Related papers: Insights into Ordinal Embedding Algorithms: A Syst…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
We propose practical algorithms for entrywise $\ell_p$-norm low-rank approximation, for $p = 1$ or $p = \infty$. The proposed framework, which is non-convex and gradient-based, is easy to implement and typically attains better…
Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
Learning the intrinsic dimensionality of subjective perceptual spaces such as taste, smell, or aesthetics from ordinal data is a challenging problem. We introduce LORE (Low Rank Ordinal Embedding), a scalable framework that jointly learns…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments…
Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of $n$ points is specified by $n^3$ triplets, making collecting…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…