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.
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires O(n3) logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regre…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a physical system. We augment the linear PDE with a functional that accounts for th…
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear reg…
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Linear Regres…
There has been a growing interest in using non-parametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally intensive, (2) it cannot efficiently implement newly obtained measurements online, and …
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full GP regression and generated paths are demonstrated to be indistinguishable from …
This paper tackles efficient and scalable estimation of a complex model involving stochastic linear combinations of non-linear regressions.
problem Estimating a model involving stochastic linear combinations of non-linear regressions efficiently and scalably.
method The paper provides algorithms for estimating the model under specific assumptions about the variate vector and sample size, using techniques like zero-bias transformation and sub-sampling.
result The paper provides theoretical guarantees for the estimation of the model, showing that the estimation errors are of the order O(np) and O(p1+np) with high probability.
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this s…
Locally adaptive interpretable regression improves linear regression's predictability.
problem Linear regression's predictability is limited; it lacks adaptability.
method Locally adaptive interpretable regression (LoAIR) uses neural networks to predict percentile of a Gaussian distribution for regression coefficients.
result LoAIR achieves comparable or better predictive performance than state-of-the-art baselines.
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…
Linear Transformer Block combines MLP and linear attention for near-optimal ICL in linear regression.
problem Achieving near-optimal in-context learning (ICL) risk for linear regression with a Gaussian prior.
method Combines linear attention and MLP components in a Linear Transformer Block (LTB). Establishes correspondence with one-step gradient descent estimators (GDext−β).
result LTB achieves nearly Bayes optimal ICL risk for linear regression with a Gaussian prior.
Bayesian optimization (BO) is a model-based approach for gradient-free black-box function optimization. Typically, BO is powered by a Gaussian process (GP), whose algorithmic complexity is cubic in the number of evaluations. Hence, GP-based BO cannot leverage large amounts of past or related function evaluations, for e…