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.
This paper optimizes object tracking on edge devices with small matrices.
The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which c…
This article provides a new toolbox to derive sparse recovery guarantees from small deviations on extreme singular values or extreme eigenvalues obtained in Random Matrix Theory. This work is based on Restricted Isometry Constants (RICs) which are a pivotal notion in Compressed Sensing and High-Dimensional Statistics a…
New method estimates large matrices' spectra from small sub-matrices.
New algorithms improve RPCA for large matrices with upper rank bounds.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
New methods for sketching non-PSD matrices improve regression and optimization tasks.
We study the problem of learning overcomplete HMMs---those that have many hidden states but a small output alphabet. Despite having significant practical importance, such HMMs are poorly understood with no known positive or negative results for efficient learning. In this paper, we present several new results---both po…
Estimates matrix trace optimization with statistical learning theory.
New framework finds more efficient linear layers over structured matrices.
Two algorithms estimate Wasserstein distance matrices from few entries for manifold learning.
Rank-one measurements limit feasible sets for low-rank PSD matrices.
New technique stabilizes singular values in concatenated matrices.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…
A new matrix concentration inequality for random products of matrices.
The properties of q-dependent cross-correlation matrices of stock market have been analyzed by using the random matrix theory and complex network. The correlation structures of the fluctuations at different magnitudes have unique properties. The cross-correlations among small fluctuations are much stronger than those a…
Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we…
New estimator learns symmetric dynamics from few observations.
New bound for neural networks with full-rank weights, independent of network width.
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA), MMF teased out hierarchical structure in symmetric matrices by constructing a se…
The paper studies stochastic optimization on matrices and its limits as dimensions grow.
Study small eigenvalues of Toeplitz operators and their relation to Mabuchi geodesics.
In this work we systematically analyze general properties of differential equations used as machine learning models. We demonstrate that the gradient of the loss function with respect to to the hidden state can be considered as a generalized momentum conjugate to the hidden state, allowing application of the tools of c…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different machines. We address communication efficiency by proposing a method where, in a si…
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, …
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c >= rank(A) columns depend on the right singular vector matrix of A. For a Monte-…
Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…
We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order in dimension with samples. Here, we study the minimax expected excess risk over the full linear class, depending on the dist…
New method improves DAG learning by using large coefficients for higher-order terms.
The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
New tests for identifying the number of latent factors in short panels with small time dimensions.
Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related …
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…
The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the network is resilient to small random noise added to its parameters. So far this observ…
Improved bounds for sensitivity sampling reducing the sample complexity for structured matrices.
Bayesian method infers transition matrices from incomplete graph data with topological constraints.
Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to a single traded asset and allows to find an optimal trading strategy which - fo…
The paper uses Betti curves to confirm hyperbolic geometry in brain, climate, and financial networks.
A new classification rule for FDA improves classification performance by accounting for unequal covariance matrices.
A new bootstrapping method reduces key sizes and runtime in FHE.
Extracts representative scenarios from large data panels.
Regularized EM algorithm improves clustering performance with small sample sizes.
According to recent findings [1,2], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can essentially be regarded as random. In [1], e.g., it is reported that about 94% of th…
A new data-adaptive prior stabilizes kernel learning in operators.
Model tracks structural changes in Brownian particle configurations on a sphere.
Method cleans covariance matrices for better statistical inference.
In this paper we give the results of a computer search for biracks of small size and we give various interpretations of these findings. The list includes biquandles, racks and quandles together with new invariants of welded knots and examples of welded knots which are shown to be non-trivial by the new invariants. Thes…
Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matri…