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.
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…
Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…
This paper tackles variance issues in GNN training by proposing a method to reduce both embedding and gradient variances.
problem High variance in estimating stochastic gradients in GNN training, especially in large graphs.
method The paper proposes a decoupled variance reduction strategy that employs approximate gradient information to adaptively sample nodes with minimal variance.
result The proposed method achieves faster convergence and better generalization compared to existing sampling methods.
Faster convergence of kernel mean embeddings using variance information.
problem Speeding up the convergence rate of kernel mean embeddings.
method Leveraging variance information in reproducing kernel Hilbert space and estimating variance from data.
result Efficiently estimate variance information from data to achieve distribution-agnostic convergence bounds.
New estimator GMIPS reduces variance in ranking policy evaluation.
problem High variance in off-policy evaluation for ranking policies.
method GMIPS estimator with user behavior model on ranking embedding spaces.
result GMIPS achieves lowest MSE and balances bias-variance trade-off.
A new approach selects tuning parameters for embedding methods.
problem Difficulty in selecting tuning parameters for embedding methods.
method Minimize a stress notion to supervise tuning parameter selection.
result Uncover a new bias--variance tradeoff phenomenon.
Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root's work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding p…
Paper explains contrastive learning using cosine similarity and proposes mitigations for batch size effects.
problem Understanding and improving contrastive learning through batch size effects.
method Unified framework of cosine similarity, theoretical insights, and auxiliary loss.
result Performance improvement in small-batch settings through proposed auxiliary loss.
Paper uses JIVE to decompose word embeddings, improving sentiment analysis performance.
problem Improving sentiment analysis performance on word embeddings.
method Joint and individual variance explained (JIVE) method for decomposition.
result Mapping word embeddings into joint components improves sentiment analysis performance.
New algorithm for training GNNs with learned weights.
problem Optimal sampling for GNNs with learned weights is intractable.
method Formulated as an adversary bandit problem, optimizing exploration and exploitation.
result Asymptotically approaches optimal variance within a factor of 3.
CAEL-MIPS learns embeddings to improve MIPS for better OPE in contextual bandits.
problem High variance in IPS weighting for OPE in large action spaces.
method Context-Action Embedding Learning (CAEL) for MIPS to minimize MSE.
result CAEL-MIPS outperforms baselines in MSE for OPE in contextual bandits.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
Proposes MDR estimator for unbiased OPE with large action spaces.
problem Severe bias and variance tradeoffs in OPE with large action spaces.
method Marginalized Doubly Robust (MDR) estimator, reducing variance and bias.
result MDR estimator is unbiased under weaker assumptions than MIPS.
Proposes a new model to optimize investment plans with varying terminal times.
problem Improving the classical mean-variance model for continuous time investments.
method Uses stochastic optimal control and varying terminal time to determine optimal strategies.
result Optimal strategies and terminal times can be determined to minimize portfolio variance.
Anchor PCA improves robustness in multi-domain PCA.
problem PCA on pooled data can focus on spurious directions.
method Anchor PCA focuses on shared directions of variation.
result Anchor PCA outperforms pooling and worst-case alternatives.
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
We seek to better understand the difference in quality of the several publicly released embeddings. We propose several tasks that help to distinguish the characteristics of different embeddings. Our evaluation of sentiment polarity and synonym/antonym relations shows that embeddings are able to capture surprisingly nua…
DTE uses tree leaf means to embed data, balancing accuracy and speed.
problem High variance in decision tree splits and computational inefficiency of ensembles.
method DTE constructs an interpretable feature representation using leaf means of a trained tree.
result DTE strikes a balance between accuracy and computational efficiency, outperforming ensembles.
TSFMs embed non-stationary time series data, revealing specific types of changes.
problem Understanding non-stationarity in TSFMs' embedding spaces.
method Examined mean shifts, variance changes, linear trends, and persistence in TSFMs.
result Different TSFMs exhibit distinct failure modes in detecting non-stationarity.
New OPE estimator improves offline policy evaluation for large action spaces.
problem Existing OPE estimators fail with large action spaces, leading to extreme bias and variance.
method Proposes a new estimator using marginalized importance weights and action embeddings.
result Empirical performance improvement enables reliable OPE even with many actions.
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, colle…
Unified framework for spectral methods, kernel learning, and manifold unfolding.
problem Tackles the unification and optimization of spectral dimensionality reduction methods.
method Unified spectral methods as kernel PCA, kernel learning by SDP, and detailed explanation of MVU variants.
result Unified understanding and optimization of manifold learning techniques.
The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a…
This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear embedding and reinforcement learning. Although existing approaches such as stochastic gr…
Centroid-Encoder reduces high-dimensional data for better visualization.
problem Visualizing high-dimensional data efficiently and accurately.
method Centroid-Encoder integrates label information to keep similar objects close in reduced space.
result Centroid-Encoder outperforms other techniques in visualizing high-dimensional data.
