Kernel improves Gaussian process scalability for wide datasets.
problem Under-performance of Gaussian processes on wide data.
method Introduces Bézier Gaussian Process kernel with exponential summarising variables growth and linear cost.
result Empirically demonstrates scalability to both tall and wide datasets.
WideBNet learns inverse scattering from wide-band data efficiently and stably.
problem Learning the inverse scattering map from wide-band scattering data.
method Combines butterfly factorization, FFT, and deep learning.
result WideBNet requires fewer training points and has stable training dynamics.
We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotically consistent algorithms is designed for clustering offline and online datasets, respectively. We also suggest a formal criterion on the eff…
The paper analyzes knowledge distillation in wide neural networks, providing theoretical insights and practical implications.
problem Lack of theoretical understanding of knowledge distillation in wide neural networks.
method Theoretical analysis of knowledge distillation in a linearized model of a wide neural network, introducing a metric of task training difficulty.
result For a perfect teacher, a high ratio of teacher's soft labels can be beneficial. For imperfect teacher, hard labels can correct wrong predictions.
Wide residual networks generalize well with uniform convergence to RNTK as width increases.
problem Understanding the generalization ability of wide residual networks.
method Uniform convergence of residual network kernel to residual neural tangent kernel (RNTK).
result Generalization error converges to kernel regression error with respect to RNTK.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
Study of common financial data patterns across stocks.
problem Understanding common patterns in financial data.
method Analysis of stock price data from multiple exchanges.
result Identification of various stylized empirical facts in financial data.
Wide neural networks on R generalize well with early stopping.
problem Understanding generalization in wide neural networks.
method Analysis of spectral properties of NTK and NNK, convergence of NNK to NTK, minimax rates, and early stopping strategy.
result Wide neural networks trained with early stopping achieve the minimax rate and generalize well.
Paper proposes a GAN-based approach for RTLMP prediction.
problem Predicting real-time locational marginal prices (RTLMPs) in power markets.
method GAN-based video prediction model for spatio-temporal correlations.
result Proposed method accurately predicts RTLMPs without confidential information.
Wide BNNs with odd activations fail to approximate data under mean-field inference.
problem Theoretical limitations of mean-field variational inference in wide, deep Bayesian neural networks.
method Analysis of mean-field variational inference in fully-connected BNNs with odd activation functions and Gaussian likelihood.
result The optimal mean-field variational posterior predictive distribution converges to the prior predictive distribution as network width increases.
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian independent sources. The problem can be seen as a likelihood maximization problem. We i…
Wide and Deep GNN learns from distributed graphs and retrain online.
problem Decentralized graph support changes over time, causing mismatch between training and testing graphs.
method Wide and Deep GNN architecture with distributed online learning.
result Convergence guarantees for online retraining of the wide part of the GNN.
Feature selection from wide datasets leads to misleading results.
problem Feature selection in wide datasets with few samples can lead to misleading results.
method Derived sample size requirement for declaring features different, used real datasets to illustrate issues.
result Feature selection from very wide datasets may lead to misleading results.
Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the regularization parameter. The type of regularization (e.g. the norm used to regularize)…
ERFit identifies dynamic equations from data with minimal supervision.
problem Data-driven sparse system identification in science and engineering.
method Entropic Regression method.
result ERFit package simplifies sparse system identification for various applications.
Gradient descent is a simple and widely used optimization method for machine learning. For homogeneous linear classifiers applied to separable data, gradient descent has been shown to converge to the maximal margin (or equivalently, the minimal norm) solution for various smooth loss functions. The previous theory does …
Wide neural networks' last hidden layers split into groups of redundant neurons.
problem Understanding why wide neural networks generalize well despite overfitting.
method Analyzed the last hidden layer representations of various convolutional neural networks.
result Wide hidden layers split into groups of redundant neurons, which help generalize.
This paper connects functional data analysis with machine learning techniques.
problem Lack of theoretical analysis for functional depths.
method Viewing functional depths as kernel mean embeddings in machine learning.
result Facilitates answers to open questions about functional depths.
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
Bayesian method reconstructs hidden higher-order interactions from network data.
problem Lack of explicit higher-order interactions in pairwise network data.
method Bayesian approach based on parsimony, infers higher-order structures when statistically supported.
result Demonstrated applicability to various datasets, synthetic and empirical.
In this paper, we explore salient questions about user interests, conversations and friendships in the Facebook social network, using a novel latent space model that integrates several data types. A key challenge of studying Facebook's data is the wide range of data modalities such as text, network links, and categoric…
Wide Bayesian neural networks have a simpler weight posterior, leading to faster MCMC sampling.
problem Sampling from the posterior of wide Bayesian neural networks is challenging.
method Introducing repriorisation, a data-dependent reparameterisation that simplifies the posterior distribution.
result The repriorisation map accelerates MCMC sampling, achieving up to 50x higher effective sample size.
Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems wi…
Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous, they depend on input distributions that are data-cleaning- and Data-Model-depende…
Paper applies NEAT for dynamic credit evaluation using streaming data.
problem Dynamic credit evaluation using streaming data.
method Neuroevolution of Augmenting Topologies (NEAT) with enhancements.
result NEAT effectively handles dynamic credit evaluation with streaming data.
