Related papers: Nonlinear Dimensionality Reduction via Path-Based …
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…
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…
Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…
We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…
In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…
Many important applications, including signal reconstruction, parameter estimation, and signal processing in a compressed domain, rely on a low-dimensional representation of the dataset that preserves {\em all} pairwise distances between…
The isometric mapping method employs the shortest path algorithm to estimate the Euclidean distance between points on High dimensional (HD) manifolds. This may not be sufficient for weakly uniformed HD data as it could lead to…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…
This paper proposes a boosting-based solution addressing metric learning problems for high-dimensional data. Distance measures have been used as natural measures of (dis)similarity and served as the foundation of various learning methods.…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
In some memory-constrained settings like IoT devices and over-the-network data pipelines, it can be advantageous to have smaller contextual embeddings. We investigate the efficacy of projecting contextual embedding data (BERT) onto a…