Develops methods to construct exchangeable sequences of random multisets.
problem Creating models for random multisets with unknown base measures.
method Uses exchangeable sequences of point processes and conditional-i.i.d. negative binomial processes.
result Provides constructions for negative binomial processes with random base measures.
New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.
problem Need for independence in bounds on random quadratic forms.
method Uniform bounds on random quadratic forms of conditionally independent and sub-Gaussian stochastic processes.
result Bounds hold under general dependencies and sequential design.
Random Tessellation Process improves multi-dimensional data analysis.
problem Axis-aligned cuts limit flexibility in space partitioning methods.
method Proposes Random Tessellation Process (RTP) for non-axis aligned cuts.
result Improved accuracies in gene expression data analysis.
Deep Random Splines model neural activity data with better dimensionality.
problem Modeling neural population data with shape constraints.
method Deep neural network transforming Gaussian noise into spline parameters.
result Better dimensionality reduction of neural spiking activity.
This brief manuscript provides an introduction to Lévy processes and their applications in finance as the random process that drives asset models. Characteristic functions and random variable generators of popular Lévy processes are presented in R.
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
We derive Gaussian approximations for random forest predictions using region-based stabilization.
problem Improving the accuracy of random forest predictions for Poisson process data.
method Region-based stabilization and Malliavin-Stein method for multivariate Gaussian approximation.
result Established Gaussian approximation bounds for random forest predictions under Poisson process.
Proposes FairRR to improve fairness in machine learning models through randomized response.
problem Achieving group fairness in machine learning models.
method Formulates group fairness as optimizing a design matrix in Randomized Response, proposing FairRR.
result Demonstrates FairRR yields excellent model utility and fairness.
Random neural networks with ReLU activations are non-Gaussian processes.
problem Understanding the behavior of neural networks with random initialization and rectified linear units.
method Proving these networks are non-Gaussian processes and deriving their properties.
result These networks can converge to non-Gaussian processes under certain conditions.
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
We develop a probabilistic framework for sequential random projection.
problem Challenges of sequential decision-making under uncertainty.
method Novel construction of a stopped process and method of mixtures.
result Achieved a non-asymptotic probability bound for random projection.
FastForest boosts Random Forest speed by 24%.
problem Efficiency in processing speed for Random Forest.
method Subsample Aggregating, Logarithmic Split-Point Sampling, Dynamic Restricted Subspacing.
result Average 24% increase in processing speed with accuracy maintained.
Study of lengths of cycles in large genus random maps converging to Poisson process.
problem Understanding the distribution of cycle lengths in large genus random maps.
method Teichmüller theory approach for uniformly random metric maps (ribbon graphs).
result The length spectrum converges to a Poisson point process with an explicit intensity as genus tends to infinity.
Method generates random numbers from sensor noise, improving accuracy and speed.
problem Improving accuracy and speed of Monte Carlo integration.
method Sampling a physical process in a controlled environment.
result Reduces error of Monte Carlo integration by 10^68 times while doubling speed.
Data-driven methods link graphon limits to random walks and spectral clustering.
problem Clustering signals evolving over time with graphon limits.
method Transfer operators, Koopman and Perron-Frobenius, for estimating graphon from signal data.
result Spectral clustering can be extended to graphons, reconstructing transition densities and graphons.
Abstract: Nonlinear random walk with distributionally robust transition probabilities.
problem Modeling nonlinear random walks with robust transition probabilities.
method Scaling limit and nonlinear semigroup approach.
result Explicit computation of the generator and corresponding PDE.
The paper analyzes and mitigates biases in scalable Gaussian Process methods.
problem Modeling biases in scalable Gaussian Process methods.
method Randomized truncation estimators to eliminate bias in exchange for increased variance.
result Randomized truncation estimators meaningfully outperform biased counterparts with minimal additional computation.
Paper develops SINNOs for approximating stochastic processes.
problem Approximating stochastic processes with neural networks.
method Developed stochastic interpolation neural network operators (SINNOs) with random coefficients.
result Established boundedness, interpolation accuracy, and approximation capabilities of SINNOs.
Paper reinterprets majorizing measure theorem in terms of coding theory.
problem Understanding boundedness of random processes.
method Information-theoretic perspective using variable-length codes.
result Boundedness of random processes linked to efficient coding.
The paper shows how particle movement on a manifold's grid approximates Brownian motion and heat diffusion.
problem Understanding particle movement on curved spaces.
method Analyzing symmetric exclusion process on random grids approximating a Riemannian manifold.
result Empirical density field converges to heat equation solution on the manifold.
