Related papers: Learning Smooth Distance Functions via Queries
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in \Re^d. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions.…
Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…
Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…
Privacy concerns in distributed learning often lead clients to return intentionally altered gradient information. We consider the problem of learning convex and $L$-smooth functions under adversarial gradient perturbation, where a client's…
Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in…
Recently, recurrent large language models (Recurrent LLMs) with linear computational complexity have re-emerged as efficient alternatives to self-attention-based LLMs (Self-Attention LLMs), which have quadratic complexity. However,…
In the past decades, feature-learning-based 3D shape retrieval approaches have been received widespread attention in the computer graphic community. These approaches usually explored the hand-crafted distance metric or conventional distance…
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn…
We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual…
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…