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.
Study shows deterministic equivalent for neural network kernel convergence.
Paper speeds up GP inference by reducing precision matrix computation.
New GPU kernels boost deep learning speed and memory efficiency.
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical generalization performance of kernel approximation methods than conventional me…
The paper examines how kernel approximations affect Gaussian process regression in large data applications.
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These…
Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize…
Characterizes RFF regression in large setting, providing precise learning phases and double descent curve.
We analyze kernel matrices in polynomial high-dimensional settings and explain double descent in KRR.
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guar…
New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.
New recursion formula for non-orientable surfaces resolves divergences.
RF models implicitly regularize kernel methods as feature count increases.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning computation-efficient kernel embeddings from specific data. In the framework, the h…
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in the neighborhood of a certain sample through metric learning. We start by using…
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Automates GPU kernel optimization for diverse applications.
New method trains sparse Gaussian processes without matrix inversion.
Three RFF-based methods for nonlinear causal discovery in mixed data.
MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a subset of the kernel matrix entries, or some form of low-rank matrix approximatio…
A new R package for high-dimensional regression and precision matrix estimation.
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.
Study of eigenvalues in nonlinear kernels for classification of separable data.
Accelerated RPCholesky speeds up kernel matrix approximations.
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…
Improves matrix multiplication throughput for asymmetric bit-width operands.
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-co…
Study compares different covariance estimation methods for portfolio allocation.
DEOT method compares distributions across agents with privacy and efficiency.
Efficient kernel methods for large datasets using GPU acceleration.
We attempt to set a mathematical foundation of immunology and amino acid chains. To measure the similarities of these chains, a kernel on strings is defined using only the sequence of the chains and a good amino acid substitution matrix (e.g. BLOSUM62). The kernel is used in learning machines to predict binding affinit…
A new optimization algorithm for Gaussian Variational Inference on precision matrices.
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
SCOPE estimator improves covariance and precision matrix estimation.
Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed b…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routi…
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorith…
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large memory that it is difficult for kernel-based clustering to deal with large-scale …
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in …
Mixed-precision CA-SGD for generalized linear models on GPUs
The paper analyzes data augmentation for precision matrix estimation in high dimensions.
A new algorithm improves sampling for graph learning models.