Related papers: Data-driven probability concentration and sampling…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…

In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained…

We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…

Anomaly detection is defined as the problem of finding data points that do not follow the patterns of the majority. Among the various proposed methods for solving this problem, classification-based methods, including one-class Support…

In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…

3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…

In this paper, we propose a sensitivity-free and multi-objective structural design methodology called data-driven topology design. It is schemed to obtain high-performance material distributions from initially given material distributions…

Identifying the obstacle space is crucial for path planning. However, generating an accurate obstacle space remains a significant challenge due to various sources of uncertainty, including motion, behavior, and perception limitations. Even…

Minimization of the (regularized) entropy of classification probabilities is a versatile class of discriminative clustering methods. The classification probabilities are usually defined through the use of some classical losses from…

We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many…

We propose a data-driven control method for systems with aleatoric uncertainty, for example, robot fleets with variations between agents. Our method leverages shared trajectory data to increase the robustness of the designed controller and…

This paper introduces and characterizes a new family of continuous probability distributions applicable to norm distributions in three-dimensional random spaces, specifically for the Euclidean norm of three random Gaussian variables with…

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…

Creative image generation has emerged as a compelling area of research, driven by the need to produce novel and high-quality images that expand the boundaries of imagination. In this work, we propose a novel framework for creative…

Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…

We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…