相关论文: Topological Learning for Motion Data via Mixed Coo…

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…

Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden…

Clustering mixed data presents numerous challenges inherent to the very heterogeneous nature of the variables. A clustering algorithm should be able, despite of this heterogeneity, to extract discriminant pieces of information from the…

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…

Meta-learning is a powerful approach that exploits historical data to quickly solve new tasks from the same distribution. In the low-data regime, methods based on the closed-form posterior of Gaussian processes (GP) together with Bayesian…

Federated learning is an active research topic since it enables several participants to jointly train a model without sharing local data. Currently, cross-silo federated learning is a popular training setting that utilizes a few hundred…

Universal time series representation learning is challenging but valuable in real-world applications such as classification, anomaly detection, and forecasting. Recently, contrastive learning (CL) has been actively explored to tackle time…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…

We describe a method for utilizing the known structure of input data to make learning more efficient. Our work is in the domain of programming languages, and we use deep neural networks to do program analysis. Computer programs include a…

Geological process models simulate a range of dynamic processes to evolve a base topography into a final 2D cross-section or 3D geological scenario. In principle, process parameters may be updated to better align with observed geophysical…

We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…

Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges…

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…