Related papers: A Note on the Relation between Recognisable Series…

We introduce the notion of minimal inversion sequences for a pattern $\rho$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $\rho$ for inversion sequences. We give a characterization of…

This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…

This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…

It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.

A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as its reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is…

We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…

The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…

Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does $\ell_1$-minimization find the sparsest solution to an underdetermined linear system? In…

We prove a conjecture about the minimal nonnegative solutions of algebraic Riccati equations associated with reducible singular M-matrices. The result enhances our understanding of the behaviour of doubling algorithms for finding the…

Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…

We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…

To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic…

We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…

Times series classification can be successfully tackled by jointly learning a shapelet-based representation of the series in the dataset and classifying the series according to this representation. However, although the learned shapelets…

In this paper we start with a simple question, how is it possible that humans can recognize different movements over skin with only a prior visual experience of them? Or in general, what is the representation of spatial sequences that are…

Sequence modeling tasks across domains such as natural language processing, time series forecasting, and control require learning complex input-output mappings. Nonlinear recurrence is theoretically required for universal approximation of…

Deep Reinforcement Learning (RL) has demonstrated success in solving complex sequential decision-making problems by integrating neural networks with the RL framework. However, training deep RL models poses several challenges, such as the…