Improved matrix approximation using randomized algorithms.
problem Finding better approximations of given matrices.
method Randomized algorithms to compute as an improved approximation.
result Computed provides a better approximation than given .
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48 results for “improved approximation”
Boosting Nyström Methodstat.ML
Boosting Nyström improves accuracy of matrix approximations.
problem Generating low-rank approximations of large matrices efficiently.
method Iteratively generate multiple weak Nyström approximations, combine them to form a strong approximation.
result Boosting Nyström yields more efficient and accurate low-rank approximations.
Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximationstat.ML
Paper improves CLT and bootstrap approximations for LSA with decreasing step size.
problem Improving normal approximation and bootstrap methods for LSA with decreasing step sizes.
method Refined Berry-Esseen bounds and multiplier bootstrap procedure for LSA.
result Approximation rates up to for LSA rescaled error distribution.
We propose a new analytical approximation to the kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments show the new approximation leads to improved performance in image classification and …
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…
Posterior refinement improves sample efficiency in Bayesian neural networks.
problem Bayesian neural networks suffer from poor predictive performance due to inaccurate posterior approximations.
method Propose refining Gaussian approximate posteriors with normalizing flows to improve predictive distributions.
result Posterior refinement yields competitive predictive performance with minimal computational overhead.
QLA improves Bayesian uncertainty estimation for DNNs without increasing computational cost.
problem Overconfident out-of-distribution predictions from DNNs.
method Proposes Quadratic Laplace Approximation (QLA) to improve Bayesian uncertainty quantification.
result QLA yields modest yet consistent uncertainty estimation improvements over Linearized Laplace Approximation (LLA) on five regression datasets.
Improved singular value approximation for convolutional layers.
problem Improving accuracy of singular value approximation for linear convolutional layers.
method Developed a new spectral density matrix method for singular value approximation with improved accuracy and reduced computational complexity.
result Obtained moderate improvement in singular value distribution compared to circular approximation.
Improves hyperparameter learning in GP models with non-conjugate likelihoods.
problem Hyperparameter learning entangled with approximate inference in GP models.
method Hybrid training procedure combining VI for inference and EP-like marginal likelihood approximation for hyperparameter learning.
result Empirically demonstrates the effectiveness of the proposed training procedure across various data sets.
ASTRA improves TDA by more accurately approximating iHVP.
problem Improving insights into training data attribution.
method ASTRA uses EKFAC-preconditioner on Neumann series iterations to accurately approximate iHVP.
result Improving iHVP approximation significantly improves TDA performance.
We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the a…
This paper proposes a new approach to RL by focusing on the value-improvement path.
problem Value prediction problems in RL are sequence-dependent and require holistic approach.
method Characterize and approximate the value-improvement path holistically.
result A representation that spans the value-improvement path provides accurate value approximations for future policy improvements.
Improved Nyström approximation for kernel quadrature with theoretical guarantees.
problem Efficiently approximating positive definite kernels for large datasets.
method Refined sampling and subspace selection in Nyström approximation.
result Novel theoretical guarantees for non-i.i.d. landmark points in kernel quadrature.
The paper provides tight bounds for improving multi-armed bandits problem.
problem Improving multi-armed bandits problem with concave reward functions.
method Upper and lower bounds for randomized online algorithms, providing an approximation.
result Achieved nearly-tight approximation guarantees for the improving multi-armed bandits problem.
A new method improves convergence in low-rank approximation.
problem Efficiently solving large-scale numerical linear algebra problems.
method Error-Powered Sketched Inverse Iteration (EPSI) Method.
result Convergence rate improves at least linearly with sketch size.
Improved neural network approximates analytic and L^p functions efficiently.
problem Efficiently approximating analytic and L^p functions using neural networks.
method Three-dimensional ReLU network architecture for sawtooth functions, improving approximation rates.
result Substantially improved exponential approximation rates for analytic functions and general L^p functions.
This paper investigates a type of instability that is linked to the greedy policy improvement in approximated reinforcement learning. We show empirically that non-deterministic policy improvement can stabilize methods like LSPI by controlling the improvements' stochasticity. Additionally we show that a suitable represe…
A practical algorithm improves approximate OT distances using quantization.
problem Substantial computational burden in computing OT distances for large samples.
method Introduces a quantization step to estimate OT distances between measures.
result The quantization step improves the performance of approximate solvers for entropy-regularized transport.
Improves efficiency of random feature approximations for dot product kernels.
problem Efficiency of random feature approximations for dot product kernels.
method Generalization of existing random feature approximations using complex-valued random features, theoretical analysis of variances, data-driven optimization approach.
result Complex-valued random features can significantly reduce the variances of approximations.
Improved Bayesian neural network inference by selectively removing redundant modes.
problem Redundant modes in Bayesian neural network posteriors complicate approximate inference.
method Structured partial stochasticity and deterministic subset selection of weights.
result Improved performance of approximate inference schemes with simplified posterior distribution.
New framework improves variational inference for high-dimensional posteriors.
problem Challenges in choosing variational objectives and approximating families for high-dimensional posteriors.
method Conceptual framework and experimental tools to understand and optimize variational objectives and families.
result For moderate-to-high-dimensional posteriors, exclusive KL divergence is recommended due to optimization ease; for low-dimensional, heavy-tailed variational families are effective.
