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.
New estimator stabilizes higher-order influence functions for stable statistical inference.
Deep kernel processes unify various models using Gram matrices and kernel functions.
This paper extends the convergence rate of DEQs with ReLU to any general activation.
New estimator stabilizes higher-order influence functions for bilinear forms.
Effective Gram matrix predicts deep network generalization.
In this paper we show that the matrix of chromatic joins and the Gram matrix of the Temperley-Lieb algebra are similar (after rescaling), with the change of basis given by diagonal matrices.
Layer normalization with activations prevents Gram matrix rank collapse at initialization.
New method corrects missing data bias in dimension reduction.
A clustering algorithm uses the left Gram matrix for high dimensional data.
Optimal data splitting improves covariance matrix estimation in large datasets.
We uncover scaling laws and statistical structure in complex datasets.
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional indepe…
New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.
The paper connects Chebyshev polynomials and Gram determinants on Möbius bands.
Paper proposes a method to recover point configurations from noisy distance data.
To any compact Riemann surface of genus g one may assign a principally polarized abelian variety of dimension g, the Jacobian of the Riemann surface. The Jacobian is a complex torus, and a Gram matrix of the lattice of a Jacobian is called a period Gram matrix. This paper provides upper and lower bounds for all the ent…
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmet…
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-…
We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.
Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet). Our analysis relies on the p…
Given i.i.d. observations of a random vector , where is a high-dimensional vector and is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix under the assumption that the set of non…
Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factoriza…
New method learns population dynamics from snapshots using JKO scheme and inverse optimization.
Estimates latent norms and Gram matrices for graphs on Euclidean balls.
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing ma…
Paper analyzes mistake and generalization of MNIC classifiers.
Mixed-precision CA-SGD for generalized linear models on GPUs
A new method uses Gram matrix for efficient multivariate functional principal components.
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on th…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an appr…
We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate, but related, subpopulations, while allowing for differences among matrices. We p…
When presented with Out-of-Distribution (OOD) examples, deep neural networks yield confident, incorrect predictions. Detecting OOD examples is challenging, and the potential risks are high. In this paper, we propose to detect OOD examples by identifying inconsistencies between activity patterns and class predicted. We …
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…
The landscape of empirical risk has been widely studied in a series of machine learning problems, including low-rank matrix factorization, matrix sensing, matrix completion, and phase retrieval. In this work, we focus on the situation where the corresponding population risk is a degenerate non-convex loss function, nam…
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel , which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into account th…
LEARNER improves low-rank matrix estimation using source population data.
Multiple cause-of-death data provides a valuable source of information that can be used to enhance health standards by predicting health related trajectories in societies with large populations. These data are often available in large quantities across U.S. states and require Big Data techniques to uncover complex hidd…
Bias correction improves language model training performance.
A new method learns dynamic graph representations from time-varying data.
This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
Neural-Kernel CME tackles scalability and expressiveness challenges in conditional distribution representation.
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_θ(x) of different parameters θin the VAR model as features to descr…
We present NN-grams, a novel, hybrid language model integrating n-grams and neural networks (NN) for speech recognition. The model takes as input both word histories as well as n-gram counts. Thus, it combines the memorization capacity and scalability of an n-gram model with the generalization ability of neural network…
Improved self-distillation reduces label noise and enhances model accuracy.
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to compute the inverse or inverse square root of a matrix whose size is quadratic of …
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when direc…
Neural networks model COVID-19 spread with partial isolation data.
PSC classifier improves HDLSS classification on class-imbalanced data.