Paper explores RKHS properties for derivative and integral operators.
problem Establishing sufficient conditions for reproducing property in RKHS.
method Establishing reproducing property for combinations of composition operators.
result Provides framework for regularized learning algorithms involving function values, gradients, or operators.
Derives properties of heat kernel for Rumin complex on Heisenberg groups.
problem Analyzing heat kernel properties for Rumin complex.
method Derives properties of heat equation with Hodge operator on Heisenberg groups.
result Constructs Calderón reproducing formula using heat kernel for Rumin forms.
Survival analysis models research reproducibility, offering new insights.
problem Reproducibility crisis in machine learning research.
method Survival analysis to model reproducibility as a continuous process.
result Survival analysis provides deeper insights into research reproducibility.
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential eq…
The paper develops a uniform function estimator in RKHS for regression.
problem Reconstructing functions from noisy data at random locations.
method Using reproducing kernel Hilbert spaces and Gaussian random fields.
result The estimator converges uniformly to the conditional expectation.
Paper introduces RKHM and KME for richer data analysis.
problem Lack of rich data structures in kernel methods.
method Proposes RKHM and KME for functional data analysis.
result RKHM captures structural properties in functional data.
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (nor…
Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RK…
Paper introduces RKHM for more explicit variable structures analysis.
problem Explicitly analyzing structures among variables.
method Orthonormal systems in Hilbert C∗-modules, RKHM. result Theoretical and practical procedures for RKHM orthonormalization.
The paper uses Banach spaces to analyze neural networks.
problem Understanding the function spaces of neural networks.
method Theory of reproducing kernel Banach spaces.
result Representer theorem for wide class of Banach spaces.
This paper extends mirror descent to Banach spaces with reproducing kernels.
problem Optimizing in Banach spaces with reproducing kernels.
method Mirror descent algorithm adapted for Banach spaces with reproducing kernels.
result Mirror descent achieves linear convergence in certain conditions and standard convergence in a constrained setting.
This study connects Gaussian processes and RKHS, bridging two machine learning communities.
problem Understanding the relationship between Gaussian processes and RKHS.
method Examining connections and equivalences in regression, interpolation, and other topics.
result Established the equivalence between Gaussian Hilbert space and RKHS.
Deep neural networks define suitable reproducing kernel Banach spaces.
problem Characterizing the function spaces of deep neural networks.
method Reproducing kernel Banach spaces and variational results.
result Deep neural networks define suitable reproducing kernel Banach spaces.
Subsampling reduces computational cost in supervised learning in reproducing kernel Hilbert spaces.
problem Reducing computational cost in supervised learning
method Subsampling minimizes empirical risk in reproducing kernel Hilbert spaces
result Optimal subsampling scheme revealed
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. …
Study of regularized least squares in RKKS with indefinite kernels.
problem Asymptotic properties of regularized least squares with indefinite kernels in RKKS.
method Introducing a bounded hyper-sphere constraint, theoretical demonstration of globally optimal solution, modified error decomposition techniques, matrix perturbation theory.
result Derivation of learning rates in RKKS, same as RKHS under certain conditions.
Proposes incorporating noise sources in machine learning evaluation for more reliable conclusions.
problem Inadequate handling of nondeterminism in machine learning research leads to unreliable results.
method Uses linear mixed effects models (LMEMs) and generalized likelihood ratio tests (GLRT) to analyze performance evaluation scores and assess performance differences.
result Demonstrates how to incorporate various sources of noise and data properties into statistical significance testing and reliability analysis.
Develops vector-valued RKBS for neural networks and operators.
problem Understanding function spaces of Rd-valued neural networks and neural operators. method Defines and constructs vector-valued RKBS (vv-RKBS) without restrictive assumptions.
result Establishes Representer Theorem for neural architectures.
We generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of those in \cite{MinhGaussian2010}.
This paper introduces a new Barron space for graph signals and proves its properties for GCNNs.
problem Understanding and optimizing the performance of GCNNs on graph signals.
method Introducing a Barron space on graph signals, proving its properties, and showing the approximation and learning capabilities of GCNNs within this space.
result GCNN outputs are contained in the Barron space and can be well approximated by functions in this space.
Deep networks are shown to be equivalent to a new type of kernel chain.
problem Identifying an appropriate function space for deep neural networks.
method Extending Reproducing Kernel Banach Spaces (RKBS) to chain RKBS (cRKBS), which composes kernels rather than functions.
result Any deep neural network function is a neural cRKBS function, and conversely, any neural cRKBS function corresponds to a deep neural network.
Study on how sampling works for complex data functions.
problem Analyzing convergence of sampling algorithms for RKHS functions.
method Minimalistic assumptions on kernel and data, error estimates in RKHS norm, uniform convergence on compact domains.
result New convergence rates for Lipschitz and Hölder continuous kernels.
The paper develops methods to handle missing data using regularized M-estimation in reproducing kernel Hilbert space.
problem Handling missing data in statistical analysis.
method Kernel ridge regression for imputation and maximum entropy method for propensity score estimation.
result The proposed methods achieve statistical consistency and asymptotic equivalence.
KEEN Universe provides reproducible and transferable knowledge graph embeddings.
problem Lack of reproducibility and transferability in KGE experiments.
method Developed an ecosystem with Python packages for reproducible and transferable KGEs.
result KEEN Universe facilitates sharing of trained KGE models across different fields.
