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.
Unified methods for fast column selection in various applications.
Unified theory and debiasing framework for random oblique projections in high dimensions.
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces . The similarity matrices thus c…
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast …
The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advanta…
The CUR decomposition provides an approximation of a matrix that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of . In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithm…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for computing U. In this work, we aim to alleviate this limitation. In particular, …
This thesis explores fast algorithms for large matrices and data augmentation to improve model efficiency.
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample specific individual rows or columns of the matrix is limited by either system constrain…
Introduces t-CCS for flexible tensor sampling.
A new NMF model for co-clustering and data approximation.
We present a method for fast resting-state fMRI spatial decomposi-tions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest …
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the ca…
Fast and accurate methods for low-rank learning problems.
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of h…
Neural-ANOVA breaks down neural networks into simpler models.
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in order to demonstrate the versatility of our method. These include: European opt…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…
How can we find patterns and anomalies in a tensor, or multi-dimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and anomalies in a tensor is a crucial problem with many applications, including buildi…
Paper speeds up Gaussian process inference using Matérn kernels.
A new algorithm speeds up matrix operations in Neural Networks.
Q-SHAP efficiently calculates feature contributions in boosting trees.
Improved graph-based multiclass classification for multilayer data.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
In this article, we initiate a geometric measure theoretic approach to symplectic Hodge theory. In particular, we apply one of the central results in geometric measure theory, the Federer-Fleming deformation theorem, together with the cohomology theory of normal cur- rents on a differential manifold, to establish a fun…
We accelerate the power method for strong low-rank approximation using fast sketching.
We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our algorithms can decompose a 4-tensor with -dimensional orthonormal components in the…
A robust method for decomposing spectral peaks robust to distortion and interference.
Paper explores robustness of CCS model for matrix completion.
New SPD metrics improve stability and efficiency in neural networks.
New method for uncertainty analysis in TabPFN, a state-of-the-art tabular transformer.
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To bui…
Revisits CP tensor decomposition for noisy, non-orthogonal data.
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performa…
Optimized DMD for fast atmospheric chemistry forecasting.
Paper solves open question about non-positive kernels by decomposing them into PD kernels.
A new method selects variables efficiently for fast and accurate dynamic system identification.
Efficient CF approach using fast adaptive PCA for recommender systems.
Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization method for NCP that can impose sparsity efficiently is required. In this paper, we co…
We consider the problem of Graphical lasso with an additional element-wise norm constraint on the precision matrix. This problem has applications in high-dimensional covariance decomposition such as in \citep{Janzamin-12}. We propose an ADMM algorithm to solve this problem. We also use a continuation st…
We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank tensor completion problem. We propose a novel online tensor subspace tracking al…
Improved SVM classification with interpretable features from scattered data.
Designing efficient and robust algorithms for accurate prediction of stock market prices is one of the most exciting challenges in the field of time series analysis and forecasting. With the exponential rate of development and evolution of sophisticated algorithms and with the availability of fast computing platforms, …
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the conjugacy problem that is successful for random braids in overwhelming probabilit…
New algorithm for decomposing multidimensional, non-stationary signals.