Mixes higher-order simplicial complexes for data augmentation.
problem Lack of labeled data for complex systems with multiway interactions.
method Proposes mixup mechanisms for simplicial complexes, including linear and nonlinear mixup, and a convex clustering mixup.
result Synthetic simplicial complexes interpolate between existing data based on homomorphism densities.
This research explores complex-valued neural networks and their implementation.
problem The challenges of implementing complex-valued neural networks and their potential for non-complex data.
method Detailed theory and implementation of CVNN, including Wirtinger calculus, complex backpropagation, and modules like complex layers and activation functions. Python implementation using cvnn toolbox.
result Demonstrates the potential of CVNN for non-complex data through simulations.
CAP-BM learns complex-valued data's amplitude and phase distributions.
problem Learning from complex-valued data with amplitude variation.
method Complex Amplitude-Phase Boltzmann machine (CAP-BM) with Gibbs sampling.
result Necessity of amplitude-amplitude coupling term in CAP-BM.
Generative model synthesizes complex data structures with composite and nested types.
problem Synthesizing complex data structures with composite and nested types.
method Generic framework using causal transformers for struct and list generation.
result Consistently outperforms state-of-the-art models on standard and complex hierarchical datasets.
Cross-regularization adapts model complexity during training.
problem Manual tuning of model complexity for overfitting prevention.
method Directly adapts regularization parameters through validation gradients during training.
result Organic emergence of architecture-specific regularization 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.
problem Learning properties of quantum systems or processing data via quantum computing.
method Information-theoretic techniques focusing on data, copy, and model complexity.
result Copy complexity due to irreversible quantum measurements limits information extraction.
Reinterprets DNF as a deep generative LDA model for complex data.
problem Limited applicability of LDA in complex data scenarios.
method Proposes a discriminative normalization flow (DNF) model and interprets it as a deep generative LDA.
result DNF and its subspace version outperform conventional LDA in modeling 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 examines how network architecture handles increasing data complexity.
problem Understanding how network architecture affects performance with complex data.
method Empirical study comparing various network architectures on an image classification task with increasing class numbers.
result Modern architectures show better generalization performance with increasing data complexity.
Study shows k k k -NN regressor consistency in complex survey designs.
problem Lack of consistency results for k k k -NN regressor in complex survey data. method Analysis of regularity conditions on sampling design and data distribution.
result Consistency of k k k -NN regressor under complex survey designs. Method infers causal direction using data discretization and complexity calculation.
problem Determining causal direction between continuous variables.
method MDL Binning technique for data discretization and complexity calculation.
result Captures the shape of the data to determine causal direction.
Proposes a new method for causal inference in high-dimensional complex data.
problem Challenges in making causal inference with high-dimensional, nonlinear data.
method Combines deep learning techniques like sparse deep learning and stochastic neural networks.
result Outperforms existing methods in numerical studies.
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 …
Proposes a Complex Transformer for complex-valued sequence modeling.
problem Lack of deep learning models for complex-valued data.
method Develops a Complex Transformer using transformer backbone with specialized attention and encoder-decoder networks.
result Achieves state-of-the-art performance on complex-valued datasets.
Private estimation with public data reduces sample complexity.
problem Estimating private distributions with limited public data.
method Differentially private estimation with public data under constraints of pure or concentrated DP.
result Public data can significantly reduce private sample complexity for estimation.
This work extends alpha-beta divergences to complex data and finds closed-form solutions.
problem Approximating complex random vectors.
method Extending alpha-beta divergences to complex data and optimizing the alpha-beta mean distortion.
result Closed-form expression for the centroid of complex random vectors.
Study shows low-complexity models can perform as well as state-of-the-art on small datasets.
problem Performance of deep learning models on small datasets.
method Wide variety of experiments with different deep learning architectures on small datasets.
result Low-complexity models can perform comparably well or better than state-of-the-art models on small datasets.
Lower bounds on query complexity for reconstructing private learner's training data.
problem Query complexity of reconstructing private learner's training data.
method Minimax analysis, Rényi DP, Metric DP framework.
result First known lower bounds on adversary's query complexity for various DP learners.
Improved loss scaling for stochastic momentum algorithms in high dimensions.
problem Improving loss scaling for stochastic momentum algorithms in high dimensions.
method Dimension-adapted Nesterov acceleration (DANA) scales momentum hyperparameters based on model size and data complexity.
result DANA improves loss scaling exponents across various data and target complexities.
BNs extract sparse, non-redundant features from climate data networks.
problem Redundant information in correlation networks limits physical feature extraction.
method Construct data-driven complex networks using Bayesian Networks.
result Sparse, non-redundant features reveal generalizable physical features.
New algorithms extract low-dimensional representations from sequential data, revealing insights into complex processes.
problem Challenges in extracting low-dimensional representations from sequential, high-dimensional, sparse, and noisy data.
method Developed new clustering algorithms based on Block Markov Chains theory, validated on real-world data.
result These algorithms can successfully extract low-dimensional representations from real-world sequential data, revealing insights into complex processes.