Solves consumption-investment problem with random horizon under Epstein-Zin preferences.
problem Maximizing consumption and investment under random time horizons with Epstein-Zin utility.
method Backward stochastic differential equations with superlinear growth on unbounded random horizons.
result Optimal strategies differ significantly when moving from fixed to random time horizons.
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based c…
Novel framework for spatio-temporal event analysis using Hawkes processes.
problem Inference of dynamics in spatio-temporal event sequences.
method Randomized Fourier feature-based transformations and gradient descent.
result Improved fitting capability in synthetic and real datasets.
In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we defin…
New random forest method provides optimal rates and confidence bands.
problem Improving random forest regression rates and constructing confidence bands.
method Proposed Ehrenfest centered purely random forests achieve optimal rates; used Gaussian approximation for supremum of empirical processes.
result Explicit asymptotic uniform confidence bands constructed for both random forest types.
New method for ancestral inference in branching processes with random environments.
problem Determining ancestor distribution parameters in branching processes with random environments.
method Generalized method of moments for ancestral inference.
result Limiting distribution of ancestor and offspring estimators decouple and converge to independent Gaussian variables under certain conditions.
Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of nodes, one can determine the genus of the surface from local observations of the proc…
New insights into tail behavior of heavy-tailed random vectors and processes.
problem Understanding tail behavior of aggregates of heavy-tailed random vectors.
method Analyzing multivariate regularly varying random vectors and Lévy processes.
result More than one large jump can determine tail behavior of aggregates.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
Theoretical study of random forests for nonlinear time series.
problem Theoretical justification for using random forests in time series modeling.
method Uniform concentration inequality for regression trees and random forests consistency proof.
result Consistency of random forests for nonlinear autoregressive processes.
GCQRF predicts survival quantiles without linearity assumptions.
problem Survival analysis with right censoring and nonlinearity.
method Global Censored Quantile Random Forest (GCQRF) for complex relationships.
result GCQRF outperforms existing methods in predictive accuracy.
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when compu…
Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…
Improved kernel ridge regression for large datasets using weighted random binning.
problem Efficiently approximating kernel matrices for large-scale datasets.
method Introduced weighted random binning features for locality sensitive hashing.
result Weighted random binning features generate Gaussian processes of any desired smoothness.
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fix…
Ensembles dynamic models using random feature approximations.
problem Online scalable Bayesian learning with dynamic models and ensembling.
method Random feature approximations and dynamic models using random walks.
result Better performance with alternative basis expansions like Hilbert space Gaussian processes.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
Unified treatment of eigenvalue processes using Riemannian geometry.
problem Eigenvalue processes in various settings.
method Riemannian submersion and gradient flow of isospectral orbits.
result Eigenvalue processes are projections of Brownian motion through Riemannian submersions.
The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference f…
Study on length spectrum of random hyperbolic 3-manifolds.
problem Understanding the length spectrum of random hyperbolic 3-manifolds.
method Modeling random hyperbolic 3-manifolds using truncated tetrahedra and analyzing their length spectrum as volume tends to infinity.
result The length spectrum converges in distribution to a Poisson point process with a computable intensity λ as volume increases.
New high-order approximations for CIR process using random grids.
problem Approximating the Cox-Ingersoll-Ross process with high order.
method Combining discretization schemes on different random grids.
result Weak approximations of order 2k for all k∈N∗. A new PCA method for analyzing point processes.
problem Analyzing variability in replicated point processes.
method Functional Principal Component Analysis (fPCA) on cumulative mass functions.
result Established convergence and introduced principal measures.
New statistical models capture double power-law behavior in data.
problem Capturing two-regime power-law behavior in datasets.
method Introducing completely random measures with double power-law behavior.
result Proposed models provide a better fit than Pitman-Yor process.
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
New method for identifying graph shift operators using vertex-time autoregressive models.
problem Identifying graph shift operators from graph signals.
method Online optimization using vertex-time autoregressive model and stochastic gradient projection.
result Successful recovery of graph shift operators from graph signals.
Paper develops metrics for random dynamical systems using vector-valued RKHSs.
problem Creating metrics for random nonlinear dynamical systems.
method Develops metrics on random dynamical systems using Perron-Frobenius operators in vector-valued reproducing kernel Hilbert spaces (vvRKHSs). Uses operator-valued kernels and time-wise independence criteria.
result Extends existing metrics for deterministic systems and introduces kernel maximal mean discrepancy for random processes.
IDPGs extend RDPGs with a Poisson process for random latent positions.
problem Modeling randomness in latent positions for graph structure.
method Introduce IDPGs using Poisson point processes on latent Euclidean space.
result Continuous analogues of adjacency matrices link latent structure to observed graphs.