arXiv research

Develops methods to construct exchangeable sequences of random multisets.

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…

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing …

New MBQC algorithm uses randomness for generative modeling.

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…

Paper estimates the order of vertices in random recursive trees.

Study models market volatility with persistent and temporary impacts.

New RF dissimilarity measures improve multi-view learning accuracy.

Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in erroneous, irreproducible results. In this work we show how to obtain an upper bo…

Paper introduces a new, tractable measure of model complexity.

Sparse RSP routing improves graph exploration and classification.

A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.

Study shows how certain stochastic models reach a steady state over time.

Paper presents a new VMBQC model with fewer parameters for better generative modeling.

Paper proves sufficient conditions for tensor recovery using t-RIP with random measurements.

Random Forest permutation importance measure is asymptotically unbiased in sparse regression models.

A new approach models exploration in continuous-time RL using random measures.

We recover phase from intensity measurements using optics-based random projections.

Paper justifies ideal point forecasts as measurable, clarifying conditions for their existence.

A new variable importance measure for DRFs detects broader impacts on output distributions.

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of …

Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized comp…

New method uses random convex polytopes to measure representation quality.

Method learns topological states from randomized measurements.

Random walks on Fuchsian Schottky groups have harmonic measures with lower dimension.

Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent literature works show that compressive image classification is possible in CS domain wi…

New local MDI variable importances derived from global scores match Shapley values.

New model uses interval-valued CVaR for better risk assessment in finance.

GCQRF predicts survival quantiles without linearity assumptions.

New method debiases feature importance in Random Forests.

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…

We describe a nonparametric topic model for labeled data. The model uses a mixture of random measures (MRM) as a base distribution of the Dirichlet process (DP) of the HDP framework, so we call it the DP-MRM. To model labeled data, we define a DP distributed random measure for each label, and the resulting model genera…

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measu…

A new PCA method for analyzing point processes.

We propose a modification that corrects for split-improvement variable importance measures in Random Forests and other tree-based methods. These methods have been shown to be biased towards increasing the importance of features with more potential splits. We show that by appropriately incorporating split-improvement as…

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…

Researchers prove hitting measure singularity for most Fuchsian and Kleinian groups.

Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.

Study examines how measurement errors impact clustering algorithms.

This paper reviews random forest methods for analyzing longitudinal data in precision medicine.

The paper examines random walks on metric spaces and finds commensurable subgroups.

Study measures rigidity for random walks and flows via generalized u-Gibbs states.

The paper equidistributes zeros of random polynomials and sections on manifolds.

Paper identifies classes vulnerable to adversarial attacks.

kdiff measures distances for time series and structured data.

Paper reinterprets majorizing measure theorem in terms of coding theory.

We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing it. The resulting measure is shown to satisfy a number of desirable properties. …

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the exchange rules in the a…