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A Newton--Kantorovich-type argument enables the a posteriori existence verification of a unique regular root near a computed approximation, purely from computable data. This framework allows for non-selfadjoint problems and extends the…
Structural Nested Mean Models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at pre-fixed time points for all subjects, which,…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
There is a family of label modification approaches including self and non-self label correction (LC), and output regularisation. They are widely used for training robust deep neural networks (DNNs), but have not been mathematically and…
We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…
Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model…
Simulated Moving Bed (SMB) chromatography is a well-known technique for the resolution of several high-value-added compounds. Parameters identification and model topology definition are arduous when one is dealing with complex systems such…
Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many…
Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…
Negative sequential pattern mining (SPM) is an important SPM research topic. Unlike positive SPM, negative SPM can discover events that should have occurred but have not occurred, and it can be used for financial risk management and fraud…
Uncertainty estimation in Neural Networks (NNs) is vital in improving reliability and confidence in predictions, particularly in safety-critical applications. Bayesian Neural Networks (BayNNs) with Dropout as an approximation offer a…
In this paper, we construct novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary…
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…
Deep-learning methods have shown promising performance for low-dose computed tomography (LDCT) reconstruction. However, supervised methods face the problem of lacking labeled data in clinical scenarios, and the CNN-based unsupervised…
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
The synthetic control method (SCM) is widely used for constructing the counterfactual of a treated unit based on data from control units in a donor pool. Allowing the donor pool contains more control units than time periods, we propose a…
Structural Health Monitoring (SHM) provides an economic approach which aims to enhance understanding the behavior of structures by continuously collects data through multiple networked sensors attached to the structure. This data is then…
It has long remained open whether smoothing Newton methods (SNMs) for symmetric cone programming (SCP) admit polynomial iteration complexity. A key difficulty lies in the lack of an analogue of the self-concordant convex framework…