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The trajectories of diffusion processes are continuous but non-differentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only…

In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially…

Anomaly detection plays a critical role in modern data-driven applications, from identifying fraudulent transactions and safeguarding network infrastructure to monitoring sensor systems for irregular patterns. Traditional approaches, such…

Accurate estimation of the Angle of Progression (AoP) from intrapartum transperineal ultrasound is critical for objective assessment of labor progression, yet remains highly sensitive to imaging noise, boundary ambiguities, and the…

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

Detecting anomalies in time series data is essential for the reliable operation of many real-world systems. Recently, time series foundation models (TSFMs) have emerged as a powerful tool for anomaly detection. However, existing methods…

Oriented object detection is a challenging task in aerial images since the objects in aerial images are displayed in arbitrary directions and are frequently densely packed. The mainstream detectors describe rotating objects using a…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Recognizing 3D objects in the presence of noise, varying mesh resolution, occlusion and clutter is a very challenging task. This paper presents a novel method named Rotational Projection Statistics (RoPS). It has three major modules: Local…

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…

Dense random sampling and surfacing of shapes encoded via implicit occupancy functions (OFs) are critical elements of many applications. Existing methods largely provide either one or the other of random sampling or mesh surfaces: ray…

Traditional tensor decomposition methods, e.g., two dimensional principal component analysis and two dimensional singular value decomposition, that minimize mean square errors, are sensitive to outliers. To overcome this problem, in this…

Field evaporation in atom probe tomography (APT) includes known processes related to surface migration of atoms, such as the so-called roll-up mechanism. They lead to trajectory aberrations and artefacts on the detector. These processes are…

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

In this paper we develop an encounter-based model of a run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ with partially absorbing, sticky boundaries at both ends. We assume that the particle switches between two constant…

This paper proposes an extension of Random Projection Depth (RPD) to cope with multiple modalities and non-convexity on data clouds. In the framework of the proposed method, the RPD is computed in a reproducing kernel Hilbert space. With…

Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers,…

We study estimation and detection of high-order moment and cumulant tensors from $n$ i.i.d.\ observations of a $p$-dimensional random vector, with performance measured in tensor spectral norm. Under sub-Gaussianity, we show that the minimax…

Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical…

Neural processes (NPs) learn stochastic processes and predict the distribution of target output adaptively conditioned on a context set of observed input-output pairs. Furthermore, Attentive Neural Process (ANP) improved the prediction…