Related papers: Estimating the Division Kernel of a Size-Structure…
We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL.…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
A kernel density is an aggregate of kernel functions, which are itself densities and could be kernel densities. This is used to decompose a kernel into its constituent parts. Pearson's test for equality of proportions is applied to…
To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…
We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
Given a finite set $X$, a collection $\mathcal{T}$ of rooted phylogenetic trees on $X$ and an integer $k$, the Hybridization Number problem asks if there exists a phylogenetic network on $X$ that displays all trees from $\mathcal{T}$ and…
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…