arXiv research

Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the related variational problems and optimization problems. Random convex analysis is …

Proposes a new random forest weighted local Fréchet regression method.

Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.

New local-search methods close the gap in sparse tensor PCA.

Quantum walks blend patterns into splines when averaged.

Algorithm learns CNF formulas from random solutions under specific conditions.

Graphs and local systems count multiwebs.

Improved kernel ridge regression for large datasets using weighted random binning.

Proposes a new method for localized uncertainty quantification in random forests using proximity measures.

Novel compression method preserves privacy while reducing communication costs.

Forest-guided smoothing uses random forest outputs for interpretable local smoothers.

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

In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …

A new random forest algorithm improves tree construction for optimal performance.

Multiplex networks, a special type of multilayer networks, are increasingly applied in many domains ranging from social media analytics to biology. A common task in these applications concerns the detection of community structures. Many existing algorithms for community detection in multiplexes attempt to detect commun…

Study reveals limits of detecting local geometry in random graphs.

New framework reduces private mean estimation error with optimal efficiency.

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…

Random translation surfaces converge to a Poisson plane as genus grows.

Corrects bias in random sampling matrices for improved ML methods.

Novel graph neural network combines random walks with local message passing.

New method identifies important features and interactions in RF models.

The aim of this paper is to establish two fundamental measure-metric properties of particular random geometric graphs. We consider $\varepsilon$-neighborhood graphs whose vertices are drawn independently and identically distributed from a common distribution defined on a regular submanifold of $\mathbb{R}^K$. We show t…

With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the secto…

We study the theoretical properties of learning a dictionary from $N$ signals $\mathbf x_i\in \mathbb R^K$ for $i=1,...,N$ via $l_1$-minimization. We assume that $\mathbf x_i$'s are $i.i.d.$ random linear combinations of the $K$ columns from a complete (i.e., square and invertible) reference dictionary $\mathbf D_0 \in…

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local li…

Locally private online quantile regression method addresses privacy constraints.

New methods for federated learning reduce communication costs.

FedShuffle improves local updates in FL, especially with data imbalance.

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…

We extend to the framework of locally $L^0$-convex modules some results from classical convex analysis. Namely, randomized versions of Mazur lemma and Krein-Smulian theorem under mild stability properties are provided.

Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape of many objective functions in learning has been conjectured to …

Random hyperbolic surfaces with punctures converge to the Brownian sphere.

Local MDI+ improves feature importance for tree-based models, enhancing interpretability and performance.

New methods for private statistical inference under local differential privacy.

Training deep neural networks with the error backpropagation algorithm is considered implausible from a biological perspective. Numerous recent publications suggest elaborate models for biologically plausible variants of deep learning, typically defining success as reaching around 98% test accuracy on the MNIST data se…

Enhances random forests by smoothing predictions for better performance.

We develop a new statistical test for comparing variables with varying scales.

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed t…

Random feature maps improve forecasting of chaotic dynamical systems.

Indoor localization based on SIngle Of Fingerprint (SIOF) is rather susceptible to the changing environment, multipath, and non-line-of-sight (NLOS) propagation. Building SIOF is also a very time-consuming process. Recently, we first proposed a GrOup Of Fingerprints (GOOF) to improve the localization accuracy and reduc…

Landmark-based node embeddings approximate shortest path distances in random graphs.

This paper develops a new method to model treatment effects that are heterogeneous across different quantiles.

Develops a new deep learning framework for privacy-preserving text representations.

We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm…

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolut…

New method improves Gaussian kernel approximations for high-frequency data.