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.
GAGA accelerates 3D molecular generation by replacing long trajectories with Gaussian approximations.
problem High computational cost of long generative trajectories in 3D molecular generation.
method GAGA identifies a characteristic step where molecular data becomes sufficiently Gaussian, replacing the trajectory with a Gaussian approximation.
result Significant improvement in both generation quality and computational efficiency.
The study examines the universality of Gaussian data in high-dimensional generalized linear estimation.
problem Understanding when Gaussian data suffices for high-dimensional generalized linear estimation.
method Sharp asymptotic expressions for test and training errors in high-dimensional Gaussian mixture data with labels from a single-index model.
result The universality of Gaussian data in error estimation depends on the alignment between target weights and mixture cluster means and covariances.
New insights on how weight structure affects generalization in deep Gaussian feature models.
problem Understanding how weight structure impacts generalization in deep learning models.
method Using the replica trick from statistical physics to derive learning curves for models with structured Gaussian features.
result Allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental.
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian processes. The proposed method can also achieve high generalization performance fo…
Diffusion models generate data with Gaussian Universality, matching linear model test errors.
problem Analyzing the performance of models trained on synthetic data generated by diffusion models.
method Investigates Gaussian Universality for data distributions generated via diffusion models, matching test errors of linear models trained on synthetic data to Gaussian Mixture models.
result The test error of a linear model trained on diffusion-generated data matches the test error of a linear model trained on Gaussian Mixture data with matching means and covariances per class.
Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.
problem Inaccurate error representations and compromised uncertainty estimation in conventional uncertainty-aware TD learning.
method Introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, incorporating higher-order moments, particularly kurtosis, to improve uncertainty estimation and mitigation.
result Significant performance gains in policy gradient algorithms with the proposed framework.
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.
problem Gaussian process regression struggles with compositional functions.
method We study information-theoretic lower bounds for posterior contraction rates in Gaussian process regression for a continuous regression model.
result Posterior based on any mean-zero Gaussian process can only recover the truth at a rate strictly slower than the minimax rate for generalized additive functions.
The study uncovers the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
problem Understanding the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
method Extending the Convex Gaussian Min-Max Theorem to non-Gaussian settings, deriving asymptotic min-max characterizations, and proving asymptotic equivalence of regularizers.
result The projection of the ERM estimator onto a test covariate approximately follows a Gaussian convolution under certain conditions.
In this paper, we propose an auto-encoder based generative neural network model whose encoder compresses the inputs into vectors in the tangent space of a special Lie group manifold: upper triangular positive definite affine transform matrices (UTDATs). UTDATs are representations of Gaussian distributions and can strai…
Dynamic Boltzmann Machine (DyBM) has been shown highly efficient to predict time-series data. Gaussian DyBM is a DyBM that assumes the predicted data is generated by a Gaussian distribution whose first-order moment (mean) dynamically changes over time but its second-order moment (variance) is fixed. However, in many fi…
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, calle…
This note explains when neural networks can be seen as Gaussian processes.
problem Understanding the relationship between neural networks and Gaussian processes.
method Formulating a Gaussian process regression based on neural network outputs and analyzing the resulting posterior mean functions.
result The posterior mean functions of neural networks follow a Gaussian process in certain cases, providing an interpretation of reproducing kernel Hilbert spaces.
This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both alg…
Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussia…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that exact inference is intractable. The current state-of-the-art inference method, …
Proposes a Bayesian Autoencoder with sparse Gaussian process priors to capture data correlations.
problem Autoencoders' i.i.d. assumption of latent representations fails to capture data correlations.
method Imposes fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder and uses stochastic gradient Hamiltonian Monte Carlo for posterior estimation.
result Consistently outperforms alternatives relying on Variational Autoencoders on various tasks.