Enhanced KS test detects tail differences more sensitively.
problem Detecting differences in data tail regions.
method Higher-order IPM defined over a total variation ball.
result Asymptotic null distribution for the test.
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48 results for “Kolmogorov test”
New test uses neural networks to compare distributions, outperforming traditional methods.
problem Comparing distributions in high dimensions and higher orders of smoothness.
method Integral probability metrics with Radon bounded variation functions and neural networks.
result The Radon-Kolmogorov-Smirnov (RKS) test outperforms traditional methods in distinguishing distributions.
Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extr…
Test to distinguish metric space distributions using pairwise distances.
problem Distinguishing between two distributions on a metric space.
method Use pairwise distances and a two-sample Kolmogorov--Smirnov test.
result Can determine if two distributions are the same using finite data.
Proposes a new TS algorithm for non-stationary bandits using KS tests.
problem Non-stationary multi-armed bandit problems.
method Active detection of change points using KS tests and adaptive Thompson Sampling.
result Sub-linear regret demonstrated for the two-armed bandit case.
Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciencesstat.ML
Study evaluates two-sample tests for validating generative models in high dimensions.
problem Validating the performance and efficiency of non-parametric two-sample tests for high-dimensional generative models.
method Proposes and evaluates the sliced Wasserstein distance, mean of Kolmogorov-Smirnov statistics, and novel sliced Kolmogorov-Smirnov statistic.
result One-dimensional-based tests provide comparable sensitivity to other multivariate metrics but with lower computational cost.
Kolmogorov-Smirnov GANstat.ML
KSGAN uses KS distance for deep generative modeling.
problem Deep generative modeling challenges, especially for multivariate distributions.
method Formulates adversarial training as minimization of KS distance, using quantile function as critic.
result KSGAN trained distributions closely match target distributions.
K-DAREK improves KKANs for efficient function approximation with robust error bounds.
problem Efficient function approximation with uncertainty quantification for large-scale problems.
method Developed a novel learning algorithm, K-DAREK, for KKANs.
result Established robust error bounds that are distance-aware, improving efficiency and scalability.
Presented are two neural network architectures for convex functions, demonstrating competitive performance.
problem Approximating convex functions efficiently and accurately.
method Developed two neural network architectures: one based on linear-by-part representation and the other on cubic splines.
result Cubic ICKAN networks produce results similar to classical ICNNs in solving convex approximation problems.
The paper introduces a spline-based method for calibrating neural networks.
problem Ensuring neural network outputs are reliable for safety-critical applications.
method Approximating the empirical cumulative distribution function using splines to map network outputs to calibrated probabilities.
result The spline-based recalibration consistently outperforms existing methods on calibration measures.
SurvLIME-KS improves survival model explanations robustly.
problem Improving explanations of unreliable survival models.
method SurvLIME-KS combines Cox proportional hazards model and Kolmogorov-Smirnov bounds for robust optimization.
result SurvLIME-KS minimizes average distance and maximizes distance in approximating cumulative hazard functions.
Support spinor machine extends SVM to handle spinor fields in time series data.
problem Handling nonstationary and nonlinear time series data for classification.
method Using wedge product to extend vector fields to spinor fields, extending SVM to support spinor machine.
result Support spinor machine outperforms SVM in one class classification of physiological time series data.
MAGDiff detects data shifts in neural networks without retraining.
problem Neural networks' sensitivity to data distribution shifts.
method Extracts MAGDiff representations from neural networks to detect shifts.
result MAGDiff representations improve data set shift detection.
This paper tackles G-ZSL by learning compositional spaces to classify unseen classes.
problem Classifying unseen classes in a test set.
method Space decomposition method to estimate and fine-tune decision boundaries between source and target classes.
result State-of-the-art performance on multiple G-ZSL benchmarks.
Kolmogorov-Arnold Networks promise scalable performance in high dimensions.
problem Curse of dimensionality in multilayer perceptrons.
method Kolmogorov-Arnold representation theorem and interpolation methods.
result Kolmogorov-Arnold Networks achieve true freedom from the curse of dimensionality.
