Paper improves estimates for Steklov eigenvalues.
problem Estimating Steklov eigenvalues and their inverses.
method Generalizes previous results using new estimates.
result New estimates for trace and inverse trace of Steklov eigenvalues.
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48 results for “trace estimates”
New method estimates matrix trace using machine learning with fewer vectors.
problem Estimating matrix trace when explicit form is not known.
method Uses machine learning to determine a small number of probing vectors for matrix multiplication to a vector.
result Precision of trace estimates with 10 probing vectors is similar to 10000 random vectors.
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.
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.
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
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 extends knowledge tracing algorithms to infer student knowledge and predict posttest performance.
problem Lack of algorithms that directly infer student knowledge and predict posttest performance.
method Extended DKT and DKVMN to infer knowledge, and applied to BKT and PFA for comparison.
result Knowledge estimates from the extended algorithms correlate better with posttest performance than existing methods.
Deep-IRT combines deep learning and IRT for explainable knowledge tracing.
problem Lack of explainability in deep learning-based knowledge tracing models.
method Synthesis of DKVMN and IRT models to estimate student and item parameters.
result Deep-IRT retains DKVMN performance while providing psychological interpretations.
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.
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\%
Study heat traces for drifting Laplacian and Schrödinger operators on manifolds.
problem Analyzing heat traces for drifting Laplacian and Schrödinger operators on manifolds.
method Proved asymptotic expansions and remainder estimates for heat traces under different regularity conditions.
result The asymptotic behavior of the remainder is determined by higher regularity of the potential or weight function.
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.
Estimates log determinants using entropy for scalable machine learning.
problem Scalable calculation of matrix determinants is a bottleneck in machine learning.
method Maximum entropy framework with moment constraints for stochastic trace estimation.
result Significant improvement over state-of-the-art methods on various UFL sparse matrices.
The paper analyzes trace regression with low-rank matrices under various regularization methods.
problem Estimating low-rank matrices with near-optimal error bounds under unknown regularization parameters.
method General spikiness notion, restricted strong convexity of sampling operator, cross-validation for parameter selection.
result Cross-validated estimators select near-optimal penalty parameters and outperform theory-inspired approaches.
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…
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.
New algorithm LSTD()-RP uses random projections and eligibility traces for efficient reinforcement learning.
problem Policy evaluation in high-dimensional feature spaces with linear function approximation.
method Proposes LSTD()-RP algorithm combining random projections and eligibility traces.
result Demonstrates improved performance and better error bounds compared to prior methods.
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.
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…
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.
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.
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…
Quantum system estimation using trace regression models and low rank density matrices.
problem Estimating unknown density matrices from quantum system measurements.
method Using trace regression models and projections onto the convex set of density matrices, with minimax lower bounds for various distances.
result Minimax lower bounds for low rank density matrices are attained up to logarithmic factors for various distances.
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.
SAKT improves knowledge tracing by focusing on relevant past activities.
problem Handling sparse data in knowledge tracing models.
method Self-attention based approach to identify relevant past activities.
result SAKT outperforms state-of-the-art models, improving AUC by 4.43%.
We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of space-time connections satisfying the Ricci flow with respect to the natural space-time degenerate metric. As a special case, we employ scal…
Paper proves stability for recovering connections from holonomy traces.
problem Recovering a connection from holonomy traces on Riemannian manifolds.
method Combination of microlocal analysis and non-Abelian approximate Livsic Theorem.
result Hölder type stability estimates for holonomy inverse problem.
FFJORD models generate complex distributions efficiently with unbiased density estimation.
problem Efficiently generating complex distributions with unbiased density estimation.
method FFJORD uses continuous-time invertible neural networks with Hutchinson's trace estimator for unbiased log-density estimation.
result FFJORD achieves state-of-the-art performance in high-dimensional density estimation, image generation, and variational inference.
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.
IdeoTrace: A Framework for Ideology Tracing with a Case Study on the 2016 U.S. Presidential Electioncs.SI
A framework traces ideology changes on social media during the 2016 U.S. election.
problem Understanding how ideology changed on social media during the 2016 U.S. election.
method Jointly estimating ideology of users and news sites, tracing changes over time.
result Both liberal and conservative users became more polarized over time.
New inequalities for Steklov eigenvalues traced and inverted.
problem Steklov eigenvalues and their traces.
method Obtained new inequalities for Steklov eigenvalues.
result New inequalities for trace and inverse trace of Steklov eigenvalues.
Study geometric quantization of Hamiltonian flows using Berezin-Toeplitz operators.
problem Quantum dynamics of Hamiltonian flows over symplectic manifolds.
method Geometric quantization, Berezin-Toeplitz operators, parallel transport.
result Established a Gutzwiller trace formula for Kostant-Souriau operator.
Regularization-free estimation in trace regression with symmetric positive semidefinite matricesstat.ML
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoye…
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, an…
An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is contr…
RKT model improves knowledge tracing by considering exercise relations and student forget behavior.
problem Traditional KT models fail to consider both exercise relations and student forget behavior.
method RKT model uses relation-aware self-attention to incorporate exercise relations and student forget behavior.
result RKT model outperforms state-of-the-art KT methods on real-world datasets.
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…
Estimates metric tensor on neuromanifolds using Fisher information and random methods.
problem Computing the metric tensor on high-dimensional neuromanifolds efficiently and accurately.
method Deterministic bounds and unbiased random estimators based on Hutchinson's trace method.
result An efficient random estimator with bounded standard deviation.
Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.
problem Estimating differences in multi-attribute Gaussian graphical models with similar structure.
method Penalized D-trace loss function with non-convex (log-sum and SCAD) penalties, proximal gradient descent methods.
result Theoretical analysis and numerical examples support consistency in support recovery and estimation.
We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix …
Model trains from wifi traces to infer public transport levels.
problem Estimate the level of service of a city-wide public transport network.
method Robust unsupervised clustering for train movement inference; classification model for real-time commuter patterns.
result Accurately estimated demand-supply gap from connected devices.