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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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121241362482 · Jun 202019922001200920172026
48 results for Leverage Score Sparsified (LESS) Embeddings

New algorithm converts data into sub-gaussian designs efficiently.

problem Efficiently converting large datasets into sub-gaussian random designs for robust performance.
method Algorithmic Gaussianization through sketching and averaging, using LESS embeddings.
result Efficient data sketches nearly indistinguishable from sub-gaussian designs.

A new method reduces the bias in estimating inverse covariance matrices from sketches.

problem Reducing the bias in estimating inverse covariance matrices from sketches.
method Developed a framework for analyzing inversion bias and proposed a new sketching technique called LEverage Score Sparsified (LESS) embeddings.
result The new sketching technique reduces the inversion bias to O(1/d)O(1/\sqrt d) for m=O(d)m=O(d), significantly smaller than the Θ(1)Θ(1) approximation error.

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)dm \geq (1+θ)d non-zeros per column.
result Sparse OSEs can achieve embedding dimension m=O(d)m=O(d), improving on previous m=O(dlog(d))m=O(d\log(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)\tilde O(1/ε) non-zeros per column.

EBMs become opaque in high dimensions; LASSO sparsifies them.

problem Reducing complexity and improving interpretability of EBMs in high-dimensional settings.
method Applying LASSO to reweight and remove less relevant terms from EBMs.
result EBMs maintain transparency and fast scoring times with reduced complexity.

We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence implicitly factorizing a matrix with a closed form, and 2)the explicit factorization o…

2019-06-26abs ↗pdf ↗

The paper examines the consistency of item embeddings in recommendation systems.

problem The relevance of averaging item embeddings for user or concept representation.
method Proposes an expected precision score to measure consistency and analyzes it theoretically and empirically.
result Real-world averages are less consistent for recommendation compared to theoretical assumptions.

Estimates mean of distributed vectors with sparsification and spatial/temporal correlations.

problem Estimating mean of high-dimensional vectors distributed across nodes with low communication cost.
method Modifies decoding method to leverage spatial and temporal correlations in sparsified vectors.
result Estimators consistently outperform more sophisticated sparsification methods.

We give a fast oblivious L2-embedding of ARnxdA\in \mathbb{R}^{n x d} to BRrxdB\in \mathbb{R}^{r x d} satisfying (1ε)Ax22Bx22<=(1+ε)Ax22.(1-\varepsilon)\|A x\|_2^2 \le \|B x\|_2^2 <= (1+\varepsilon) \|Ax\|_2^2. Our embedding dimension rr equals dd, a constant independent of the distortion ε\varepsilon. We use as a black-box any L2-embedding $Π…

2019-09-27abs ↗pdf ↗

We give the first algorithm for kernel Nyström approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of ss landmark points sampled by their *rid…

2016-05-24abs ↗pdf ↗

Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add introspection and error detection capabilities to neural network classifiers. Fir…

2019-05-19abs ↗pdf ↗

Regularization improves spectral embedding by focusing on the largest blocks.

problem Improving the quality of spectral embedding for graph data.
method Explained the impact of complete graph regularization on spectral embedding of a block model.
result Regularization forces spectral embedding to focus on the largest blocks, making it less sensitive to noise or outliers.

Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.

problem Misleading visual artifacts in t-SNE and UMAP due to lack of data-independent manifold learning interpretations.
method LOO-map framework that extends embedding maps to the entire input space, identifying and correcting map discontinuities.
result Developed point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection.

BSAC improves credit scoring models by leveraging autoencoders and addressing imbalanced datasets.

problem Imbalanced and heterogeneous credit scoring datasets.
method Bagging Supervised Autoencoder Classifier (BSAC) that uses autoencoders and undersampling.
result BSAC improves classification of loan applicants, demonstrating robustness and effectiveness.

Spectral graph sparsification preserves geometry of GNN embeddings.

problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.

