Related papers: Flat Sampled Data Systems, an Algorithmic Approach

An approach to amputation, the process of introducing missing values to a complete dataset, is presented. It allows to construct missingness indicators in a flexible and principled way via copulas and Bernoulli margins and to incorporate…

A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…

Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…

Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…

Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…

We revisit the flatland paradox proposed by \cite{ston1976} which is an example of non-conglomerability. The aim of the paper is to show that the improperness of the prior is not directly involved in the inconsistency. First, we show that…

Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of…

Traditionally, in supervised machine learning, (a significant) part of the available data (usually 50% to 80%) is used for training and the rest for validation. In many problems, however, the data is highly imbalanced in regard to different…

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…

The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations…

Recent literature generalization in deep learning has examined the relationship between the curvature of the loss function at minima and generalization, mainly in the context of overparameterized neural networks. A key observation is that…

We systematize the approach to the investigation of deep neural network landscapes by basing it on the geometry of the space of implemented functions rather than the space of parameters. Grouping classifiers into equivalence classes, we…

Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…

In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…

Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…

Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient…

Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…

This paper deals with system representations in finite-sample signal subspaces and their application to data-driven fault detection. The first part addresses concepts of finite-sample image and kernel system representations and, associated…

In general, flat outputs of a nonlinear system may depend on the system's state and input as well as on an arbitrary number of time derivatives of the latter. If a flat output which also depends on time derivatives of the input is known,…