Related papers: Encoding of data sets and algorithms

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…

We introduce an algorithm for estimating the entropy of pairwise, probabilistic graph models by leveraging bridges between social communities and an accurate entropy estimator on sparse samples. We propose using a measure of investment from…

The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…

Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

The accuracy of machine learning systems is a widely studied research topic. Established techniques such as cross-validation predict the accuracy on unseen data of the classifier produced by applying a given learning method to a given…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional…

The rapid developments of various machine learning models and their deployments in several applications has led to discussions around the importance of looking beyond the accuracies of these models. Fairness of such models is one such…

We present an information-theoretic framework for understanding overfitting and underfitting in machine learning and prove the formal undecidability of determining whether an arbitrary classification algorithm will overfit a dataset.…

The reliable prediction of the temporal behavior of complex systems is key in numerous scientific fields. This strong interest is however hindered by modeling issues: often, the governing equations describing the physics of the system under…

The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…

The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…

When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…

Nowadays, the analysis of complex phenomena modeled by graphs plays a crucial role in many real-world application domains where decisions can have a strong societal impact. However, numerous studies and papers have recently revealed that…

Distributed algorithms for network science applications are of great importance due to today's large real-world networks. In such algorithms, a node is allowed only to have local interactions with its immediate neighbors. This is because…

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…