Kolmogorov neural networks can represent various types of functions.
problem Representing different types of functions with neural networks.
method Continuous, discontinuous bounded or unbounded activation functions in a two hidden layer model.
result Kolmogorov neural networks can represent continuous, discontinuous bounded and all unbounded multivariate functions.
Study gradient bounds for Kolmogorov type diffusions using coupling and Γ-calculus.
problem Gradient bounds for Kolmogorov type diffusions.
method Coupling techniques and Γ-calculus.
result Advantages and drawbacks of each method discussed.
Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail events and core events contribute equally to the test (in the standard Kolmogorov-S…
New method solves high-dimensional Kolmogorov PDEs without curse of dimensionality.
problem Solving high-dimensional Kolmogorov PDEs efficiently and accurately.
method Deep learning-based numerical approximation method.
result Effective numerical approximation of Kolmogorov PDEs in high dimensions.
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
The paper introduces a new method to detect rough volatility and market states using fractional derivatives.
problem Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence.
method The paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Grünwald--Letnikov (GL) fractional derivative.
result The method detects rough volatility and persistent, anti-persistent, or efficient market states in financial applications.
Revisits the connection between neural networks and the Kolmogorov-Arnold theorem.
problem Explains the limitations of using the Kolmogorov-Arnold theorem to explain neural networks with multiple hidden layers.
method Derives modifications of the Kolmogorov-Arnold representation that transfer smoothness properties to the outer function and can be well approximated by ReLU networks.
result Shows that a deep neural network with most layers approximating the interior function is a more natural interpretation of the Kolmogorov-Arnold representation.
Researchers use estimated Kolmogorov complexity for better link prediction in graphs.
problem Improving link prediction accuracy in complex networks.
method Regularization based on an approximation of Kolmogorov complexity, which is differentiable and compatible with recent link prediction algorithms.
result The regularization method shows good performance on diverse real-world networks, but the success is likely due to an aggregation method rather than actual estimation of Kolmogorov complexity.
New measure LMN explains neural network grokking.
problem Delayed generalization after memorization in neural networks.
method Defined LMN to measure network complexity, showing LMN correlates with test losses linearly.
result LMN reveals intriguing XOR network behavior and is a promising complexity measure.
GC-KAN uses KANs to detect Granger causality in time series data.
problem Detecting causal relationships in nonlinear time series data.
method Developed GC-KAN framework using Kolmogorov-Arnold networks for Granger causality detection.
result KANs outperform MLPs in identifying sparse Granger causal relationships.
P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimizationcs.LG
A new Kolmogorov-Arnold network improves function approximation and optimization.
problem Approximating potentially irregular functions in high dimensions.
method Proposes a new Kolmogorov-Arnold network (KAN) and provides error bounds and universal approximation theorems.
result Outperforms multilayer perceptrons in accuracy and convergence speed for irregular functions.
SVGP KAN integrates uncertainty quantification into Kolmogorov-Arnold networks.
problem Uncertainty quantification in scientific machine learning models.
method Sparse variational Gaussian process inference with Kolmogorov-Arnold topology.
result Demonstrated ability to distinguish aleatoric and epistemic uncertainty in various scientific applications.
Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.
problem Estimating the probability of missing deadlines in series-parallel schedules.
method An efficient algorithm that computes a random variable with minimal Kolmogorov distance to a given discrete random variable.
result The algorithm efficiently approximates the probability of missing deadlines with minimal Kolmogorov distance.
This study examines crypto-asset returns and finds strong evidence of non-Gaussian innovations.
problem Examining the time series properties of cryptocurrencies.
method Used GARCH models, Kolmogorov tests, Khmaladze's martingale transformation, and maximum likelihood estimation.
result Strong evidence of non-Gaussian innovations in crypto-asset returns, contradicting previous assumptions.
We prove time series data forms a Kolmogorov space with hidden dimensions.
problem Understanding the structure of time series data.
method Defining cyclic coordinates and spinor fields in time series data.
result Time series data has hidden eight dimensions.
