Related papers: On the classification problem for Poisson Point Pr…
Probabilistic k-nearest neighbour (PKNN) classification has been introduced to improve the performance of original k-nearest neighbour (KNN) classification algorithm by explicitly modelling uncertainty in the classification of each feature…
This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting…
This paper proposes a model of interactions between two point processes, ruled by a reproduction function h, which is considered as the intensity of a Poisson process. In particular, we focus on the context of neurosciences to detect…
Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of…
The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning…
This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…
We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…
The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…
We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…
The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
We introduce a doubly stochastic marked point process model for supervised classification problems. Regardless of the number of classes or the dimension of the feature space, the model requires only 2--3 parameters for the covariance…
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…