Related papers: Hyperbolic Sets in Incomplete Tables
In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
In this paper, we present an infinite hierarchical non-parametric Bayesian model to extract the hidden factors over observed data, where the number of hidden factors for each layer is unknown and can be potentially infinite. Moreover, the…
Training models on highly unbalanced data is admitted to be a challenging task for machine learning algorithms. Current studies on deep learning mainly focus on data sets with balanced class labels or unbalanced data, but with massive…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Deep learning methodologies have been employed in several different fields, with an outstanding success in image recognition applications, such as material quality control, medical imaging, autonomous driving, etc. Deep learning models rely…
This paper studies a panel data setting where the goal is to estimate causal effects of an intervention by predicting the counterfactual values of outcomes for treated units, had they not received the treatment. Several approaches have been…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
Many different machine learning algorithms exist; taking into account each algorithm's hyperparameters, there is a staggeringly large number of possible alternatives overall. We consider the problem of simultaneously selecting a learning…
The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter…
Certain answers are a principled method for coping with uncertainty that arises in many practical data management tasks. Unfortunately, this method is expensive and may exclude useful (if uncertain) answers. Thus, users frequently resort to…
We prove a Closing Lemma for nonuniformly hyperbolic measures of meromorphic maps. We prove also a theorem of approximation of the dynamics of such measures by Bernoulli coding maps.
Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we…
In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…
We introduce a new multi-objective optimization approach to determine uncertainty-quantified nuclear reaction parameters in the Hauser-Feshbach framework. By simultaneously accounting for all available data across multiple reaction channels…
We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
For data sets populated by a very well modeled process and by another process of unknown probability density function (PDF), a desired feature when manipulating the fraction of the unknown process (either for enhancing it or suppressing it)…
We study a class of two dimensional partially hyperbolic systems, not necessarily skew products, trying to establish the germ of a general theory. To illustrate the scope of the theory, we apply our results to the case of fast-slow…