Related papers: Testing the validity of the Kirkwood approximation…
Laplace distribution is popular in the field of economics and finance. Still, data sets often show a lack of symmetry and a tendency of being bounded from either side of their support. In view of this, we introduce a new family of skew…
We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e.,…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We analyze the Sznajd opinion formation model, where a pair of neighboring individuals sharing the same opinion on a square lattice convince its six neighbors to adopt their opinions, when a fraction of the individuals is updated according…
We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive…
We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We…
The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently…
We investigated the fidelity susceptibility in the one-dimension (1D) Hubbard model and the extended Hubbard model at half-filling via the density matrix renormalization group. From the numerical results, we argue that in the 1D Hubbard…
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here…
We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
In this survey we explore the salient connections made between Brownian motion, symmetrization and complex analysis in the last 60 years starting with Kakutani's paper (1944) equating harmonic measure and exit probability. To exemplify…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in…