off between convergence rate and computational cost when minimizing a composite functional with proximal-gradient methods, which are popular optimisation tools in machine learning. We consider the…
Novel view synthesis for dynamic scenes is still a challenging problem in computer vision and graphics. Recently, Gaussian splatting has emerged as a robust technique to represent static scenes and enable high-quality and real-time novel…
Convolved Gaussian Process (CGP) is able to capture the correlations not only between inputs and outputs but also among the outputs. This allows a superior performance of using CGP than standard Gaussian Process (GP) in the modelling of…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabr\'e, Fontich and…
Gradient clipping is widely used to stabilize deep network training, but its formulation as a hard, fixed threshold limits flexibility and ignores gradient distribution dynamics. We propose SPAMP (Statistical Per-layer Adaptive Modulation…
This study proposes coarse-to-fine spatial modeling (CFSM) as a scalable and machine learning-compatible alternative to conventional spatial process models. Unlike conventional covariance-based spatial models, CFSM represents spatial…
In this paper we study the approximability of (Finite-)Valued Constraint Satisfaction Problems (VCSPs) with a fixed finite constraint language {\Gamma} consisting of finitary functions on a fixed finite domain. An instance of VCSP is given…
We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as ``the simple method'') optimizes a design using only…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…