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We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…

We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. PaLD is best known for unsupervised, parameter-free clustering, but its robustness is based…

Density-adaptive domain discretization is essential for high-utility privacy-preserving analytics but remains challenging under Local Differential Privacy (LDP) due to the privacy-budget costs associated with iterative refinement. We…

Reconstructing large-scale latent networks from observed dynamics is crucial for understanding complex systems. However, the existing methods based on compressive sensing are often rendered infeasible in practice by prohibitive…

Histograms are among the most popular methods used in exploratory analysis to summarize univariate distributions. In particular, irregular histograms are good non-parametric density estimators that require very few parameters: the number of…

We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…

Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous…

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…

To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because…

Domain generalization aims to learn a generalization model that can perform well on unseen test domains by only training on limited source domains. However, existing domain generalization approaches often bring in prediction-irrelevant…

Fine-grained image classification remains challenging due to the large intra-class variance and small inter-class variance. Since the subtle visual differences are only in local regions of discriminative parts among subcategories, part…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

The Minimum Description Length (MDL) principle is solidly based on a provably ideal method of inference using Kolmogorov complexity. We test how the theory behaves in practice on a general problem in model selection: that of learning the…

Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…

We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…

Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…

This paper proposes a novel pixel-level distribution regularization scheme (DRSL) for self-supervised domain adaptation of semantic segmentation. In a typical setting, the classification loss forces the semantic segmentation model to…