Stochastic trace estimation with tensor train random vectors
problem Stochastic trace estimation for large-scale matrices
method Gaussian random tensor train vectors
result Median-of-means variant achieves dimension-independent guarantees
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48 results for “stochastic trace estimation”
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the random noise vectors in Hutchison estimator, we use small number of probing vectors…
Hutch++ optimizes trace estimation for generative models, reducing variance and improving quality.
problem High variance and scalability issues in Hutchinson estimators for generative models.
method Hutch++ is an optimal stochastic trace estimator designed to minimize training variance while maintaining transport optimality.
result Hutch++ leads to higher quality generations and effective variance reduction in various applications.
Spectral regularization simplifies sequence models by focusing on grammatical simplicity.
problem Sequence modeling challenges in learning tasks.
method Introduces spectral regularization based on Hankel matrices and trace norm, addressing bi-infinite matrices with an unbiased estimator.
result Demonstrates spectral regularization's potential benefits on Tomita grammars.
Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theorystat.ML
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework o…
Method uses deep learning to estimate traffic intensity.
problem Estimating stochastic intensity of traffic processes.
method Deep neural networks for nonlinear filtering.
result Deep learning method accurately estimates traffic intensity.
Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.
problem Computing heat kernel traces for Ricci flat manifolds.
method Quantum stochastic differential equation (qsde) on Fock space over differential 1-forms, adapted flow construction.
result Trace of the connection Laplacian heat kernel can be computed over any compact Ricci-flat Riemannian manifold.
Generative model for condensed matter using Riemannian flow matching.
problem Sampling equilibrium distributions in condensed-phase systems.
method Riemannian flow matching to incorporate periodicity, using Hutchinson's trace estimator and cumulant expansion for bias correction.
result Highly accurate free energy estimates on monatomic ice without multistage estimators.
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.
Efficient GP framework for scalable non-stationary processes.
problem Heavy memory and computational requirements in Gaussian process regression for large data sets.
method Exploits structure in the kernel matrix, uses multiple sets of non-equidistant inducing points, and employs Toeplitz and Kronecker structure for efficient inference.
result Demonstrated scalability on numerical examples and large biomedical datasets.
Bayesian generative models can flag performance loss, bias, and out-of-distribution image contentcs.LG
SLUG method detects bias and out-of-distribution content in generative models.
problem Generative models can underrepresent certain groups and fail on out-of-distribution data.
method SLUG: A new uncertainty quantification method for VAEs combining Laplace approximations and stochastic trace estimators.
result SLUG's UQ score correlates with bias and out-of-distribution content.
New rigidity result for Steklov eigenvalues on manifolds.
problem Steklov eigenvalues on manifolds.
method Decomposition theorem for flat and totally geodesic Riemannian submersions.
result Equality of trace estimate holds if and only if the manifold is a direct product of a round ball and a closed manifold.
Ray tracing sampler improves neural network sampling efficiency and resilience.
problem Sampling neural network posterior distributions efficiently and robustly.
method Markov Chain Monte Carlo using ray tracing through likelihood space.
result Significantly higher resilience to gradient heating compared to HMC.
This work improves trace norm regularization for multi-task learning with limited data.
problem Learning from few samples across multiple tasks.
method Trace norm regularization for a linear shared representation model.
result First estimation error bound for trace norm regularized estimator with scarce data.
TracIn measures how training examples affect model predictions.
problem Measuring the influence of training examples on model predictions.
method Tracing changes in loss during training when a specific example is used.
result TracIn provides a scalable method to estimate example influence.
Estimates the degree of trace fields of hyperbolic Dehn fillings.
problem Estimating the complexity of hyperbolic 3-manifolds.
method Using Lehmer's conjecture, bounds the degree of trace fields.
result Estimates the degree of trace fields of hyperbolic Dehn fillings.
Paper improves efficiency in matrix computations for Gaussian processes.
problem Efficiency in matrix computations for Gaussian processes.
method Variance reduction via matrix factorization.
result Factorized estimator can be up to 1,000 times more efficient.
Using the -norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, ca…
Deep learning model improves seismic rock property estimation.
problem Estimating reservoir rock properties from seismic reflection data.
method Proposes a deep learning-based seismic inversion workflow that models seismic traces spatiotemporally.
result Achieves best performance on SEAM dataset with coefficient of 79.77\%
Deep learning based knowledge tracing model has been shown to outperform traditional knowledge tracing model without the need for human-engineered features, yet its parameters and representations have long been criticized for not being explainable. In this paper, we propose Deep-IRT which is a synthesis of the item res…
A new method predicts student skill success rates in real-time.
problem Accurate and explainable prediction of student skill success rates in real-time.
method Performance Distribution Tracing (PDT) using a Dynamic Bayesian Network with continuous random variables.
result PDT provides both explainability and accuracy in real-time predictions of student skill success rates.