ParKCa combines multiple causal inference methods to infer new causes from known and unknown factors.
problem Causal inference from observational data when randomized experiments are not feasible.
method ParKCa uses a stacking approach to combine results from multiple causal inference methods.
result ParKCa infers more causes than existing methods in real-world and simulated datasets.
With the wealth of high-throughput sequencing data generated by recent large-scale consortia, predictive gene expression modelling has become an important tool for integrative analysis of transcriptomic and epigenetic data. However, sequencing data-sets are characteristically large, and previously modelling frameworks …
Wide neural networks converge to Gaussian processes, improving generalization.
problem Understanding the generalization of wide neural networks, especially deep equilibrium models.
method Investigation of deep equilibrium models (DEQs) with infinite-depth layers, focusing on their convergence to Gaussian processes as width and depth approach infinity.
result Wide DEQs converge to Gaussian processes, maintaining generalization performance.
We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedbac…
Study on connectivity of Morse boundaries of Coxeter groups.
problem Connectivity of Morse boundaries of Coxeter groups.
method Defined conditions on defining graphs (wide-avoidant, wide-spherical-avoidant) and characterized Morse boundaries based on these conditions.
result Characterization of Morse boundary connectivity for different classes of Coxeter groups.
CFMI improves missing data imputation across various data types and dimensions.
problem Imputing missing data in complex, high-dimensional datasets.
method Combines normalising flows, flow-matching, and shared conditional modelling.
result Outperforms traditional and modern imputation methods across multiple metrics.
This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.
problem Exact data interpolation using sparse, infinitely wide neural networks.
method Atomic norm framework to derive convex hulls and equivalent convex formulations.
result Simple characterizations of convex hulls for different constraints on network weights and biases.
2 Diabetes is a leading worldwide public health concern, and its increasing prevalence has significant health and economic importance in all nations. The condition is a multifactorial disorder with a complex aetiology. The genetic determinants remain largely elusive, with only a handful of identified candidate genes. G…
Wide networks learn from adversarial perturbations effectively.
problem Understanding why adversarial examples deceive classifiers and transfer between models.
method Assumed wide two-layer networks, proved with theoretical analysis.
result Adversarial perturbations contain class-specific features for networks to generalize.
Assessing world-wide financial integration constitutes a recurrent challenge in macroeconometrics, often addressed by visual inspections searching for data patterns. Econophysics literature enables us to build complementary, data-driven measures of financial integration using graphs. The present contribution investigat…
Wide neural networks with weight decay exhibit neural collapse.
problem Proving neural collapse in wide neural networks trained with weight decay.
method Generic guarantees on neural collapse for wide networks with weight decay, proving low training error and balancedness, and bounded conditioning.
result First proof of neural collapse in end-to-end training of wide neural networks with weight decay.
The paper reviews and improves concentration inequalities for statistical inference.
problem Analyzing statistical inference in various settings with high-dimensional data.
method Review and improvement of concentration inequalities for different types of random variables and statistical measures.
result Fresh new results and improved bounds with sharper constants.
Wide Boosting improves GB's performance on multivariate output tasks.
problem Lack of flexibility in fitting probabilistic multi-dimensional outputs.
method Inserts matrix multiplication between GB output and loss function.
result Wide Boosting outperforms Gradient Boosting on multivariate output tasks.
Improved traffic forecasting model handles missing data.
problem Short-term traffic forecasting with missing values.
method Proposed SBU-LSTM architecture with bidirectional and unidirectional LSTM.
result Superior performance in accuracy and robustness for network-wide traffic prediction.
A new CA-GAN architecture improves minority class data generation in health datasets.
problem Algorithmic bias due to health data poverty and underrepresentation of minority groups.
method Proposes CA-GAN architecture to address shortcomings of resampling and GAN-based approaches.
result CA-GAN outperforms SMOTE and WGAN-GP* in generating authentic minority class data and maintaining original distribution.
Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic and real data.
Google Trends can lead to misleading forecasts if not used carefully.
problem Misleading forecasts due to the variability of Google Trends data.
method Analyzing the variability of Google Trends data and proposing solutions.
result Google Trends can be a problem if not used with caution.
A new framework for private Bayesian tests maintains interpretability and computational efficiency.
problem Lack of interpretability and inability to quantify evidence in confidential data.
method Differentially private Bayesian tests based on test statistics.
result Established results on Bayes factor consistency under the proposed framework.
Machine learning categorizes mutual funds for better investment strategies.
problem Identifying similar mutual funds for diversified investment applications.
method Machine learning to learn and reproduce a well-regarded categorization system.
result Machine learning can learn and reproduce a categorization system that is widely regarded.
We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation is exponential in the ratio of network depth to width. Thus, even in the limit of infinite overparameterization, the NTK is not determinist…
Novel mutual information bound improves statistical inference rates.
problem Improving statistical inference rates in Bayesian nonparametrics.
method Introduces a novel mutual information bound.
result Improved contraction rates for fractional posteriors.
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…
Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient algorithm to c…