arXiv research

This paper tackles efficient optimization for nonlinear embeddings in similarity learning.

EGORSE optimizes high-dimensional problems using random and supervised embeddings.

SA-REMBO adapts to nonstationary high-dimensional optimization.

Sparse OSEs achieve optimal embedding dimension of O(d).

Optimal subspace embedding with near-optimal sparsity for high-dimensional data.

Motivated by the model- independent pricing of derivatives calibrated to the real market, we consider an optimization problem similar to the optimal Skorokhod embedding problem, where the embedded Brownian motion needs only to reproduce a finite number of prices of Vanilla options. We derive in this paper the correspon…

This note optimizes distributions using kernel mean embeddings with a new parameterization.

PyKEEN 1.0 simplifies KGE model creation and optimization.

This work improves understanding of dimension reduction algorithms and their probabilistic embeddings.

Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying b…

We in this paper propose a realizable framework TECU, which embeds task-specific strategies into update schemes of coordinate descent, for optimizing multivariate non-convex problems with coupled objective functions. On one hand, TECU is capable of improving algorithm efficiencies through embedding productive numerical…

New insights show embedding lengths correlate with semantic properties.

This work optimizes induced correlation in joint graph embeddings.

Optimizes embedding accuracy for data variance and error.

Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.

We study the problem of stopping a Brownian motion at a given distribution $ν$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set $\mathcal{T}(ν)$ of stopping times embedding $ν$ is weakly dense in the set $\mathc…

Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.

Unsupervised text embedding has shown great power in a wide range of NLP tasks. While text embeddings are typically learned in the Euclidean space, directional similarity is often more effective in tasks such as word similarity and document clustering, which creates a gap between the training stage and usage stage of t…

Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.

Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity in embedding space is not optimized in the learning. In this paper we propose a …

In this paper, we provide a theoretical understanding of word embedding and its dimensionality. Motivated by the unitary-invariance of word embedding, we propose the Pairwise Inner Product (PIP) loss, a novel metric on the dissimilarity between word embeddings. Using techniques from matrix perturbation theory, we revea…

This paper improves topic modeling by embedding words and topics together.

Estimates for graph embeddings into symmetric spaces derived from coarse geometry.

Recommendation problems with large numbers of discrete items, such as products, webpages, or videos, are ubiquitous in the technology industry. Deep neural networks are being increasingly used for these recommendation problems. These models use embeddings to represent discrete items as continuous vectors, and the vocab…

Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensi…

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem to the case of finitely-many marginal constraints. Using the classic…

Proposes Gromov-Wasserstein methods for multi-view embedding.

Bayesian optimization for high-dimensional combinatorial spaces using embeddings.

For a polarized Kähler manifold $(X, L)$, we show the equivalence between relative balanced embeddings introduced by Mabuchi and $σ$-balanced embeddings introduced by Sano, answering a question of Hashimoto. We give a GIT characterization of the existence of a $σ$-balanced embedding, and relate the optimal weight $σ$ t…

A new method embeds distributions in a common space for optimal transport comparison.

NNLMs optimize poorly for word probabilities due to embedding space structure.

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. S…

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 theory on sets of integers with no three-term arithmetic progressions. We also carr…

This work studies an explicit embedding of the set of probability measures into a Hilbert space, defined using optimal transport maps from a reference probability density. This embedding linearizes to some extent the 2-Wasserstein space, and enables the direct use of generic supervised and unsupervised learning algorit…

Study optimizes learning rates for conditional mean embedding estimates.

Improved bound for optimal Moebius band aspect ratio.

We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the averag…

The article calculates the near horizon limit of Wang--Yau quasi-local mass.

New algorithm reduces sketching dimension to effective problem size.

LPL optimizes embeddings to align local neighborhoods, improving cross-lingual word alignment.

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the…

AMES framework selects optimal embedding space for latent graph inference.

SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.

Embedding principle explains loss landscape of deep neural networks.

A new method speeds up SoftMax normalization for embedding learning.

The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sam…

New method learns state embeddings from demonstrations for improved reinforcement learning.

A new method for hierarchical clustering using continuous embeddings and optimization.