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Change point detection (CPD) methods aim to identify abrupt shifts in the distribution of input data streams. Accurate estimators for this task are crucial across various real-world scenarios. Yet, traditional unsupervised CPD techniques…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…
This paper proposes novel pilot optimization and channel estimation algorithm for the downlink multiuser massive multiple input multiple output (MIMO) system with $K$ decentralized single antenna mobile stations (MSs), and time division…
In this work, we propose two methods that utilize data symbols in addition to pilot symbols for improved channel estimation quality in a multi-user system, so-called semi-blind channel estimation. To this end, a subspace is estimated based…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
Existing online change-point detection (CPD) methods rely on fixed-dimensional Euclidean summaries, implicitly assuming that distributional changes are well captured by moment-based or feature-based representations. They can obscure…
The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…
This paper presents distributed adaptive algorithms based on the conjugate gradient (CG) method for distributed networks. Both incremental and diffusion adaptive solutions are all considered. The distributed conventional (CG) and modified…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
With the increasing availability of data objects in the form of probability distributions, there is a growing need for statistical methods tailored to distributional data. Distance measures, especially the pairwise distance matrix between…
Minimum expected distance estimation (MEDE) algorithms have been widely used for probabilistic models with intractable likelihood functions and they have become increasingly popular due to their use in implicit generative modeling (e.g.…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and…
Pre-trained vision transformers have strong representation benefits to various downstream tasks. Recently, many parameter-efficient fine-tuning (PEFT) methods have been proposed, and their experiments demonstrate that tuning only 1\% extra…
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of…