arXiv research

The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.

New results on financial equilibria in markets with general semimartingales.

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.

Study policy gradient for large-agent mean-field control and game in continuous time.

Mean-field approximations simplify insurance liability calculations.

This work extends Ledoit-Wolf shrinkage to unknown mean covariance estimation.

New method optimizes non-linear functionals over probability measures.

We analyze linear factor models for asset pricing panels.

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost functions, while the aggregated effect of the agents is captured by the population mean o…

This work shows linear convergence for two-layer neural networks in mean-field regime.

Paper proves linear convergence of SCMS algorithm for directional data.

Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.

Analyzes multi-day stock returns, showing linear volatility and mean dependence.

Double Q-learning has the same mean-squared error as Q-learning under certain conditions.

Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.

PEA improves PCA and k-means for non-linear data and complex clusters.

In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of $K_n$ in a cube, the mean sum of squared linking numbers and the mean sum of square…

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …

Proposes PKM for soft K-means clustering.

Improved disability insurance model with collective health claims.

Our aim is to study invariant hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, whose mean curvature is given as a linear function in the unit sphere $\mathbb{S}^n$ depending on its Gauss map. These hypersurfaces are closely related with the theory of manifolds with density, since their weighted mean cu…

Diffusion means converge to extrinsic means for long times on spheres.

This paper achieves optimal regret bounds for locally private linear contextual bandit.

New findings allow infinite mean intensity Hawkes processes to be stable.

Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately, kernel means are faced with scalability issues. A single point evaluation of the …

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …

New method recovers causal order from dependent data.

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…

Efficient algorithms for $k$-means clustering frequently converge to suboptimal partitions, and given a partition, it is difficult to detect $k$-means optimality. In this paper, we develop an a posteriori certifier of approximate optimality for $k$-means clustering. The certifier is a sub-linear Monte Carlo algorithm b…

The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work \cite{Mon, Brendle,BE} considering constant mean curvature functions. Secondly, …

The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well as the associated parallel transport and curvature.

GBMixed boosts mixed models for clustered data, estimating mean and variance flexibly.

Neural networks improve geospatial data analysis by relaxing linearity assumptions.

Develops a control framework for systemic risk under uncertainty.

New method for high-dimensional linear regression using empirical Bayes.

Study on PG learning for LQ MFC problems with common noise, proving convergence and sample complexity.

Developed LQ MFG theory with common noise, proving existence and uniqueness.

Novel probabilistic solver speeds up solving related linear systems.

Study surfaces with specific curvature properties in 3D space.

In this paper, we consider compact free boundary constant mean curvature surfaces immersed in a mean convex body of the Euclidean space or in the unit sphere. We prove that the Morse index is bounded from below by a linear function of the genus and number of boundary components.

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning th…

New numerical method for non-linear asset price model with CEV volatility.

New algorithm learns Bayesian networks robustly in nearly-linear time.

When we implement a portfolio selection methodology under a mean-risk formulation, it is essential to correctly model investors' risk aversion which may be time-dependent, or even state-dependent during the investment procedure. In this paper, we propose a behavior risk aversion model, which is a piecewise linear funct…