相关论文: The random Tukey depth

Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Neural networks have shown great success in extracting geometric information from color images. Especially, monocular depth estimation networks are increasingly reliable in real-world scenes. In this work we investigate the applicability of…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension,…

Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…

The halfspace depth of a $d$-dimensional point $x$ with respect to a finite (or probability) Borel measure $\mu$ in $\mathbb{R}^d$ is defined as the infimum of the $\mu$-masses of all closed halfspaces containing $x$. A natural question is…

We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…

For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that the convex hull of $n$ independent copies of $X$ contains a given point $\theta$. We provide several sharp inequalities regarding $p_{n, X}(\theta)$ and…

We give explicit theoretical and heuristical bounds for how big does a data set sampled from a reach-1 submanifold M of euclidian space need to be, to be able to estimate the dimension of M with 90% confidence.

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…

Motivated by the astonishing capabilities of natural intelligent agents and inspired by theories from psychology, this paper explores the idea that perception gets coupled to 3D properties of the world via interaction with the environment.…

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…