相关论文: Optimal Rescaling and the Mahalanobis Distance

In many real-world binary classification tasks (e.g. detection of certain objects from images), an available dataset is imbalanced, i.e., it has much less representatives of a one class (a minor class), than of another. Generally, accurate…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\'e…

Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…

This work explores use of novel advances in best subset selection for regression modelling via continuous optimization for offline change point detection and estimation in univariate Gaussian data sequences. The approach exploits…

We study the problem of change point detection for covariance matrices in high dimensions. We assume that we observe a sequence {X_i}_{i=1,...,n} of independent and centered p-dimensional sub-Gaussian random vectors whose covariance…

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…

This paper proposes an inexpensive way to learn an effective dissimilarity function to be used for $k$-nearest neighbor ($k$-NN) classification. Unlike Mahalanobis metric learning methods that map both query (unlabeled) objects and labeled…

This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are…

We provide algorithms for isotonic regression minimizing $L_0$ error (Hamming distance). This is also known as monotonic relabeling, and is applicable when labels have a linear ordering but not necessarily a metric. There may be…

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…

There has been considerable interest in making Bayesian inference more scalable. In big data settings, most literature focuses on reducing the computing time per iteration, with less focused on reducing the number of iterations needed in…

We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics,…

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Rayleigh quotient to an unconstrained difference formulation,…

Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…

In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…