Fast approximates orthogonal matrices for PCA.
problem Approximating orthogonal matrices for fast computation.
method Optimization over structured matrices and greedy algorithm.
result Efficient approximation balances accuracy and speed.
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48 results for “fast approximation”
We accelerate the power method for strong low-rank approximation using fast sketching.
problem Efficiency bottleneck in power method for large target ranks.
method Developed an algorithmic and theoretical framework for accelerating the power method using fast sketching.
result Simple and provably efficient methods for singular value decomposition, low-rank factorization, and Nyström approximation.
A fast algorithm for generalized matrix regression improves machine learning performance.
problem Efficiently solving generalized matrix regression problems in machine learning.
method Utilizes sketching technique to achieve relative error with sketching sizes of order $\cO(ε^{-1/2})$.
result The Fast GMR algorithm achieves better performance in symmetric positive definite matrix approximation and single pass singular value decomposition.
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
This study explains why approximate NGD works well in wide neural networks.
problem Understanding why NGD with approximate Fisher information converges fast in wide neural networks.
method Analyzing asymptotic training dynamics in function space via the neural tangent kernel.
result NGD with approximate Fisher information achieves the same fast convergence as exact NGD under specific conditions.
Fast Approximate Time-Delay Estimation in Ultrasound Elastography Using Principal Component Analysiseess.IV
A fast method for approximate TDE in ultrasound elastography.
problem Challenging and critical step in ultrasound elastography.
method PCA-GLUE, exploiting PCA to find TDE principal components.
result PCA-GLUE is more than ten times faster than Dynamic Programming.
Study improves kernel quadrature for infinitely wide models with faster approximation and estimation rates.
problem Efficiently approximating and estimating expectations in infinitely wide models.
method Developed general kernel quadrature (GKQ) for parameter distributions, achieving faster rates.
result Achieved a fast approximation rate of and a fast estimation rate of .
We extend natural-gradient methods to mixtures of exponential-family distributions, improving inference speed.
problem Complex, multimodal posterior distributions are difficult to approximate with simple exponential-family distributions.
method We use minimal conditional-EF representations and derive simple natural-gradient updates.
result Our natural-gradient method converges faster than black-box methods with reparameterization gradients.
We propose fast approximations for the generalized sliced-Wasserstein distance.
problem Efficient approximation of the generalized sliced-Wasserstein distance in high dimensions.
method Deterministic approximations using random projections and concentration of measure results.
result One-dimensional projections of high-dimensional random vectors are approximately Gaussian.
New algorithms for approximating stochastic processes efficiently.
problem Finding accurate finite approximations for stochastic processes.
method Develops new algorithms and fast implementations for approximating stochastic processes.
result Efficient approximations for stochastic processes can be found.
This paper speeds up Gaussian process regression for autocorrelated data.
problem Temporal overfitting in Gaussian process models for autocorrelated data.
method Modifying existing Gaussian process approximations to handle blocked, de-correlated data.
result Proposed methods accelerate Gaussian process regression on autocorrelated data without sacrificing performance.
The paper develops fast Bayesian methods for estimating huge PVARs with competitive forecasts.
problem Computational and statistical issues in estimating PVARs with many parameters.
method Integrated rotated Gaussian approximations, exploiting domestic over international information, and fast approximations for international coefficients.
result Produces competitive forecasts quickly using a huge world economy model.
We provide a fast approximation to eNTKs for neural networks.
problem Efficiently computing eNTKs for large networks.
method Developed and proved the 'sum of logits' approximation.
result The 'sum of logits' approximation converges to eNTKs at initialization.
Paper develops fast low-rank approximation for smoothing splines.
problem Computational infeasibility of fitting cubic smoothing splines to large datasets.
method Low-rank approximation using eigensystem truncation.
result The method provides accurate, fast estimates with error bounds.
Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.
problem Non-asymptotic bounds for accuracy of normal approximation in linear two-timescale stochastic approximation algorithms.
method Established bounds for normal approximation in terms of convex distance, focusing on last iterate and Polyak-Ruppert averaging.
result Normal approximation rate for the last iterate improves with increased timescale separation, while it decreases in the averaged setting.
Efficiently approximates statistical leverage scores for faster KRR.
problem Accurately estimating statistical leverage scores for fast KRR.
method Analytic formula for statistical leverage scores, leveraging kernel spectral density.
result Linear time approximation with theoretical guarantees, significantly faster than existing methods.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
Simulation of conditional expectations under fast mean-reverting stochastic volatility modelsmath.NA
The paper studies efficient simulation methods for financial firm values under fast mean-reverting volatility.
problem Estimating the probability of firm default under fast mean-reverting stochastic volatility models.
method Approximations using ergodic averages and central limit theorem corrections for efficient simulation.
result Accuracy of approximations assessed through numerical simulation and payoff function estimation.
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their ov…
Recursive nearest agglomeration (ReNA): fast clustering for approximation of structured signalsstat.ML
In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure…
Constructing fast approximate eigenspaces with application to the fast graph Fourier transformscs.LG
Efficiently approximates eigenspaces for symmetric and general matrices.
problem Fast computation of eigenspaces for large matrices.
method Factor eigenspaces into fundamental components using transformations, solve minimization problems, and iteratively update.
result Improved computational efficiency for eigenspace approximation.