New findings show a balance between data fit and complexity in kernel hyperparameters.
problem Overcorrelation due to reparametrization of kernel hyperparameters.
method Reparametrization of kernel hyperparameters and analysis of marginal likelihood.
result Data fit term influences all other kernel hyperparameters, not just the complexity penalty.
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.
problem Developing models for data on complex topological domains.
method Introducing combinatorial complexes and developing attention-based CCNNs.
result CCNNs outperform existing models in tasks involving mesh shape analysis and graph learning.
Improved VAE estimation from incomplete data using variational mixtures.
problem Estimating VAEs from incomplete data increases posterior complexity.
method Introducing variational mixtures based on finite and imputation distributions.
result Variational mixtures improve VAE estimation accuracy from incomplete data.
A new clustering method for simplicial complexes using homology.
problem Clustering simplicial complexes efficiently and accurately.
method Inspired by graph spectral clustering, the method uses sparse eigenproblems.
result Produces clusters sensitive to simplicial complex homology.
Improved NODEs for long-term time series forecasting.
problem Dealing with complex, multi-frequency data.
method Progressive learning paradigm with curriculum learning.
result Performance improved by over 64%.
ENN method uses expectile regression for genetic data analysis of complex diseases.
problem Discover additional genetic variants contributing to complex diseases.
method Developed an expectile neural network (ENN) method integrating expectile regression and neural networks.
result ENN method outperforms existing expectile regression in discovering genetic variants predisposing to sub-populations.
Complex embeddings handle non-metric proximity data better than traditional methods.
problem Proximities not always metric or inner product-based, causing convergence issues.
method Proposes complex-valued embeddings for non-vectorial data.
result Complex embeddings outperform traditional techniques on benchmarks.
New framework minimizes model complexity for improved few-shot learning.
problem Empirical benefits of pre-training scale with data size but lack theoretical explanation.
method Complexity Minimization framework for meta-representation learning.
result Theoretical analysis shows error rate improves with more meta-training data.
Develops a measure-theoretic framework for complex co-occurrence data.
problem Modeling and interpreting complex co-occurrences in high-dimensional data.
method Introduces measure-theoretic probability and conditional probability, investigates E-integrals.
result Establishes a rigorous measure-theoretic foundation for co-occurrence modeling.
Enhances random forest consistency and introduces DMRF for improved performance.
problem Improving the consistency and efficiency of random forest algorithms.
method Strengthened proof methods and propose DMRF algorithm.
result DMRF achieves better theoretical and experimental performance than previous variants.
Researchers decompose Forman-Ricci curvature for efficient computation in VR complexes.
problem Efficiently computing Forman-Ricci curvature in higher-dimensional data.
method Decomposition and set-theoretical proof for local computation of FRC in VR complexes.
result Reveals critical geometric insights overlooked by conventional techniques.
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.
problem Learning with dependent data sequences.
method Derives uniform risk bounds for dependent data using VC-dimension and Rademacher complexity.
result Standard classification risk bounds hold for dependent data, same as for independent data.
A new algorithm splits Gaussian processes for efficient streaming data.
problem Poor scaling of Gaussian processes in streaming data.
method Sequential partitioning of input space and localized Gaussian process fitting.
result The algorithm achieves linear memory complexity and superior time and space complexity.
New conditions show proxy data can improve policy learning in sparse expert data contexts.
problem Improving sample complexity of policy learning with sparse expert data.
method Sufficient conditions for proxy data to improve sample complexity, adaptable to LLMs.
result Provable improvement in sample complexity for policy learning with proxy data.
Proves Hölder continuity of complex Monge-Ampère solutions.
problem Global Hölder continuity of solutions to complex Monge-Ampère equation.
method Analyzes Dirichlet problem on strictly pseudoconvex domains or Hermitian manifolds.
result Proves global Hölder continuity of solutions under given conditions.
Proposes a method to learn policies from offline data with reduced bias.
problem Learning policies from offline data with reduced bias and complexity constraints.
method Cross-fitted debiasing device for policy learning from offline data.
result Achieves N \sqrt N N regret for complex policy classes with a product-of-errors nuisance remainder. New metrics assess class overlap and imbalance in datasets.
problem Class overlap and imbalance make datasets hard to classify.
method Developed new metrics based on ball coverage by classes.
result Metrics correlate well with classifier performance.
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.
problem Complex, high-dimensional data.
method Unsupervised dimension reduction techniques.
result Simplified representation of high-dimensional data.
Novel framework uses synthetic data to quantify uncertainty in complex data.
problem Uncertainty quantification in complex, unstructured data.
method Perturbation-Assisted Sample Synthesis (PASS) and Perturbation-Assisted Inference (PAI) framework.
result Statistically guaranteed validity in inference, enhancing reliability of synthetic data.
Paper defines and evaluates DR complex for persistent homology.
problem Computing persistent homology of Euclidean point cloud data.
method Delaunay-Rips complex construction for speed and stability.
result DR produces stable persistence diagrams under point cloud perturbations.
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.
problem Accurately representing complex, locally distorted metric spaces.
method Integrates UMAP and Isomap with Vietoris-Rips filtrations.
result Significant improvements in data representation quality.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.