相关论文: Out-of-sample generalizations for supervised manif…
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…
We consider the problem of vertex classification for graphs constructed from the latent position model. It was shown previously that the approach of embedding the graphs into some Euclidean space followed by classification in that space can…
The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Common dimensionality reduction methods embed a set of fixed, latent points, but are not capable of…
This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…
We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered.…
Semi-supervised learning is becoming increasingly important because it can combine data carefully labeled by humans with abundant unlabeled data to train deep neural networks. Classic methods on semi-supervised learning that have focused on…
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Understanding how agents learn to generalize -- and, in particular, to extrapolate -- in high-dimensional, naturalistic environments remains a challenge for both machine learning and the study of biological agents. One approach to this has…
Impressive advances in acquisition and sharing technologies have made the growth of multimedia collections and their applications almost unlimited. However, the opposite is true for the availability of labeled data, which is needed for…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
Despite the data labeling cost for the object detection tasks being substantially more than that of the classification tasks, semi-supervised learning methods for object detection have not been studied much. In this paper, we propose an…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
This paper addresses the problem of accurately estimating a function on one domain when only its discrete samples are available on another domain. To answer this challenge, we utilize a neural network, which we train to incorporate prior…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…
Unsupervised embedding learning aims to extract good representation from data without the need for any manual labels, which has been a critical challenge in many supervised learning tasks. This paper proposes a new unsupervised embedding…
Recent semi-supervised learning methods have shown to achieve comparable results to their supervised counterparts while using only a small portion of labels in image classification tasks thanks to their regularization strategies. In this…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
The problem of regression extrapolation, or out-of-distribution generalization, arises when predictions are required at test points outside the range of the training data. In such cases, the non-parametric guarantees for regression methods…