arXiv research

Mixes higher-order simplicial complexes for data augmentation.

This research explores complex-valued neural networks and their implementation.

CAP-BM learns complex-valued data's amplitude and phase distributions.

Generative model synthesizes complex data structures with composite and nested types.

Cross-regularization adapts model complexity during training.

The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a global minimizer of the error. Previous work showed that a global solution could b…

Quantum learning complexity reviewed using information theory.

Reinterprets DNF as a deep generative LDA model for complex data.

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry…

Study shows $k$-NN regressor consistency in complex survey designs.

Proposes a new method for causal inference in high-dimensional complex data.

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their …

Private estimation with public data reduces sample complexity.

This work extends alpha-beta divergences to complex data and finds closed-form solutions.

Study shows low-complexity models can perform as well as state-of-the-art on small datasets.

Lower bounds on query complexity for reconstructing private learner's training data.

Improved loss scaling for stochastic momentum algorithms in high dimensions.

New algorithms extract low-dimensional representations from sequential data, revealing insights into complex processes.

New findings show a balance between data fit and complexity in kernel hyperparameters.

Large datasets represented by multidimensional data point clouds often possess non-trivial distributions with branching trajectories and excluded regions, with the recent single-cell transcriptomic studies of developing embryo being notable examples. Reducing the complexity and producing compact and interpretable repre…

A new deep learning framework for topological data.

Improved VAE estimation from incomplete data using variational mixtures.

ENN method uses expectile regression for genetic data analysis of complex diseases.

Complex embeddings handle non-metric proximity data better than traditional methods.

New framework minimizes model complexity for improved few-shot learning.

Develops a measure-theoretic framework for complex co-occurrence data.

Enhances random forest consistency and introduces DMRF for improved performance.

Researchers decompose Forman-Ricci curvature for efficient computation in VR complexes.

We consider the problems of robust PAC learning from distributed and streaming data, which may contain malicious errors and outliers, and analyze their fundamental complexity questions. In particular, we establish lower bounds on the communication complexity for distributed robust learning performed on multiple machine…

Paper extends learning theory to dependent data with uniform risk bounds.

A new algorithm splits Gaussian processes for efficient streaming data.

New conditions show proxy data can improve policy learning in sparse expert data contexts.

Proves Hölder continuity of complex Monge-Ampère solutions.

Proposes a method to learn policies from offline data with reduced bias.

New metrics assess class overlap and imbalance in datasets.

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper bounded in terms of data-independent Rademacher complexity; for generalized Baye…

Modern techniques simplify complex high-dimensional data.

Novel framework uses synthetic data to quantify uncertainty in complex data.

Paper defines and evaluates DR complex for persistent homology.

We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothe…

IsUMap improves data visualization of complex geometries.

New neural network models for complex functional data analysis.

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximator…

Rectified flows achieve optimal sample complexity for generating data.

We study the sample complexity of private synthetic data generation over an unbounded sized class of statistical queries, and show that any class that is privately proper PAC learnable admits a private synthetic data generator (perhaps non-efficient). Previous work on synthetic data generators focused on the case that …

New method measures generalizability of deep neural networks based on decision boundary complexity.

No free lunch theorems suggest inductive biases are needed, but we show neural networks prefer low-complexity data.

FGBoost boosts gradient boosting for complex data.