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Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…
In a noiseless linear estimation problem, one aims to reconstruct a vector x* from the knowledge of its linear projections y=Phi x*. There have been many theoretical works concentrating on the case where the matrix Phi is a random i.i.d.…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
For nonlinear inverse problems that are prevalent in imaging science, symmetries in the forward model are common. When data-driven deep learning approaches are used to solve such problems, these intrinsic symmetries can cause substantial…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…
Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…
Neural networks are omnipresent, but remain poorly understood. Their increasing complexity and use in critical systems raises the important challenge to full interpretability. We propose to address a simple well-posed learning problem:…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
This paper addresses the following questions pertaining to the intrinsic dimensionality of any given image representation: (i) estimate its intrinsic dimensionality, (ii) develop a deep neural network based non-linear mapping, dubbed…
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…
Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…
We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at…
While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…
Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses…
The underspecification of most machine learning pipelines means that we cannot rely solely on validation performance to assess the robustness of deep learning systems to naturally occurring distribution shifts. Instead, making sure that a…