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Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…
The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…
Recent studies of multimodal industrial anomaly detection (IAD) based on 3D point clouds and RGB images have highlighted the importance of exploiting the redundancy and complementarity among modalities for accurate classification and…
Detecting out-of-distribution (OOD) samples is important for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. Existing research has mainly focused on unimodal scenarios…
Equivocal 3D lesion segmentation exhibits high inter-observer variability. Conventional deterministic models ignore this aleatoric uncertainty, producing over-confident masks that obscure clinical risks. Conversely, while generative methods…
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
In recent years, the rapid development of deep neural networks has brought increased attention to the security and robustness of these models. While existing adversarial attack algorithms have demonstrated success in improving adversarial…
In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…
Uncertainty quantification is critical in scientific inverse problems to distinguish identifiable parameters from those that remain ambiguous given available measurements. The Conditional Diffusion Model-based Inverse Problem Solver (CDI)…
Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…
Multimodal sentiment analysis (MSA) aims to understand human sentiment through multimodal data. In real-world scenarios, practical factors often lead to uncertain modality missingness. Existing methods for handling modality missingness are…
Diffusion distillation represents a highly promising direction for achieving faithful text-to-image generation in a few sampling steps. However, despite recent successes, existing distilled models still do not provide the full spectrum of…