One-pass algorithm finds small subset for ℓp subspace approximation with additive error.
problem Finding a small subset of data points for ℓp subspace approximation. method One-pass subset selection with additive approximation guarantee for p∈[1,∞). result First one-pass algorithm with additive error for ℓp subspace approximation. Proposes an additive approximation method for multiplicative noise.
problem Limitations in existing approaches to marginalize over multiplicative errors.
method Embeds multiplicative noise in an additive error term.
result Proposed approach provides feasible error estimates.
New insights into brain networks show they can approximate complex functions efficiently.
problem Understanding how brain networks learn and approximate functions.
method Characterized function spaces induced by sparse random features in brain networks.
result Sparse brain networks can approximate functions of high dimensionality.
HARFE approximates sparse additive functions using random features and ridge regression.
problem Approximating high-dimensional sparse additive functions.
method Hard-ridge random feature expansion with sparse ridge regression and hard-thresholding pursuit.
result HARFE method converges with a given error bound and achieves lower error than other algorithms.
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIB…
Thompson Sampling with bilateral uncertainty improves performance in Bayesian Optimization.
problem Twin difficulties of modeling and searching complex functions in high dimensions.
method Exploiting conditional independence, Thompson Sampling respecting bilateral uncertainty (BU).
result Thompson Sampling with BU is more effective than the additive approximation in small budgets.
Proposes DAK model for improved GP computations.
problem Challenges in high-dimensional GP layers in DKL.
method Additive structure and induced prior approximation for GP units.
result Outperforms state-of-the-art DKL methods in regression and classification.
New algorithm approximates optimal transport cost with additive error in near-linear time.
problem Scalable approximation of optimal transport cost with additive error.
method Adapted classical graph algorithm of Gabow and Tarjan, with novel analysis.
result Achieves execution time of $O( rac{n^2 C}{δ} + rac{nC^2}{δ^2})$.
Constant-time approximation of partition functions for dense models.
problem Approximating partition functions in dense graphical models efficiently.
method Combining techniques from Markov Chain Monte Carlo and Variational Methods.
result An O(εn) additive approximation of the log partition function found in constant time. Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator, a GP model can beneficially be used for tasks such as prediction, optimization, …
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…
New GaussianSketch approximates kernel distances with almost relative error and small additive term.
problem Approximating kernel distances between point sets efficiently.
method Truncating Gaussian kernel expansions and using RecursiveTensorSketch.
result Approximates kernel distance with almost (1+ε)-relative error and small additive α term. We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic…
Privacy preserving mechanisms such as differential privacy inject additional randomness in the form of noise in the data, beyond the sampling mechanism. Ignoring this additional noise can lead to inaccurate and invalid inferences. In this paper, we incorporate the privacy mechanism explicitly into the likelihood functi…
The paper tackles learning smooth distance functions using query-based methods.
problem Learning smooth distance functions under query constraints.
method Global and local approaches using Mahalanobis distance functions.
result Quadratic query complexity for both additive and multiplicative approximations.
New method recovers causal graphs from data scores in non-linear models.
problem Recovering causal graphs from data scores in non-linear models.
method Score matching algorithms and efficient Jacobian approximation.
result New method, SCORE, is competitive and faster than state-of-the-art methods.
We prove that a compactly supported homeomorphism of a smooth manifold of dimension greater or equal to 5 can be approximated uniformly by compactly supported diffeomorphisms if and only if it is isotopic to a diffeomorphism. If the given homeomorphism is in addition volume preserving, then it can be approximated unifo…
Replicable clustering algorithms for k-medians, k-means, and k-centers are proposed.
problem Designing clustering algorithms that produce the same partition on repeated runs under the same distribution.
method Utilizing approximation routines for combinatorial clustering problems in a black-box manner.
result Replicable algorithms for statistical k-medians, k-means, and k-centers with specified approximation and sample complexities. Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more s…
In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of the nuclear norm over the spectral norm. The presented bound has i…
New neural networks combine additive regression with traditional architectures.
problem Performance limitations and high parameter requirements of traditional neural networks.
method Introduce hybrid deep additive neural networks with simpler activation and basis functions.
result Hybrid neural networks achieve better performance with fewer parameters.
We derive caplet volatilities for quadratic models, providing an asymptotic approximation.
problem Calculating caplet volatilities for quadratic term-structure models.
method Asymptotic approximation for caplet volatilities under quadratic models.
result Asymptotic accuracy of the derived caplet volatilities.
Study approximates unknown function levels with queries.
problem Approximating unknown function levels through sequential queries.
method Introduce Bisect and Approximate algorithms to reduce to local function approximation.
result Rate-optimal sample complexity guarantees for H{ö}lder functions.