This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.
problem Improving approximation of fully connected deep neural networks for optimal convergence rates.
method Deriving approximation bounds specifically for a narrower fully connected deep neural network.
result Achieves an optimal rate (up to a logarithmic factor) for fully connected deep neural networks.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
Improves Laplace approximation for Bayesian inference on Riemannian manifolds.
problem Inaccurate Gaussian approximations for complex targets and finite-data posteriors.
method Develops alternative variants of the Laplace approximation using a Riemannian metric.
result Exact approximations at the limit of infinite data, improving practical performance.
Novel confidence intervals improve convergence rates for sparse kernel-based models.
problem High computational cost in kernel-based learning models.
method Novel confidence intervals for Nyström method and sparse variational Gaussian process approximation.
result Improved performance bounds in regression and optimization problems.
Improved API to achieve optimal error bound and query complexity in local planning.
problem Efficient local planning in discounted MDPs with linear approximation.
method Confident Approximate Policy Iteration (CAPI) for stationary policies, applying to local access simulators.
result Achieves optimal accuracy and query complexity bounds, improving over API.
Improved semialgebraic choices with linear complexity.
problem Finding semialgebraic choices in projections with exponential complexity.
method Allowing approximate selections in Hausdorff sense.
result Constructed an approximate selection with linear degree in complexity.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
Improves learning of spectral mixture kernels with approximate Bayesian inference.
problem Difficult optimization of large number of SM kernel parameters.
method Approximate Bayesian inference using variational distribution of spectral points and random Fourier features.
result Accelerates convergence and leads to better optimal parameters.
Paper improves kernel approximations for better statistical learning.
problem Improving kernel approximations for better statistical learning.
method Taylor series approximations of radial kernel functions.
result Establishes upper bounds for eigenfunctions, leading to better approximations.
Bayesian interpretation of deep ensembles improves uncertainty quantification.
problem Improving uncertainty estimation in deep learning models.
method Viewing deep ensembles as an approximate Bayesian method and specifying corresponding assumptions.
result Improved approximation leads to larger epistemic uncertainty, potentially more reliable predictions.
MPNN improves on UniFL approximation with provable guarantees.
problem Uniform Facility Location (UniFL) optimization problem.
method Graph Neural Network (MPNN) incorporating approximation-algorithmic principles.
result Empirically outperforms standard approximation algorithms.
The intrinsic error tolerance of neural network (NN) makes approximate computing a promising technique to improve the energy efficiency of NN inference. Conventional approximate computing focuses on balancing the efficiency-accuracy trade-off for existing pre-trained networks, which can lead to suboptimal solutions. In…
CTE improves explanation estimation with less data and faster computation.
problem Inefficient and inaccurate explanation estimation in machine learning models.
method Distribution compression through kernel thinning to reduce sample size.
result CTE significantly improves accuracy and stability of explanation estimation.
Improved Gaussian Process regression using TQFF over RFF and Gaussian QFF.
problem Limited performance of Quadrature Fourier Features (QFF) in approximating highly oscillatory functions.
method Developed Trigonometric Quadrature Fourier Features (TQFF) using a novel non-Gaussian quadrature rule.
result TQFF provides better approximation accuracy and fewer features compared to RFF and Gaussian QFF.
ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of both hyperbolic tangent and sigmoid functions. These functions are expensive to co…
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function e…
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows…
This paper analyzes and improves GANs' approximation ability.
problem Theoretical and algorithmic analysis of GANs' approximation property.
method Theoretical analysis and SDG approach to enhance GANs' approximation ability.
result The generator of GANs can universally approximate the potential data distribution.
Express improves causal attention guarantees for language models.
problem Improving causal attention guarantees for language models.
method Introducing Express, a tool for converting non-causal attention into causal with matching guarantees.
result Express improves causal attention guarantees to log^(3/2)(n)/s with minimal memory and compression overhead.
Efficiently private clustering algorithms with tight approximation ratios.
problem Differentially private clustering of various types.
method Efficient algorithms achieving tight approximation ratios for clustering problems.
result Achieves approximation ratios similar to non-private algorithms with small additive errors.
This work shows how approximate reward models can significantly improve inference-time scaling.
problem Improving the efficiency of inference for large language models.
method Identifying the Bellman error of approximate reward models and using Sequential Monte Carlo (SMC) for inference.
result Approximate reward models can reduce computational complexity from exponential to polynomial in .
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, …
New algorithms improve approximation of matrix norms, with applications in statistics and machine learning.
problem Improving approximation of matrix norms for in polynomial time.
method Polynomial-time multiplicative approximation algorithms for norm, leveraging sum-of-squares certificates.
result Achieved polynomially improved approximation factors, notably for .
Bayesian method improves approximate model posteriors.
problem Poor uncertainty quantification in approximate Bayesian inference.
method Optimizing a transformation of the approximate posterior to maximize a scoring rule.
result Significant reduction in bias and improvement in posterior coverage properties.
This work improves sample efficiency in neural function approximation for reinforcement learning.
problem Improving sample efficiency in reinforcement learning with neural function approximation.
method Study of function approximation with two-layer neural networks (ReLU and polynomial activations) under generative and realizability models.
result Significant improvement in sample complexity compared to linear methods.
Improved sample complexity for Gaussian process approximations.
problem Efficiently approximating Gaussian processes with sparse spectrum.
method Improved sample complexity analysis and auto-encoding algorithm.
result Gaussian process predictions and model evidence can be well-approximated with low sample complexity.
SIM-Shapley improves SV approximation efficiency and stability.
problem High computational costs of Shapley value methods in high-dimensional settings.
method Stochastic Iterative Momentum for Shapley Value Approximation (SIM-Shapley).
result Reduced computation time by up to 85% while maintaining feature attribution quality.