The paper solves a stability issue in pricing derivatives using optimal Skorokhod embedding.
problem Optimizing the Skorokhod embedding problem for derivative pricing.
method Derives dualities and geometric characterizations, analyzes convergence rates.
result The optimization problem converges to an optimal Skorokhod embedding problem as more prices are given.
This paper tackles efficient optimization for nonlinear embeddings in similarity learning.
problem Learning similarity with nonlinear embeddings is challenging due to the large number of pairs.
method Detailed derivations and efficient optimization methods for nonlinear embeddings are developed.
result Efficient optimization methods for nonlinear embeddings are shown to be highly effective.
EGORSE optimizes high-dimensional problems using random and supervised embeddings.
problem Efficiently solving computationally expensive high-dimensional optimization problems.
method EGORSE combines random and supervised linear embeddings for adaptive optimization.
result EGORSE outperforms state-of-the-art methods in high-dimensional optimization.
Study optimal Skorokhod embedding problem for Brownian motion.
problem Optimizing stopping times for Brownian motion with given distribution.
method Weak density of stopping times, dual optimization, compactness property.
result Existence of dual solutions and absence of duality gap for irregular reward functions.
Proposes spherical text embedding for better directional similarity.
problem Directional similarity is more effective but unsupervised text embeddings are typically learned in Euclidean space.
method Develops a spherical generative model and an efficient optimization algorithm for unsupervised word and paragraph embeddings.
result Achieves state-of-the-art performances on various text embedding tasks.
Proposes TECU framework for efficient non-convex optimization.
problem Multivariate non-convex optimization problems with coupled objective functions.
method Embeds task-specific strategies into coordinate descent update schemes.
result Demonstrates improved efficiency and effectiveness in solving practical problems.
Paper proposes a new word embedding method optimizing word similarity.
problem Optimizing word similarity in embedding space.
method Two-step random walks between words via topics to learn an optimal embedding simplex.
result Our method outperforms existing approaches in various queries.
NIS learns optimal embedding sizes for recommendation models.
problem Finding optimal embedding sizes for large-scale recommendation models.
method Neural Input Search (NIS) uses reinforcement learning to automatically find optimal vocabulary sizes and embedding dimensions.
result NIS improves prediction accuracy by 6.8% on Recall@1 and 1.8% on ROC-AUC.
This paper examines linear embeddings for high-dimensional Bayesian optimization, identifying and addressing issues to improve performance.
problem Scaling Bayesian optimization to high-dimensional spaces while maintaining sample efficiency.
method Study and empirical evaluation of linear embeddings for BO, addressing design choices and their impact on performance.
result Properly addressing issues in linear embeddings significantly improves their efficacy in BO.
SA-REMBO adapts to nonstationary high-dimensional optimization.
problem Bayesian Optimization in high-dimensional spaces is limited by the curse of dimensionality and rigidity of global assumptions.
method SA-REMBO uses multiple random Gaussian embeddings and an index variable to adaptively select the best embedding for the optimization problem.
result SA-REMBO outperforms traditional REMBO and other low-rank BO methods across synthetic and real-world benchmarks.
Sparse OSEs achieve optimal embedding dimension of O(d).
problem Achieving optimal embedding dimension for sparse OSEs.
method Random sparsified matrix with m≥(1+θ)d non-zeros per column. result Sparse OSEs can achieve embedding dimension m=O(d), improving on previous m=O(dlog(d)). Optimal subspace embedding with near-optimal sparsity for high-dimensional data.
problem Efficiently preserving norms of vectors in high-dimensional subspaces.
method Near-optimal sparsity oblivious subspace embedding with decoupling argument and cumulant method.
result Achieved near-optimal sparsity of O~(1/ε) non-zeros per column. Binary embeddings speed up graph data retrieval.
problem Efficiently retrieving graphical data.
method Binary valued embeddings modeled as coin flips with varying bias, optimized using continuous optimization techniques.
result Binary embeddings outperform other methods on various datasets.
Optimal bounds proven for ordinal embedding convergence rate.
problem Optimal bounds for ordinal embedding convergence rate in 1D.
method Utilized results from additive number theory and conducted computational experiments.
result Proved optimal bounds for convergence rate in 1D.
