Related papers: Toy Model for Large Non-Symmetric Random Matrices
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
Strongly interacting systems can be described in terms of correlation functions at various orders. A quantum analog of high-order correlations is the topological entanglement in topologically ordered states of matter at zero temperature,…
This work gives an overview of analytic tools for the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
Recent numerical results show that non-Bayesian knowledge revision may be helpful in search engine training and optimization. In order to demonstrate how basic assumption about about the physical nature (and hence the observed statistics)…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
Direct design of a robot's rendered dynamics, such as in impedance control, is now a well-established control mode in uncertain environments. When the physical interaction port variables are not measured directly, dynamic and kinematic…
In this paper, we discover that the class of random polynomials arising from the equilibrium analysis of random asymmetric evolutionary games is \textit{exactly} the Kostlan-Shub-Smale system of random polynomials, revealing an intriguing…
Stochastic processes out-of-equilibrium often involve asymmetric contributions that break detailed balance and lead to non-monotonic entropy production, limiting thermodynamic interpretations and inference techniques. Here we use Dyson maps…
A new approach to solving random matrix models directly in the large $N$ limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large $N$ loop equations are then used to generate values of…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…