The statistical leverage scores of a complex matrix ACn×dA\in\mathbb{C}^{n\times d} record the degree of alignment between col(A)(A) and the coordinate axes in Cn\mathbb{C}^n. These score are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebr…

2016-09-29abs ↗pdf ↗

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.

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance i…

2018-03-06abs ↗pdf ↗

We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain provable guarantees, previous work requires randomized sampling of the columns wi…

2014-04-06abs ↗pdf ↗

Generalizes leverage score sampling for neural networks, accelerating kernel methods and deep learning.

problem Accelerating kernel methods and deep learning training.
method Generalizes leverage score sampling to neural networks and proves equivalence to neural tangent kernel ridge regression.
result Equivalence between regularized neural network and neural tangent kernel ridge regression under leverage score sampling initialization.

Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores sampling is a challenge in its own right requiring further approximations. In th…

2018-10-31abs ↗pdf ↗

In order to mimic the human ability of continual acquisition and transfer of knowledge across various tasks, a learning system needs the capability for continual learning, effectively utilizing the previously acquired skills. As such, the key challenge is to transfer and generalize the knowledge learned from one task t…

2019-08-01abs ↗pdf ↗

ECS evaluates synthetic CXR images' distributional fidelity.

problem Evaluating synthetic CXR images' distributional fidelity under privacy constraints.
method Characteristic function transforms of feature embeddings.
result ECS uncovers clinically relevant distributional discrepancies.

Improved bounds for p\ell_p sensitivity sampling reducing the sample complexity for structured matrices.

problem Improving the sample complexity for structured matrices using p\ell_p sensitivity sampling.
method Developed new bounds for p\ell_p sensitivity sampling, achieving a bound of roughly S22/p\mathfrak{S}^{2-2/p} for 2<p<2 < p < \infty.
result Achieved improved bounds for p\ell_p sensitivity sampling, reducing the sample complexity for structured matrices.

Efficiently approximates statistical leverage scores for faster KRR.

problem Accurately estimating statistical leverage scores for fast KRR.
method Analytic formula for statistical leverage scores, leveraging kernel spectral density.
result Linear time approximation with theoretical guarantees, significantly faster than existing methods.

A new model improves CT image quality from low-dose scans.

problem Improving CT image quality from low-dose scans.
method Multi-layer Residual Sparsifying Transform (MRST) learning model for low-dose CT reconstruction.
result The MRST model outperforms conventional methods in maintaining subtle details.

Binary testing for softmax models requires many samples, similar to leverage score models.

problem Binary hypothesis testing for softmax models and leverage score models.
method Analyzing sample complexity and drawing analogies between models.
result Sample complexity is asymptotically \(O(ε^{-2})\), where \(ε\) is the distance between model parameters.

Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which sample queries based on informativeness or representativeness of unlabeled data poi…

2015-07-15abs ↗pdf ↗

In many real-world machine learning applications, unlabeled data are abundant whereas class labels are expensive and scarce. An active learner aims to obtain a model of high accuracy with as few labeled instances as possible by effectively selecting useful examples for labeling. We propose a new selection criterion tha…

2018-12-06abs ↗pdf ↗

Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression quality often fail to distinguish between embeddings that perform well and those th…

2019-09-03abs ↗pdf ↗

SALSA efficiently approximates leverage scores for big data, improving ARMA model fitting.

problem Efficiently approximating leverage scores for large matrices.
method Sequential approximate leverage-score algorithm (SALSA) using randomized numerical linear algebra.
result SALSA approximates leverage scores within (1+O(ε))(1 + O({\varepsilon})) with high probability.

Quizlet is the most popular online learning tool in the United States, and is used by over 2/3 of high school students, and 1/2 of college students. With more than 95% of Quizlet users reporting improved grades as a result, the platform has become the de-facto tool used in millions of classrooms. In this paper, we expl…

2018-09-21abs ↗pdf ↗