Optimizes global optimization with random embeddings by defining a minimal low-dimensional domain.
problem Complexity in defining bounds for a low-dimensional domain under box constraints.
method Detailed study of random embedding properties, minimal low-dimensional set definition, and alternative embedding procedure.
result Enhanced performance and robustness in global optimization with random embeddings.
This note optimizes distributions using kernel mean embeddings with a new parameterization.
problem Optimizing distributions using kernel mean embeddings is challenging due to the difficulty of characterizing probability distribution vectors.
method Proposes a new parameterization of positive functions using kernel sums-of-squares to fit distributions in the MMD geometry.
result Distributions with kernel sum-of-squares densities are dense in the MMD geometry, allowing optimization in the finite-sample setting.
PyKEEN 1.0 simplifies KGE model creation and optimization.
problem Training and evaluating knowledge graph embeddings (KGEs).
method Composes KGEMs with various interaction models, training approaches, and loss functions. Implements automatic memory optimization and extensive HPO functionalities.
result PyKEEN 1.0 streamlines KGE model creation and optimization.
This work improves understanding of dimension reduction algorithms and their probabilistic embeddings.
problem Improving theoretical understanding of non-linear dimension reduction algorithms.
method Analytical investigation of a generalized multidimensional scaling optimization problem.
result Probabilistic formulation of the problem leads to deterministic embeddings, contrary to standard implementations.
New insights show embedding lengths correlate with semantic properties.
problem Contrastive embedding norms ignore embedding magnitudes but correlate with semantic properties.
method Formal theoretical framework and analysis of optimization dynamics.
result Embedding lengths encode semantic information as a byproduct of training.
This work optimizes induced correlation in joint graph embeddings.
problem Optimizing correlation across embedded networks in joint graph embeddings.
method Developed corr2Omni algorithm to estimate optimal Omnibus weights.
result corr2Omni algorithm improves inference fidelity compared to classical Omnibus construction.
Develops techniques to align word embeddings from different sources.
problem Aligning word embeddings from diverse datasets or methods.
method Simple closed-form techniques for optimal rotation, translation, and scaling.
result Maximizes cosine similarity and minimizes root mean squared errors.
Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.
problem Challenges in Euclidean embedding from noisy observations containing outliers.
method Matrix optimization based embedding model to detect and remove outliers.
result The model provides high accuracy estimators and successfully identifies outliers.
Optimizes embedding accuracy for data variance and error.
problem Efficiently embedding data while minimizing distortion.
method Uses Johnson-Lindenstrauss embeddings with orthogonal matrices and singular-value latent variables.
result Achieves best accuracy in variance, mean-squared error, and length distortion.
Equivalence found between two types of embeddings for Kähler manifolds.
problem Equivalence between two types of embeddings for Kähler manifolds.
method GIT characterization and action of automorphism group on Chow line.
result Equivalence of σ-balanced and balanced embeddings. Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
Proposes TTNPE for tensor data embedding with improved trade-offs.
problem Embedding multi-dimensional tensor data into low dimensions.
method Tensor Train Neighborhood Preserving Embedding (TTNPE) with novel optimization approaches.
result Improves classification, computation, and dimensionality reduction trade-offs.
Optimal martingale transport plans without structural assumptions.
problem Finding optimal martingale transport plans.
method Left-monotone martingale coupling and Skorokhod embedding.
result Left-monotone coupling is optimal under specific conditions.
Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.
problem Training neural networks to global optimality via convex optimization.
method Randomized algorithms in Clifford's Geometric Algebra for hypercomplex vector spaces.
result Convex optimization and geometric algebra improve LLMs' robustness and reliability in transfer learning.
Paper explains word embedding dimensionality and proposes a new metric.
problem Understanding the optimal dimensionality of word embeddings.
method Proposed Pairwise Inner Product (PIP) loss to measure dissimilarity.
result Revealed a bias-variance trade-off in dimensionality selection.
This paper improves topic modeling by embedding words and topics together.
problem Topic models struggle with short documents and approximate inference.
method Model each document as a mixture of word embeddings and each topic as a mixture of topic embeddings.
result The method optimizes topic embeddings to minimize semantic differences between words and topics.
Estimates for graph embeddings into symmetric spaces derived from coarse geometry.
problem Estimating optimal volume of graph embeddings into symmetric spaces.
method Coarse geometric thick embeddings and wiring techniques.
result Optimal and lower bounds for graph embeddings in symmetric spaces of different ranks.