This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR)…
Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang we showed that a…
Optimization can learn Johnson-Lindenstrauss embeddings without randomization.
problem Achieving compact data representations with theoretical guarantees.
method A novel optimization-based approach over the space of random solution samplers.
result The method avoids bad stationary points and converges to a deterministic solution.
Representation learning has recently been successfully used to create vector representations of entities in language learning, recommender systems and in similarity learning. Graph embeddings exploit the locality structure of a graph and generate embeddings for nodes which could be words in a language, products of a re…
A new algorithm reduces the time for ordinal embedding, making it faster and more scalable.
problem Efficiently learning representations from ordinal comparisons, especially for large datasets.
method SVRG-SBB: Stochastic variance reduced gradient with adaptive step size.
result Achieves $O( rac{1}{T})$ convergence rate and global linear convergence under certain assumptions.
Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of the market calibration is the computation of the variance of the asset. Energy commodities are commonly represented by multi-factor linear…
New approach combines PCA and t-sne for better data analysis.
problem Multiscale complexity in high-dimensional data.
method Multiscale joint characterization using PCA and t-sne.
result Joint characterization detects signals not seen by PCA or t-sne alone.
Survey of Locally Linear Embedding and its variants.
problem Representing high-dimensional data in a lower-dimensional space while preserving local structure.
method Explains various LLE and variant methods, including kernel LLE, inverse LLE, feature fusion, out-of-sample embedding, incremental LLE, landmark LLE, supervised LLE, robust LLE, fusion with other methods, and weighted LLE.
result Comprehensive overview of LLE and its variants.
New method learns state embeddings from demonstrations for improved reinforcement learning.
problem Difficult relationship between observed state and useful policy actions in dynamic problems.
method Variational framework for learning state embeddings that optimize trajectory linearity.
result Learning embedding spaces improves policy gradient reinforcement learning performance.
The paper addresses data uncertainty in graph embedding by modeling data points as Gaussian distributions.
problem Data uncertainty in machine learning pipelines leads to misleading embeddings and lower accuracy.
method The paper proposes modeling data uncertainty using Gaussian distributions and reformulates graph embedding techniques.
result The proposed methods improve the accuracy of graph embedding by accounting for data uncertainty.
OPORP combines permutation and random projection for efficient data vector compression.
problem Efficiently estimating cosine similarity in embedding-based retrieval applications.
method OPORP uses a permutation followed by a random vector dot product, then aggregates and normalizes the results into bins.
result OPORP improves the estimation of cosine similarity, reducing variance and improving accuracy.
In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which prevents the direct application of existing modelling tools for complet…
A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.
problem Proxy-based deep metric learning struggles with image uncertainties and class-specific structures.
method Introduces non-isotropic probabilistic proxy-based deep metric learning using directional von Mises-Fisher distributions.
result Improves generalization performance and competitive on standard benchmarks.
Develops a kernel-based framework for dynamic trading strategies.
problem Optimizing portfolios with temporal dependencies in asset dynamics.
method Parameterizes trading strategies as functions in RKHS, enabling flexible, non-Markovian approaches.
result Significantly outperforms classical Markovian methods in synthetic and market-data examples.
Proposes deep hedging for index options using implied volatility surface.
problem Managing risk in index option portfolios with complex dynamics.
method Integrates surface-informed decisions with multiple hedging instruments, accounting for transaction costs and variance risk premium.
result Consistently outperforms traditional hedging strategies across various market conditions.
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability issues for very large datasets. Rahimi and Recht (2007) suggested a popular approa…
To study how mental object representations are related to behavior, we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories. These representations predicted a latent similarity structure between objects, which captured most of the…
Paper introduces S-SSE for stable sparse subspace embedding.
problem Inefficient sparse random projection matrices with uneven non-zero distribution.
method Uses uniform sampling without replacement to create a stable sparse subspace embedded matrix (S-SSE).
result S-SSE maintains Euclidean distance better after dimension reduction.
A new framework for lightweight BNNs learns heteroscedastic uncertainties efficiently.
problem Learning heteroscedastic uncertainties from BNNs for lightweight networks.
method Embedding heteroscedastic variances into BNN parameters and using moment propagation for inference.
result Improves predictive performance for lightweight BNNs without increasing parameter count.
DINOSAUR improves retrieval by accounting for embedding uncertainty in recommender systems.
problem Retrieval bias towards popular items due to noisy embeddings.
method Samples multiple embeddings per item and queries with sampled embeddings to account for uncertainty.
result Improves coverage of long-tail niche content without sacrificing recall.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
problem Node degree heterogeneity in spectral clustering.
method Graph spectral embedding using the random walk Laplacian.
result The embedding provides uniformly consistent estimates of degree-corrected latent positions.
Attention improves edge prediction in e-commerce graphs.
problem Predicting edges in graphs from node attributes in e-commerce.
method Used attention mechanism in simple feedforward networks, derived analytically tractable model AttEST.
result Attention network outperforms LSTM architectures by over 20% on F-1 score.