Related papers: Subspace Learning with Partial Information

Meta-learning, or "learning to learn," is a subfield of machine learning where the goal is to develop models and algorithms that can learn from various tasks and improve their learning process over time. Unlike traditional machine learning…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…

We study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces…

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…

We study non-convex empirical risk minimization for learning halfspaces and neural networks. For loss functions that are $L$-Lipschitz continuous, we present algorithms to learn halfspaces and multi-layer neural networks that achieve…

Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to…

In this work we provide an analysis of the distribution of the post-adaptation parameters of Gradient-Based Meta-Learning (GBML) methods. Previous work has noticed how, for the case of image-classification, this adaptation only takes place…

We investigate the generalization properties of a self-training algorithm with halfspaces. The approach learns a list of halfspaces iteratively from labeled and unlabeled training data, in which each iteration consists of two steps:…

We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…

Deep networks are successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are usually much less suited for semi-supervised problems because of…

We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as…

Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…

In lifelong learning, a learner faces a sequence of tasks with shared structure and aims to identify and leverage it to accelerate learning. We study the setting where such structure is captured by a common representation of data. Unlike…

Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network…

Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are…

We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…

Recent research has seen numerous supervised learning-based methods for 3D shape segmentation and remarkable performance has been achieved on various benchmark datasets. These supervised methods require a large amount of annotated data to…