Novel approach to OT using kernel mean embeddings controls overfitting and achieves dimension-free sample complexity.
problem Consistently estimate optimal transport plan from samples.
method Pose OT as learning kernel mean embedding, employ MMD regularization.
result ε-optimal recovery of transport plan and map with dimension-free sample complexity.
Kernel-embedding tests can be suboptimal, but a simple modification improves their performance.
problem Optimizing goodness-of-fit tests using kernel embeddings.
method Analyzing and modifying kernel-embedding based goodness-of-fit tests within a minimax framework.
result A moderated kernel-embedding approach provides optimal tests for various deviations and is adaptive over a wide range of spaces.
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.
problem Integrating multiple representations of the same samples in heterogeneous geometries.
method Gromov-Wasserstein optimal transport for multi-view embedding.
result Preserves intrinsic relational structure across views effectively.
Bayesian optimization for high-dimensional combinatorial spaces using embeddings.
problem Optimizing expensive functions over large, complex input spaces.
method Dictionary-based ordinal embeddings for high-dimensional combinatorial structures, using Gaussian process models.
result The proposed method outperforms state-of-the-art BO methods on diverse real-world benchmarks.
Proposes a novel framework for graph matching and node embedding.
problem Graph matching and node embedding in real-world networks.
method Gromov-Wasserstein discrepancy for graph dissimilarity, optimal transport for correspondence, structural regularizers for learning.
result Superior performance in graph matching compared to alternative approaches.
New approach solves multi-marginal Skorokhod Embedding Problem.
problem Solving multi-marginal Skorokhod Embedding Problem.
method Extending theory from one-marginal to multi-marginal setup.
result All classical optimal embeddings have natural multi-marginal counterparts.
A new method embeds distributions in a common space for optimal transport comparison.
problem Comparing distributions in different metric spaces.
method Sub-embedding robust Wasserstein (SERW) distance.
result SERW mimics GW distance properties and provides a cost relation.
This research embeds data as discrete probability distributions in Wasserstein spaces, capturing semantic structures more effectively.
problem Limitations of Euclidean embeddings in capturing latent semantic structures.
method Learning embeddings into entropic Wasserstein spaces, capturing semantic information in Wasserstein distance.
result Wasserstein embeddings can embed a wider variety of metric structures with smaller distortion than Euclidean embeddings.
Poincaré embeddings learn hierarchical symbolic data representations.
problem Learning hierarchical representations for complex symbolic data like text and graphs.
method Embedding into hyperbolic space (Poincaré ball) for efficient Riemannian optimization.
result Poincaré embeddings outperform Euclidean embeddings on data with latent hierarchies.
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
Study linearizes 2-Wasserstein space using optimal transport maps.
problem Stability and linearization of the 2-Wasserstein space.
method Explicit embedding of probability measures into a Hilbert space using optimal transport maps.
result The embedding is (bi-)Hölder continuous, with stability results for optimal transport maps.
New algorithm speeds up model optimization for time series data.
problem Slow convergence in model optimization due to continuous symmetry.
method Gauge theory-inspired optimization algorithm.
result Orders of magnitude faster convergence and interpretable representations.
Paper improves data embeddings with Lagrange duality.
problem Near isometric orthogonal embeddings for data points.
method Formulated as non-convex optimization, used Lagrange duality for relaxation, and provided a polynomial time algorithm.
result Achieved better approximation guarantees and lower distortion compared to baselines.
Autoencoder optimizes data embedding for accurate PDF reproduction.
problem Inaccurate PDF reproduction in latent space of VAEs.
method Rate-Distortion Optimization guided autoencoder with isometric property.
result Our method achieves isometric data embedding and tractable PDF relations.
Study optimizes learning rates for conditional mean embedding estimates.
problem Consistency of kernel ridge regression for conditional mean embedding.
method Adaptive statistical learning rate derived for misspecified setting.
result Upper bound matches optimal O(logn/n) rates without assuming finite dimensionality. A new forecasting framework uses suboptimal embeddings to improve multivariate time series prediction.
problem Randomly selecting embeddings or brute force methods often lead to suboptimal forecasts.
method Develops a framework that uses various suboptimal embeddings obtained via combinatorial optimization.
result Achieves the best results among existing frameworks for various datasets.