arXiv research

AutoEncoder smooths noisy sensor data and interpolates missing values.

Proves a new law of robustness for interpolating arbitrary data distributions.

In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder network to map data samples into latent space and perform interpolation via an int…

Near-interpolating models grow norms quickly, affecting generalization.

Deep networks can interpolate noisy data without losing generalization.

The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small testing error, and sometimes even {\em outperform} traditional algorithms which ar…

Uniform convergence of interpolators proven for Gaussian data.

In sparse-view Computed Tomography (CT), only a small number of projection images are taken around the object, and sinogram interpolation method has a significant impact on final image quality. When the amount of sparsity (the amount of missing views in sinogram data) is not high, conventional interpolation methods hav…

Paper investigates optimal interpolation methods in linear regression.

Study tightens bounds for interpolating noisy data using minimum l1-norm.

We improve autoencoder image interpolation by shaping latent space.

Gaussian Processes improve data interpolation from diverse experiments.

A physics-based method improves data interpolators and regression tasks.

The paper improves interpolation in generative models by using specific base distributions.

SoftKI combines SKI and variational methods for scalable GP regression.

Exploiting the deep generative model's remarkable ability of learning the data-manifold structure, some recent researches proposed a geometric data interpolation method based on the geodesic curves on the learned data-manifold. However, this interpolation method often gives poor results due to a topological difference …

Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.

Interpolation improves performance in nearest neighbor algorithms without over-parametrization.

Enhances interpolation paths in latent space using particle filters.

Study interpolating estimators for causal learning from observational data.

New method interpolates high-dimensional scattered data using kernel theory.

A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solut…

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framewor…

Study shows how networks converge to minimum norm solutions with regularization.

Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex combination of the latent codes for two datapoints, the autoencoder can produce …

Two methods for interpolating manifold-valued data are presented.

Fair Mixup improves fairness in classifiers by interpolating between groups.

Interpolation can prevent classifiers from having desired invariance properties.

We show that learning methods interpolating the training data can achieve optimal rates for the problems of nonparametric regression and prediction with square loss.

This research solves Hermite interpolation on manifolds using retractions.

Regression models can interpolate noisy data and still perform well, contrary to the bias-variance tradeoff.

Deep neural networks can interpolate any dataset in the overparametrized regime.

New algorithm interpolates data with neural nets, independent of sample size.

Paper analyzes mistake and generalization of MNIC classifiers.

Study improves sugarcane plot prediction using data interpolation.

This paper explores how deep learning models can fit data exactly and why this is important.

Neural networks learn incrementally from orthogonal data, interpolating with minimal complexity.

A new method uses denoising diffusion models to improve seismic data interpolation.

The paper proves approximation and interpolation theorems for maxfaces with singularities.

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for thes…

Interpolating estimators in nonparametric regression become suboptimal under adversarial attacks.

New insights into Nadaraya-Watson interpolators show varied generalization behaviors.

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point a…

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed …

Combines spline interpolation and ARIMA for stock market forecasting.

Covariance shrinkage via stochastic interpolation

The paper connects flatness to generalization in learning multi-index models with neural networks.

We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on data. The result supports the empirical observation that minimum-norm …