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Identifying spatially contiguous clusters and repeated spatial patterns (RSP) characterized by similar underlying distributions that are spatially apart is a key challenge in modern spatial statistics. Existing constrained clustering…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
Pre-trained models have achieved success in Chinese Short Text Matching (STM) tasks, but they often rely on superficial clues, leading to a lack of robust predictions. To address this issue, it is crucial to analyze and mitigate the…
In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Mobile channel modeling has always been the core part for design, deployment and optimization of communication system, especially in 5G and beyond era. Deterministic channel modeling could precisely achieve mobile channel description,…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the…
Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A Central Limit Theorem (CLT) is only…
Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for…
For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control algorithm incorporating online model adaptation is proposed. Sets of model parameters are…
Learning from a continuous stream of non-stationary data in an unsupervised manner is arguably one of the most common and most challenging settings facing intelligent agents. Here, we attack learning under all three conditions…
Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent…
Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…
To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…