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We compute the auto-correlations functions of order $m\ge 1$ for the characteristic polynomials of random matrices from certain subgroups of the unitary groups $\U(2)$ and $\U(3)$ by applying branching rules. These subgroups can be…
Multi-objective alignment aims to align LLM responses with multiple human preference objectives. Among existing methods, guiding the generation of frozen LLMs through autoregressive reward models (ARMs) to accomplish multi-objective…
Auto-Associative models cover a large class of methods used in data analysis. In this paper, we describe the generals properties of these models when the projection component is linear and we propose and test an easy to implement…
Representational similarity analysis (RSA) is a multivariate technique to investigate cortical representations of objects or constructs. While avoiding ill-posed matrix inversions that plague multivariate approaches in the presence of many…
Producing probabilistic guarantee for several steps of a predicted signal follow a temporal logic defined behavior has its rising importance in monitoring. In this paper, we derive a method to compute the joint probability distribution of…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…
Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, and as such the identification of model orders remains a…
A transformation relation between multivariate ARMA and CARMA processes is derived through a discretization procedure. This gives a direct relationship between the discrete time and continuous time analogues, serving as the basis for an…
The paper considers high frequency sampled multivariate continuous-time ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior…
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering…
We face the factor analysis problem using a particular class of auto-regressive processes. We propose an approximate moment matching approach to estimate the number of factors as well as the parameters of the model. This algorithm…
The problem of estimating ARMA models is computationally interesting due to the nonconcavity of the log-likelihood function. Recent results were based on the convex minimization. Joint model selection using penalization by a convex norm,…
In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…
Periodicity is a common feature of time series. For finite-dimensional data, periodic autoregressive moving average (ARMA) models have been extensively studied. In functional time series analysis, AR models have been extended to incorporate…
Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell…
Real time model based control of high dimensional nonlinear systems presents severe computational challenges. Conventional reduced order model control relies heavily on expert tuning or parameter adaptation and seldom offers mechanisms for…
In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a…
Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their…