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.
NGD models have higher effective dimension than SGD models.
problem Measuring model complexity accurately.
method Comparison of NGD and SGD models using effective dimension measures.
result NGD models have a higher effective dimension than SGD models.
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…
New algorithms for collaborative reinforcement learning with limited communication.
problem Efficiently learning value functions in multi-agent systems with strict information constraints.
method Distributed gradient-based temporal difference algorithms with consensus schemes.
result Parameter estimates converge to ODEs with defined invariant sets under general assumptions.
Early training phase affects deep neural network optimization and generalization.
problem The choice of learning rate influences generalization in deep learning models.
method Showed that SGD implicitly penalizes the trace of the Fisher Information Matrix (FIM) from the start of training, and explicitly penalizing the trace of FIM improves generalization.
result Catastrophic Fisher explosion (large trace of FIM early in training) is linked to poor generalization.
In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C^*-algebra, the La…
New method estimates log-determinant using trace powers, avoiding classical limitations.
problem Estimating log-determinant of large matrices efficiently and accurately.
method Interpolating moment-generating function and its derivative at zero using trace powers.
result No continuous estimator using finite moments can be uniformly accurate over unbounded conditioning.
We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) an…
GL-LowPopArt improves minimax-optimal estimation for trace regression.
problem Minimizing estimation error in generalized low-rank trace regression.
method Two-stage approach: nuclear norm regularization followed by matrix Catoni estimation.
result Achieves instance-wise optimal error bounds up to condition number.
The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces. The paper is based on an invariant version of the classical Littlewood -Paley the…
Near-Optimal differentially private low-rank trace regression with guaranteed private initializationstat.ML
Paper develops DP methods for low-rank matrix estimation with near-optimal performance.
problem Estimating a low-rank matrix under differential privacy constraints.
method Introduced computationally efficient DP-initialization and Riemannian optimization-based DP-RGrad algorithm.
result DP-RGrad achieves near-optimal convergence rate under weak differential privacy constraints.
We study a relative trace formula for a compact Riemann surface with respect to a closed geodesic . This can be expressed as a relation between the period spectrum and the ortholength spectrum of . This provides a new proof of asymptotic results for both the periods of Laplacian eigenforms along as well estim…
Efficiently learns distributions corrupted by both global and local adversarial modifications.
problem Learning distributions with both global and local adversarial corruptions.
method Develops an efficient algorithm to minimize Wasserstein distance with orthogonal projections.
result Achieves optimal risk bounds with error .
SGD improves generalization by using gradient variability as a proxy for data randomness.
problem Improving generalization in machine learning models trained with stochastic gradient descent.
method Bootstrap perspective on SGD, analyzing gradient variability and algorithmic variability.
result SGD avoids spurious solutions and improves generalization by implicitly regularizing the trace of the gradient covariance matrix.
Recent student knowledge modeling algorithms such as Deep Knowledge Tracing (DKT) and Dynamic Key-Value Memory Networks (DKVMN) have been shown to produce accurate predictions of problem correctness within the same learning system. However, these algorithms do not attempt to directly infer student knowledge. In this pa…
Study multi-task learning with low-rank representation in stochastic linear bandits.
problem Transfer learning across multiple linear bandit tasks with shared low-dimensional representation.
method Proposes a greedy policy with trace norm regularization to implicitly learn a low-rank representation without knowing the rank.
result Upper bound on multi-task regret of , showing benefit over independent task solving.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few t…
We study the heat trace for both the drifting Laplacian as well as Schrödinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term) asymptotic expansion of the heat trace for small times as well as a suitable remainder…
We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. A corollary of this dynamical trace formula is a dynamical resonance-wave trac…
Improved contact tracing models outperform NIST challenge results.
problem Contact tracing using phone data and machine learning.
method Developed two machine learning models (GBM and MLP) from phone instrumental data features.
result Outperformed the leading NIST challenge result by HKUST.
This paper optimizes matrix-based Renyi's entropy computation for large datasets.
problem Efficiently calculating matrix-based Renyi's entropy for large-scale applications.
method Develops randomized approximations for matrix-based Renyi's entropy with arbitrary α orders.
result Achieves a significant reduction in time complexity from O(n^3) to O(n^2sm), where s, m << n.
Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…
TRACE analyzes risk changes in models trained on shifted data.
problem Understanding performance changes when a model trained on shifted data is used.
method TRACE framework decomposes risk change into four factors: generalization gaps, model change penalty, and covariate shift penalty.
result TRACE provides a diagnostic tool to understand and quantify risk changes due to covariate shift.
Develops interpolation methods for matrix functions in statistics and machine learning.
problem Estimating matrix functions in statistics and machine learning.
method Interpolates log-determinant and trace of matrix powers using modified sharp bounds.
result Accuracy and performance demonstrated in numerical examples.
A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be u…