Efficient algorithms for online learning with changing action sets, achieving no-approximate-regret guarantees.
problem Online learning with sleeping experts/bandits, where only a subset of actions are available each time.
method Developed computationally efficient algorithms providing no-approximate-regret guarantees for the general problem and better approximation ratios for special cases.
result Achieved no-approximate-regret guarantees for the general sleeping expert/bandit problems and better approximation ratios for specific cases.
New algorithm improves quantized neural networks for image classification.
problem Improving approximation capabilities of quantized neural networks.
method Proposed a novel gradient-based training algorithm for quantized neural networks.
result State-of-the-art performance on image classification benchmarks.
Paper optimizes GAIL for online and offline learning with linear approximations.
problem Imitation learning from expert demonstrations with linear function approximations.
method Proposes optimistic and pessimistic algorithms for online and offline settings.
result Proves optimality and efficiency of proposed algorithms.
Normalizing flow regression approximates posterior distributions without additional sampling.
problem Bayesian inference with computationally expensive likelihood evaluations.
method Normalizing flow regression (NFR) for offline inference.
result NFR yields a tractable posterior approximation through regression on existing log-density evaluations.
Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matri…
In this paper we present a new algorithm for computing a low rank approximation of the product ATB by taking only a single pass of the two matrices A and B. The straightforward way to do this is to (a) first sketch A and B individually, and then (b) find the top components using PCA on the sketch. Our algori…
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trad…
New algorithms approximate Rashomon set for sparse models, aiding expert interaction.
problem Lack of interaction between models and domain experts in classical machine learning.
method Approximate Rashomon set of sparse, generalized additive models using ellipsoids.
result Efficiently approximated Rashomon set facilitates model selection and exploration.
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
Automates VI divergence selection for efficient few-shot learning.
problem Efficiently selecting divergence measures for VI to improve performance.
method Meta-learning algorithm to learn optimal divergence metric and variational parameter initialization.
result Meta-learning approach outperforms standard VI methods across various tasks.
BackPACK extends PyTorch to compute additional gradient info.
problem Lack of efficient tools for computing mini-batch variance and Hessian approximations.
method BackPACK builds on PyTorch to automatically compute additional derivatives.
result BackPACK enables efficient computation of various derivative quantities.
Study on Wasserstein distance for numerical approximations of stochastic differential equations.
problem Estimating the Wasserstein distance between stochastic differential equation distributions and their numerical approximations.
method Unified framework for analyzing different integrators and a novel splitting method for underdamped Langevin dynamics.
result A novel splitting method for underdamped Langevin dynamics with optimal complexity.
Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…
Paper speeds up GP inference by reducing precision matrix computation.
problem High computational complexity in computing kernel precision matrices.
method Splitting precision matrix into Hankel-Toeplitz matrices and computing only unique entries.
result Precision matrix computation reduced from O(NM2) to O(NM). This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. …
New method for automatically smoothing GAMs in large datasets.
problem Lack of reliable and fast methods for automatic smoothing in large datasets of GAMs.
method Empirical Bayes approach with an approximate expectation-maximization algorithm involving double Laplace approximation.
result The method achieves state-of-the-art accuracy and is faster than existing methods.
Paper reveals free information from differential privacy mechanisms improving query accuracy.
problem Improving query accuracy with differential privacy mechanisms.
method Analysis of Noisy Max and Sparse Vector mechanisms.
result Noisy Max releases the noisy gap between the approximate maximizer and runner-up.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
Unified scalable GPCs for various likelihoods using additive noise.
problem Scalability issues and intractable inference in GPC for big data and non-Gaussian likelihoods.
method Additive noise to unify scalable GPCs for multiple likelihoods, using variational inference.
result Empirically superior results for binary/multi-class classification tasks with up to two million data points.
Optimal square matrices for image approximation under translation and rotation.
problem Approximating images with translation and rotation invariant subspaces.
method Abstract harmonic analysis for constructing optimal square matrices.
result Optimal approximation of images with minimal quadratic error.
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
A fast Monte Carlo method for additive processes and option pricing.
problem Efficiently pricing path-dependent options with additive processes.
method Developed a fast Monte Carlo scheme for additive processes, analyzing and reducing numerical error sources.
result Shows significant reduction in error (1 bp or below) for pricing path-dependent options.
Bayesian principles improve neural additive models for better feature selection and uncertainty.
problem Lack of calibrated uncertainties and feature selection in neural additive models.
method Augmenting NAMs with Bayesian principles to provide credible intervals, feature selection, and interaction ranking.
result Improved performance on tabular datasets and real-world medical tasks.
Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical covariance kernels when the dimension of input increases. In oder to get round the cu…