Related papers: Local transfer learning from one data space to ano…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…
Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an explicit model of the phenomenon or the measurement…
Reducing domain divergence is a key step in transfer learning problems. Existing works focus on the minimization of global domain divergence. However, two domains may consist of several shared subdomains, and differ from each other in each…
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…
Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…
The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…
Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…
Transfer learning is a popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. It has enjoyed numerous empirical successes and inspired a growing number of theoretical studies.…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
In this study, we develop a method for multi-task manifold learning. The method aims to improve the performance of manifold learning for multiple tasks, particularly when each task has a small number of samples. Furthermore, the method also…
Federated learning enables many applications benefiting distributed and private datasets of a large number of potential data-holding clients. However, different clients usually have their own particular objectives in terms of the tasks to…
Transfer learning refers to the transfer of knowledge or information from a relevant source task to a target task. However, most existing works assume both tasks are sampled from a stationary task distribution, thereby leading to the…
A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…
Meta-learning algorithms adapt quickly to new tasks that are drawn from the same task distribution as the training tasks. The mechanism leading to fast adaptation is the conditioning of a downstream predictive model on the inferred…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
Flow-based models typically define a latent space with dimensionality identical to the observational space. In many problems, however, the data does not populate the full ambient data space that they natively reside in, rather inhabiting a…
We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…