Related papers: Subspace Learning with Partial Information

Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…

Deep Reinforcement Learning (RL) is mainly studied in a setting where the training and the testing environments are similar. But in many practical applications, these environments may differ. For instance, in control systems, the robot(s)…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polyhedron as an intersection of about $t \log t$…

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

We present a subspace method based on neural networks for solving the partial differential equation in weak form with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

We consider graph drawing algorithms for learning spaces, a type of st-oriented partial cube derived from antimatroids and used to model states of knowledge of students. We show how to draw any st-planar learning space so all internal faces…

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image),…

In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory,…

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…

This work studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features.…

Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…

Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube…

In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense…

Semisupervised learning is a learning standard which deals with the study of how computers and natural systems such as human beings acquire knowledge in the presence of both labeled and unlabeled data. Semisupervised learning based methods…

Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

The "curse of dimensionality" is a well-known problem in pattern recognition. A widely used approach to tackling the problem is a group of subspace methods, where the original features are projected onto a new space. The lower dimensional…

Meta-learning synthesizes and leverages the knowledge from a given set of tasks to rapidly learn new tasks using very little data. Meta-learning of linear regression tasks, where the regressors lie in a low-dimensional subspace, is an…