Paper develops a new kernel approximation framework.
problem High time and space complexity of kernel methods for large datasets.
method Perturbation-based kernel approximation framework using classical perturbation theory.
result Framework generalizes and improves upon existing methods.
In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex functions. The proposed framework is based on a nontrivial combination of the majorizatio…
Develops consistent approximations for composite optimization problems.
problem Significant errors in solutions due to approximations in optimization problems.
method Specifies conditions for well-behaved approximations in minimizers, stationary points, and level-sets for a broad class of composite problems.
result Framework of consistent approximations for composite problems, including stochastic, neural-network, and multi-objective optimization.
Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficien…
Framework for universal graph function approximators outperforms existing methods.
problem Graph classification and separation of graph classes.
method Inspired by persistent homology, dependency parsing, and multivalued functions, the framework constructs universal approximators on graph isomorphism classes.
result Achieves state-of-the-art performance on four graph datasets.
A new TwinGP framework for efficient large-scale GP modeling.
problem Efficiently modeling large-scale Gaussian processes with computational constraints.
method Combines global and local approximations using a subset-of-data approach.
result TwinGP framework performs on par or better than state-of-the-art methods at a fraction of the computational cost.
New framework reduces cost of financial option pricing simulations on FPGAs.
problem Efficiently simulate financial option pricing with reduced computational cost.
method Nested MLMC framework with low precision calculations on FPGAs.
result Higher computational savings compared to existing mixed-precision MLMC frameworks.
A framework isolates and learns approximately shared features for better domain adaptation.
problem Reducing performance degradation in unseen domains using machine learning models.
method Statistical framework distinguishing feature utilities based on correlation variance across domains. Learning approximately shared features from source tasks and fine-tuning on target tasks.
result Improved population risk compared to previous results on both source and target tasks, resolving the paradox of feature selection.
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
In real-world applications, not all instances in multi-view data are fully represented. To deal with incomplete data, Incomplete Multi-view Learning (IML) rises. In this paper, we propose the Joint Embedding Learning and Low-Rank Approximation (JELLA) framework for IML. The JELLA framework approximates the incomplete d…
INNs can approximate diverse functions despite layer restrictions.
problem Can INNs approximate sufficiently diverse functions?
method Developed a theoretical framework based on differential geometry to simplify the approximation problem of diffeomorphisms.
result INNs have the universal approximation property.
Novel active learning framework using sparse approximation for efficient model training.
problem Efficient model training with limited labeled data.
method Formulates batch active learning as sparsity-constrained discontinuous optimization problems, using greedy or proximal iterative hard thresholding algorithms.
result Achieves competitive performance with lower computational complexity across different settings.
Unified framework approximates gradient descent's implicit bias in high dimensions.
problem Understanding gradient descent's behavior in overparameterized settings with convex losses.
method Unified framework for convex losses, including sensitivity analysis.
result Approximation of minimum-norm interpolation in high dimensions.
There has been recent interest in developing scalable Bayesian sampling methods such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) for big-data analysis. A standard SG-MCMC algorithm simulates samples from a discrete-time Markov chain to approximate a target distribution, thus samp…
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
Framework purifies approximate differential privacy to pure differential privacy.
problem Achieving pure differential privacy from approximate differential privacy.
method Randomized post-processing with calibrated noise to eliminate δ parameter.
result First statistically and computationally efficient reduction from approximate DP to pure DP.
A new framework for recycling Gaussian process approximations.
problem Efficiently combining multiple Gaussian process approximations.
method Construct variational ensembles using a dictionary of fitted Gaussian processes.
result Framework allows for various tasks and scalability.
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the GP model is itself parameterized using the exponential family distribution (EFD).…
Unified quadrature framework for large-scale kernel machines.
problem Efficiently approximating kernel functions for large-scale machine learning.
method Deterministic and randomized interpolatory rules for numerical integration of kernel functions.
result The proposed method reduces the number of nodes needed for accurate kernel approximation.
In this paper we present a framework to analyze the asymptotic behavior of two timescale stochastic approximation algorithms including those with set-valued mean fields. This paper builds on the works of Borkar and Perkins & Leslie. The framework presented herein is more general as compared to the synchronous two times…
A new framework reduces RL sample complexity for complex MDPs.
problem Handling large state and action spaces in reinforcement learning.
method Unified model-based and model-free RL framework with ABC class, novel estimation function, and functional eluder dimension.
result OPERA algorithm achieves sample-efficient regret bounds for various MDP models.
Develops an efficient approximation for full conformal prediction regions.
problem Computing exact full conformal prediction regions is computationally infeasible.
method Generates an approximate confidence region that can be efficiently computed.
result Introduces a new notion of thickness to quantify approximation tightness.
