Related papers: Consistency of archetypal analysis
We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
Changepoint analysis deals with unsupervised detection and/or estimation of time-points in time-series data, when the distribution generating the data changes. In this article, we consider \emph{offline} changepoint detection in the context…
We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…
Panel data of our interest consist of a moderate or relatively large number of panels, while the panels contain a small number of observations. This paper establishes testing procedures to detect a possible common change in means of the…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
Short-term patterns in financial time series form the cornerstone of many algorithmic trading strategies, yet extracting these patterns reliably from noisy market data remains a formidable challenge. In this paper, we propose an…
High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…