The paper fits a seven-parameter GTS distribution to financial data.
problem Nonexistence of GTS probability density function makes MLE inadequate.
method Used fractional Fourier transform to circumvent MLE and provide good parameter estimation.
result The GTS distribution fits financial data significantly better than other models.
Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memorycond-mat.stat-mech
The usual derivation of the Fokker-Planck partial differential eqn. assumes the Chapman-Kolmogorov equation for a Markov process. Starting instead with an Ito stochastic differential equation we argue that finitely many states of memory are allowed in Kolmogorov's two pdes, K1 (the backward time pde) and K2 (the Fokker…
We developed a method to learn Kolmogorov models for binary variables.
problem Interpreting complex relationships among binary random variables.
method Proposed a framework linking outcomes of binary variables and an algorithm for model computation.
result First-order optimality of the proposed algorithm despite combinatorial complexity.
We study the solution to Kolmogorov-Feller equation and by using it provide pricing formulas of well known some options under jump-diffusion model.
Study finds conjugate points in geodesics of Kolmogorov flows on torus.
problem Characterizing pairs of integers (m,n) for which geodesics have conjugate points.
method Analysis of geodesics in the group of volume-preserving diffeomorphisms of a torus using stream functions.
result Existence of conjugate points for all pairs of strictly positive integers (m,n).
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs and SDEs.
method Stochastic weighted minimization and stochastic gradient descent with Malliavin weights.
result Accurate approximation of high-dimensional Kolmogorov PDEs and SDEs without curse of dimensionality.
DKL-KAN combines deep learning and kernel methods for scalable, expressive models.
problem Combining deep learning's depth with kernel methods' flexibility for scalable models.
method DKL-KAN uses Kolmogorov-Arnold Networks (KAN) to optimize kernel attributes within a Gaussian process framework.
result DKL-KAN outperforms DKL-MLP on datasets with a low number of observations and DKL-MLP on large datasets.
Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why i…
A Nonlocal Approach to The Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometryq-fin.MF
Paper derives quantum Kolmogorov equations using nonlocal quantum mechanics.
problem Quantum finance equations derived from quantum stochastic calculus.
method Nonlocal approach to quantum mechanics for deriving equations.
result Nonlocal diffusions and quantum stochastic processes linked.
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
New method uses MDL to infer causal direction between variables.
problem Inferring causal direction from observational data of two variables.
method Information theoretic approach based on Kolmogorov complexity and MDL principle.
result Proposes a compression scheme for encoding local and global functional relations.
Smooth KANs improve model reliability in computational biomedicine.
problem Limited convergence of KANs in representing generic smooth functions.
method Introducing smooth, structurally informed KANs that can approximate MLPs in specific function classes.
result Smooth KANs can achieve equivalence to MLPs in specific function classes, enhancing model reliability and performance.
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate for Sobolev space functions.
Improved KAN model explains brain dynamics through edge learning and synaptic strength.
problem Explaining brain dynamics and frequencies in different brain regions.
method ELKAN (Edge Learning KNN) model with edge learning and trimming, inspired by brain science.
result ELKAN model outperforms KAN in explaining brain frequencies and dynamics.
We present a novel modulation level classification (MLC) method based on probability distribution distance functions. The proposed method uses modified Kuiper and Kolmogorov-Smirnov distances to achieve low computational complexity and outperforms the state of the art methods based on cumulants and goodness-of-fit test…
Kolmogorov-Arnold Networks improve deep learning adaptivity and can approximate Besov functions optimally.
problem Improving deep learning adaptivity and understanding approximation rates.
method Analyzing Besov norms and using Res-KANs for approximation.
result KANs can optimally approximate Besov functions at the optimal rate.
We consider several ways to measure the `geometric complexity' of an embedding from a simplicial complex into Euclidean space. One of these is a version of `thickness', based on a paper of Kolmogorov and Barzdin. We prove inequalities relating the thickness and the number of simplices in the simplicial complex, general…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently desi…