arXiv research

A new statistical model uses Orlicz-Sobolev spaces with Gaussian weight.

Study provides guarantees for kernel clustering under non-parametric mixtures.

This paper finds a unique partition of a sample space for estimating continuous distributions.

A tractable pseudo-metric for non-parametric distributions via SPD geometry.

A graph-based method for two-sample testing across connected nodes.

The paper provides stability guarantees for non-parametric maximum likelihood estimation using statistical mechanics.

Estimates neural drift for stochastic equations, improving inference on noisy data.

We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. samples are assigned to agents. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gra…

KQT-EWMA monitors multivariate data streams online with flexible and practical change detection.

We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we firs…

Estimates conditional Brenier maps using entropic optimal transport.

Study finds a method to discover causal relationships that are invariant to marginal distributions.

Develops non-parametric tests for group symmetry in data.

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…

Datasets with hundreds of variables and many missing values are commonplace. In this setting, it is both statistically and computationally challenging to detect true predictive relationships between variables and also to suppress false positives. This paper proposes an approach that combines probabilistic programming, …

New test assesses probabilistic model calibration without expensive approximations.

Paper proposes a machine learning-based method for estimating mediation effects.

Study non-parametric value function estimation from a single path.

The paper reviews methods for estimating individual treatment effects using non-parametric regression models.

New tests detect high-order interactions without permutations.

Improved change point detection using matched filters for non-parametric tests.

Paper introduces an online method for estimating the difference between two probability distributions.

Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$ and $\mathcal{O}(n^2)$ respectively, and so is prohibitive in many cases. We prop…

Estimates latent positions in 1D torus from noisy pairwise affinities.

Develops a goodness-of-fit test for self-exciting processes.

This work develops a non-parametric test for relational independence in non-i.i.d. data.

Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristi…

The article applies Occam's Razor to non-parametric model building, minimizing the number of bits for data encoding.

This paper solves the intractability barrier in non-parametric information geometry by introducing a novel framework.

Unified review of Conformal Prediction theory and applications.

The paper proposes a new evaluation framework for causal inference models.

The paper provides theoretical guarantees for transformation-based models in variational inference.

A new MFG framework for evolving clusters from Gaussian mixtures.

Near-optimal tests and confidence sequences for non-parametric data.

Bayesian approach improves uncertainty in deep learning models.

We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…

Unified theory of optimal transport for random measures.

A new principle for extrapolating regression outside training data.

Non-parametric bootstrap improves robust portfolio and trading strategy optimization.

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method co…

New measure assesses predictive dependence between continuous variables, capturing non-functional relationships.

Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is. For practical use, such a measure should be universal in the sense that it capt…

Improves reliability diagrams for probabilistic forecasts.

A new framework improves kernel Stein discrepancy tests for validating distributions.

Theory establishes optimal rates for estimating linear functionals without structural assumptions.

We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case $k=\infty$, in which the manifolds are modelled on Fréchet spaces, is included.…

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to some lower dimensional Euclidean space, as many manifold learning methods have b…