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In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy…
A product relative error estimation method for single index regression model is proposed as an alternative to absolute error methods, such as the least square estimation and the least absolute deviation estimation. It is scale invariant for…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Randomized controlled experiments assess new policy impacts on performance metrics to inform launch decisions. Traditional approaches evaluate metrics independently despite correlations, and mixed results (e.g., positive revenue impact,…
Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…
The paper deals with the problem of controlling the state of industrial devices according to the readings of their sensors. The current methods rely on one approach to feature extraction in which the prediction occurs. We proposed a…
Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response…
We construct a toy a model which demonstrates that large field single scalar inflation can produce an arbitrarily small scalar to tensor ratio in the window of e-foldings recoverable from CMB experiments. This is done by generalizing the…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. The fault signal, as an unknown input, is reconstructed from its projections onto two subspaces. One projection is…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…
Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data…
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…
A dimensionless parameter $\Lambda$ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repul- sion. Structural transitions…
This paper introduces an innovative method for constructing copula models capable of describing arbitrary non-monotone dependence structures. The proposed method enables the creation of such copulas in parametric form, thus allowing the…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…