Related papers: Geometric median and robust estimation in Banach s…

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…

The spatial resolution of a detector, using a reference detector telecscope, can be measured applying the geometric mean method, with tracks reconstructed from hits of all the detectors, including ($\sigma_\mathrm{in}$) and excluding…

In this paper we have proposed a median based estimator using known value of some population parameter(s) in simple random sampling. Various existing estimators are shown particular members of the proposed estimator. The bias and mean…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…

In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…

Consider linear ill-posed problems governed by the system $A_i x = y_i$ for $i =1, \cdots, p$, where each $A_i$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y_i$. In case $p$ is huge, solving the problem by an…

In this paper we study greedy approximation in Banach spaces. We discuss a modification of the Weak Chebyshev Greedy Algorithm, in which steps of the algorithm can be executed imprecisely. Such inaccuracies are represented by both absolute…

This paper investigates a general robust one-shot aggregation framework for distributed and federated Independent Component Analysis (ICA) problem. We propose a geometric median-based aggregation algorithm that leverages $k$-means…

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…

Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…

The primary objective of this paper is to develop methodologies for investigating Schwarz type lemmas and to present their applications in Banach spaces. First, we improve upon the main results obtained by Osserman [Proc. Am. Math. Soc.…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

Let $X$ be an $n$-dimensional manifold and $V_1,\ldots,V_n\subset C^\infty(X,\mathbb R)$ finite-dimensional vector spaces. For systems of equations $\{f_i = a_i\colon\: f_i\in V_i,\:a_i \in\mathbb R,\:i=1,\ldots,n\}$ we discover a…