A new EVI framework improves ParVI methods by maintaining variational structure and reducing KL-divergence.
problem Improving variational inference methods for better approximation of target distributions.
method EVI framework that minimizes the VI objective function based on an energy-dissipation law, including a new 'Approximation-then-Variation' scheme.
result The new scheme significantly decreases KL-divergence and outperforms existing ParVI methods in fidelity.
Improved sparse Gaussian processes using structured scaling matrices and Power-EP framework.
problem Scaling Gaussian processes for large datasets.
method Structured diagonal scaling matrix and Power-EP framework.
result Structured approximations improve performance without increasing computational cost.
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.
Unified framework for Gaussian process methods in differential equations.
problem Fragmented approaches to Gaussian process methods in differential equations.
method Unified Bayesian perspective integrating differential equation constraints.
result Consolidation of existing methods and foundation for future research.
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …
Unified framework for analyzing batch updating methods with noisy gradients.
problem Analyzing convergence of batch updating methods with noisy gradients and approximations.
method Unified framework using convergence of stochastic processes.
result Establishes a general theorem for most known convergence results.
Develops hierarchical reinforcement learning value function approximators.
problem Estimating long-term returns in reinforcement learning with multiple goals.
method Introduces hierarchical universal value function approximators (H-UVFAs) using the options framework.
result Demonstrates generalization and improved performance of H-UVFAs over UVFAs.
A new framework improves fairness in clustering and Wasserstein Barycenter problems.
problem Fair clustering in datasets with multiple groups.
method Relax and Merge framework for (1+4ρ+O(ε))-approximate solutions. result Improved approximation guarantees for fairness constraints.
Efficiently approximates Sparse PCA with significant speedups and minor error.
problem Sparse Principal Component Analysis (Sparse PCA) is NP-hard and computationally expensive.
method Approximates the covariance matrix with block-diagonal form, solves sub-problems in each block, and reconstructs the solution.
result Significant computational speedups with minor additive error.
Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between …
New framework connects two neural network theories, improving finite-width approximations.
problem Theoretical guarantees for neural network training in general cases.
method Developed a general framework linking mean-field and constant kernel theories.
result Discrete-time MF limit provides better approximation for finite-width nets.
We study critera for a pair ({Xn}, {Yn}) of approximating processes which guarantee closeness of moments by generalizing known results for the special case that Yn=Y for all n and Xn converges to Y in probability. This problem especially arises when working with surrogate models, e.g. …
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two…
EBUCB framework achieves optimal regret with bounded approximate inference error.
problem Theoretical gap between practical performance and theoretical justification of Bayesian bandit algorithms with approximate inference.
method Enhanced Bayesian Upper Confidence Bound (EBUCB) framework that accommodates bandit problems with approximate inference.
result EBUCB achieves optimal regret order O(logT) under certain conditions on inference error. Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future observations, offers a principled solution, but is intractable. We review, then…
A-NeSI scales approximate inference for probabilistic neurosymbolic learning.
problem Combining neural networks with symbolic reasoning for scalable inference.
method A-NeSI: a new framework for PNL using neural networks for approximate inference.
result A-NeSI achieves scalable approximate inference without semantic changes.
Empirical study of IRMv1, an invariant risk minimization framework.
problem Learning predictors invariant to spurious correlations across different training environments.
method Extending ColoredMNIST experiment to various settings.
result IRMv1 performs better as spurious correlation varies more widely.
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable function…
Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict …
New method approximates curvature from symmetries in deep networks.
problem Hard to approximate curvature in large deep networks.
method Analytically averaging over group actions that leave the loss invariant to construct structured Hessian approximations.
result Structured Hessian approximations from single gradients can be estimated, stored, and inverted.
Unified framework interprets SSL models, revealing biases.
problem Interpreting black-box SSL models for transparency.
method KREPES framework using Representer Landmarks and Nyström approximation.
result Direct audit of SSL latent space without supervision.
New framework for consistent submodular maximization with insertions and deletions.
problem Maintaining near-optimal solutions in a dynamic setting with insertions and deletions.
method Developed a general framework for fully dynamic submodular maximization, instantiated for cardinality and rank-k matroid constraints.
result First constant-factor approximations with sublinear consistency for both cardinality and rank-k matroid constraints.
Paper introduces deterministic EM approximations for non-convex likelihood functions.
problem Deterministic approximations for the E-step of EM algorithm are lacking.
method Developed a theoretical framework for deterministic approximations, analyzed Riemann sums and tempered EM.
result Proved convergence guarantees for deterministic approximations and new non-trivial temperature profiles.
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for universal approximation using continuous-time deep residual networks, which can …
Unified framework for FDR control in knockoffs, validating Gaussian knockoffs.
problem Asymptotic FDR control in knockoffs with user-specified distributions.
method Unified theoretical framework, three conditions on approximate knockoff statistics, Gaussian knockoffs generator based on moments matching.
result Gaussian knockoffs generator achieves asymptotic FDR control.
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building …