We develop a fast inference method for non-conjugate Gaussian process models on spike count data.
problem Non-Gaussian spike count data complicates Gaussian Process Factor Analysis.
method We introduce Polynomial Approximate Log-Likelihood (PAL) estimators for non-conjugate GPFA models.
result PAL estimators achieve fast and accurate extraction of latent structure from spike train data.
Paper optimizes multi-fidelity function with fast learning rates.
problem Optimizing a locally smooth function with limited budget and varying fidelity approximations.
method Kometo algorithm that achieves simple regret rates without knowing function smoothness or fidelity assumptions.
result Kometo algorithm outperforms previous methods empirically.
Combines fast evaluation with Bayes consistency in nearest neighbors.
problem Balancing fast evaluation time with Bayes consistency in nearest neighbors.
method Combines locality-sensitive hashing (LSH) with a missing-mass argument.
result Fast and Bayes-consistent classifier with comparable risk decay rates.
Paper proposes faster incremental subclass discriminant analysis.
problem Efficiently classify subclasses in incremental data.
method Exact and approximate linear and kernelized solutions.
result Superior training time and accuracy compared to existing methods.
Improved stochastic approximation method reduces residual error.
problem Reducing residual error in stochastic approximation algorithms.
method Fixed-schedule one-quarter barrier and bias-corrected acceleration.
result Achieves residual reduction with primitive samples.
The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.
problem Estimating weights and quality functions in reinforcement learning with function approximation.
method The paper uses minimax methods for estimating marginal importance weights and q-functions.
result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
problem Efficient and accurate distribution estimation in statistics and machine learning.
method Piecewise polynomial approximation using empirical probability interpolation and divide-and-conquer merging.
result Surpassing state-of-the-art algorithms in efficiency and accuracy, SURF estimates distributions robustly and quickly.
FAST algorithm maximizes submodular functions efficiently.
problem Maximizing submodular functions under cardinality constraints.
method Fast Adaptive Sequencing Technique (FAST) for submodular maximization.
result FAST achieves an approximation ratio of with adaptive queries and total queries.
The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several B…
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, nam…
Optimizes trading large volumes of volatile assets with fast mean-reverting volatility.
problem Challenges of executing large volumes of illiquid or volatile assets.
method Modeling uncertain volatility and liquidity with fast mean-reverting dynamics, using singular perturbation arguments and high-frequency data.
result Approximately optimal trade execution strategies under fast mean-reversion.
A fast and practical method for learning transport maps.
problem Slow and computationally expensive methods for learning transport maps.
method Approximated transport mapping using Gaussian (Bures-Wasserstein) transport and local transport plans.
result Significantly faster and more efficient than existing methods.
We provide a fast L2-embedding for arbitrary accuracy with applications to regression and L1 tasks.
problem Efficiently embedding high-dimensional data while maintaining accuracy.
method Oblivious L2-embedding with dimension independent of accuracy.
result Achieves arbitrary accuracy with constant embedding dimension.
Develops a fast variational approximation for high-dimensional empirical Bayes posteriors.
problem Optimal posterior computation in high-dimensional settings with prior tails effect.
method Variational approximation of empirical Bayes posterior with data-driven centers and thin-tailed conjugate priors.
result Retains optimal concentration rate properties and superior performance compared to existing methods.
Novel framework proves fast RL convergence in continuous spaces.
problem Analyzing stability in continuous state-action RL.
method Introduces a novel framework to analyze stability properties of RL.
result Highlights two key stability properties and demonstrates their satisfaction in RL.
Flexible empirical Bayes for large-scale multiple linear regression.
problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clusterin…
FFCP improves FCP's speed without sacrificing accuracy.
problem Inefficient feature transformation in FCP.
method Introduces FFCP using Taylor expansion for faster computation.
result FFCP achieves a 50x speedup with comparable accuracy.
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing optimization algorithms with fast convergence. However, the studies of EBC in st…
Semi-analytic approximate stability selection for correlated data in generalized linear modelsstat.ML
A fast, approximate method for variable selection in GLMs tackles correlated data.
problem Variable selection in generalized linear models with correlated data.
method Replica method of statistical mechanics and vector approximate message passing.
result The proposed algorithm provides fast convergence and high approximation accuracy.
A fast, robust AMP algorithm for quadratic optimization problems.
problem Implementing robust approximate-message passing algorithms for quadratic optimization problems.
method Spectral pre-processing and mild modification of AMP algorithm iterates.
result Output solution close to AMP algorithm output for perturbed inputs.
Unified theory and debiasing framework for random oblique projections in high dimensions.
problem Systematic statistical bias in random oblique projections induced by sampling.
method Unified non-asymptotic theory and debiasing framework.
result Sharp bias--variance characterizations and improved approximation accuracy.
New algorithm approximates conditional expectations with fast convergence.
problem Approximating conditional expectations in stochastic derivative weights.
method Least-squares Monte Carlo with brute-force SVD truncation.
result Convergence rate is arbitrarily fast polynomial in number of samples.
Approximation of stochastic insurer balance-sheet results using signatures of economic scenariosq-fin.RM
This work proposes a fast ALM model approximation using signature theory.
problem High computational cost in ALM model outputs for large-scale sensitivity analyses.
method Approximation of ALM outputs using signature terms derived from economic scenarios.
result The proposed surrogate model reduces computational costs significantly while maintaining strong predictive performance.
This paper defines a generalized column subset selection problem which is concerned with the selection of a few columns from a source matrix A that best approximate the span of a target matrix B. The paper then proposes a fast greedy algorithm for solving this problem and draws connections to different problems that ca…