Generating molecules with desired chemical properties is important for drug discovery. The use of generative neural networks is promising for this task. However, from visual inspection, it often appears that generated samples lack diversity. In this paper, we quantify this internal chemical diversity, and we raise the …
We study simultaneous price drops of real stocks and show that for high drop thresholds they follow a power-law distribution. To reproduce these collective downturns, we propose a minimal self-organized model of cascade spreading based on a probabilistic response of the system elements to stress conditions. This model …
In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on Rd. We prove that only affine transforms can do so in a pretty large class of RKHS. Our result covers not only the …
The paper tackles noisy combinations of continuous and step functions, providing conditions for their identification.
problem Recovering noisy observations as a combination of continuous and step functions.
method Topological and local properties of the functions are used to determine conditions for identification. A practical estimation algorithm is provided.
result Conditions for the identification of continuous and step functions based on their global and local properties.
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our…
A new method learns Hamiltonian functions from noisy data.
problem Learning Hamiltonian functions from noisy observations.
method Structure-preserving kernel ridge regression method.
result The method yields excellent numerical performances.
Study on reproducibility in optimization with bounds on limits.
problem Limits of reproducibility in noisy or error-prone optimization procedures.
method Defined a quantitative measure of reproducibility and analyzed convex optimization settings.
result Revealed a fundamental trade-off between computation and reproducibility.
This study approximates neural network features for modeling relations and attention mechanisms.
problem Approximating neural network features for modeling relations and attention mechanisms.
method Analyzes inner products of multi-layer perceptrons for universal approximation of symmetric and asymmetric relation functions.
result Universal approximation of relation functions and attention mechanisms using inner products of neural networks.
The paper revisits and improves on a Bayesian relevance vector machine method for small sample sizes.
problem Statistical modeling with small sample sizes relative to the number of covariates.
method Introduces a new class of global-local priors and provides theoretical properties.
result Results on posterior consistency and contraction rates are provided.
In de novo drug design, computational strategies are used to generate novel molecules with good affinity to the desired biological target. In this work, we show that recurrent neural networks can be trained as generative models for molecular structures, similar to statistical language models in natural language process…
Study on learning strategies in matching markets with uncertain preferences.
problem Decision-making in scarcity of shared resources with unknown agent preferences.
method Representation of preferences in a reproducing kernel Hilbert space, learning algorithm for uncertainty.
result Optimal strategies derived to maximize agents' expected payoffs, with stability and fairness properties.
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…
Generative model uses ODEs and RKHSs for measure matching.
problem Minimum divergence generative modeling and sampling.
method Diffeomorphic matching and image registration principles applied to ODEs and RKHSs.
result Theoretical error bounds and extensive numerical experiments demonstrate the method's properties and applicability.
Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel machines have experienced great success by operating via inner-products in a theoret…
Paper converts deep networks to flat, equivalent kernel machines.
problem Capacity control and uniform convergence in deep learning.
method Push-forward transformation from deep networks to indefinite kernel machines.
result Flat network weights are Lp-norm regularized (0<p<1).
Clarifies the scope of 'reproducibility' in AI and ML.
problem Unclear meaning of 'reproducibility' in AI and ML.
method Analyzes the community's works on reproducibility.
result Identifies eight general topic areas of reproducibility.
In this paper it was developed a modification of the known multiagent model Minority Game, designed to simulate the behavior of traders in financial markets and the resulting price dynamics on the abstract resource. The model was implemented in the form of software. The modified version of Minority Game was investigate…
We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns. A non-parametric fit on NYSE stock data sho…
This chapter introduces reproducibility in machine learning for medical imaging.
problem Lack of reproducibility in machine learning for medical imaging.
method Distinguishes and defines types of reproducibility, outlines requirements, and discusses utility.
result Discussion on benefits and a plea for a non-dogmatic approach to reproducibility.
New algorithms ensure reproducibility and optimal convergence in convex optimization.
problem Trade-off between reproducibility and convergence rate in convex optimization.
method Regularization-based algorithms for smooth convex minimization and minimax optimization.
result Achieves optimal reproducibility and near-optimal gradient complexity for various oracle settings.
The article analyzes LCE in Hilbert space, deriving new formulas and regularisation methods.
problem Analyzing conditional expectation in infinite-dimensional Hilbert space.
method Establishing analytical properties and regularisation for LCE in Hilbert space, deriving new formulas.
result Simple derivation and intuitive justification of conditional mean embedding formula.
Proposes a method to improve neural architectures reproducibly.
problem Lack of reproducibility in Neural Architecture Transformer (NAT).
method Differentiable Neural Architecture Transformation (DNAT).
result DNAT outperforms NAT and is applicable to various models and datasets.
The paper aims to improve reproducibility of machine learning experiments.
problem Lack of reproducibility in machine learning experiments.
method Investigates factors affecting reproducibility and proposes FAIR data practices.
result Preliminary results show the role of ProvBook in capturing and comparing provenance.
NeurIPS 2019 program improves reproducibility in machine learning.
problem Ensuring machine learning research results are reproducible and reliable.
method Code submission policy, reproducibility challenge, and checklist integration.
result Improved reproducibility standards across the machine learning community.