arXiv subjects

Giorgio Gnecco

Publications and source records attributed to Giorgio Gnecco.

At least 19 recordsLinked to original sources

arXiv2026

A Generative Adversarial Graph Neural Network for Synthetic Time Series Data

Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain their effectiveness. Deep learning models, particularly Generative Adversarial Networks (GANs), have exhibited considerable potential in emulating complex probability distributions. GANs employ a generator-discriminator framework, where the generator creates data samples, while the discriminator distinguishes real from generated data. In this research, we introduce the Sig-Graph GAN model, which integrates the time-series signature, offering a structured summary of its temporal evolution; the Long Short-Term Memory network, capturing its inherent autoregressive structure; and Graph Neural Networks (GNNs), leveraging geometric patterns within the time-series data. To employ GNNs optimally, we use the visibility graph algorithm to derive a graph-based representation of the underlying time series. Numerical evaluations demonstrate that the Sig-Graph GAN model outperforms baseline methods in replicating the distribution of logarithmic returns across different stock exchanges. The integration of the graph structure with the autoregressive component effectively captures both geometric and temporal patterns embedded in time-series data. This research advances the field of GAN models for time series by introducing a model capable of leveraging both autoregressive properties and geometric structures for synthetic data generation.

cs.CE↗

arXiv2026

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

cs.CE↗

arXiv2026

The Statistical Significance of the Inclusion of Graph Neural Networks in the Financial Time Series Forecasting Problem

Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing temporal patterns within the time series data. In this research, we study the statistical significance of the inclusion of geometric patterns in enhancing forecasting accuracy within the context of time series analysis. We introduce the Time-Geometric model, a combination of models designed to exploit both geometric and temporal patterns. The contribution of this research lies in advancing the domain of univariate time series prediction,as demonstrated through extensive empirical evaluations. Our findings underscore that leveraging geometric patterns, captured through Graph Neural Networks, yields statistically significant improvements in forecasting accuracy.

cs.CE↗

arXiv2026

Human-Like Trajectories Generation via Receding Horizon Tracking Applied to the TickTacking Interface

TickTacking is a rhythm-based interface that allows users to control a pointer in a two-dimensional space through dual-button tapping. This paper investigates the generation of human-like trajectories using a receding horizon approach applied to the TickTacking interface in a target-tracking task. By analyzing user-generated trajectories, we identify key human behavioral features and incorporate them in a controller that mimics these behaviors. The performance of this human-inspired controller is evaluated against a baseline optimal-control-based agent, demonstrating the importance of specific control features for achieving human-like interaction. These findings contribute to the broader goal of developing rhythm-based human-machine interfaces by offering design insights that enhance user performance, improve intuitiveness, and reduce interaction frustration

cs.HC↗

arXiv2023

Signature-Based Community Detection for Time Series

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models. These methods suffer from assuming temporal stationarity and are influenced by the granularity of observation intervals. In this study, we propose an approach based on the signature matrix, a concept from path theory for studying stochastic processes. By employing a signature-derived similarity measure, our method overcomes drawbacks of traditional correlation-based techniques. Through a series of numerical experiments, we demonstrate that our method consistently yields higher modularity compared to baseline models, when tested on the Standard and Poor's 500 dataset. Moreover, our approach showcases enhanced stability in modularity when the length of the underlying time series is manipulated. This research contributes to the field of community detection by introducing a signature-based similarity measure, offering an alternative to conventional correlation matrices.

cs.SI↗

arXiv2023

Counter-example guided inductive synthesis of control Lyapunov functions for uncertain systems

We propose a counter-example guided inductive synthesis (CEGIS) scheme for the design of control Lyapunov functions and associated state-feedback controllers for linear systems affected by parametric uncertainty with arbitrary shape. In the CEGIS framework, a learner iteratively proposes a candidate control Lyapunov function and a tailored controller by solving a linear matrix inequality (LMI) feasibility problem, while a verifier either falsifies the current candidate by producing a counter-example to be considered at the next iteration, or it certifies that the tentative control Lyapunov function actually enjoys such feature. We investigate the Lipschitz continuity of the objective function of the global optimization problem solved by the verifier, which is key to establish the convergence of our method in a finite number of iterations. Numerical simulations confirm the effectiveness of the proposed approach.

eess.SY↗

arXiv2022

Hierarchical Clustering and Matrix Completion for the Reconstruction of World Input-Output Tables

World Input-Output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (part of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and Matrix Completion (MC) with a LASSO-like nuclear norm penalty, to impute missing entries of a partially unknown I/O matrix. Through simulations based on synthetic matrices we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input-Output Database (WIOD) tables - which are an example of industry-by-industry I/O tables - is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.

stat.ML↗

arXiv2021

Heterogeneous causal effects with imperfect compliance: a Bayesian machine learning approach

This paper introduces an innovative Bayesian machine learning algorithm to draw interpretable inference on heterogeneous causal effects in the presence of imperfect compliance (e.g., under an irregular assignment mechanism). We show, through Monte Carlo simulations, that the proposed Bayesian Causal Forest with Instrumental Variable (BCF-IV) methodology outperforms other machine learning techniques tailored for causal inference in discovering and estimating the heterogeneous causal effects while controlling for the familywise error rate (or - less stringently - for the false discovery rate) at leaves' level. BCF-IV sheds a light on the heterogeneity of causal effects in instrumental variable scenarios and, in turn, provides the policy-makers with a relevant tool for targeted policies. Its empirical application evaluates the effects of additional funding on students' performances. The results indicate that BCF-IV could be used to enhance the effectiveness of school funding on students' performance.

stat.ME↗

arXiv2021

Principal Component Analysis Applied to Gradient Fields in Band Gap Optimization Problems for Metamaterials

A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based iterative optimization algorithms to the numerical solution of such problems is typically highly demanding, due to the complexity of the underlying physical models. Nevertheless, supervised machine learning techniques can reduce such a computational effort, e.g., by replacing the original objective functions of such optimization problems with more-easily computable approximations. In this framework, the present article describes the application of a related unsupervised machine learning technique, namely, principal component analysis, to approximate the gradient of the objective function of a band gap optimization problem for an acoustic metamaterial, with the aim of making the successive application of a gradient-based iterative optimization algorithm faster. Numerical results show the effectiveness of the proposed method.

cs.CE↗

arXiv2021

On principal component analysis of the convex combination of two data matrices and its application to acoustic metamaterial filters

In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of two data matrices. The application of the theoretical analysis to multi-objective optimization problems (e.g., those arising in the design of acoustic metamaterial filters) is briefly discussed, together with possible extensions.

math.OC↗

arXiv2019

Machine-learning techniques for the optimal design of acoustic metamaterials

Recently, an increasing research effort has been dedicated to analyse the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet-Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.

physics.comp-ph↗

arXiv2019

Estimating Heterogeneous Causal Effects in the Presence of Irregular Assignment Mechanisms

This paper provides a link between causal inference and machine learning techniques - specifically, Classification and Regression Trees (CART) - in observational studies where the receipt of the treatment is not randomized, but the assignment to the treatment can be assumed to be randomized (irregular assignment mechanism). The paper contributes to the growing applied machine learning literature on causal inference, by proposing a modified version of the Causal Tree (CT) algorithm to draw causal inference from an irregular assignment mechanism. The proposed method is developed by merging the CT approach with the instrumental variable framework to causal inference, hence the name Causal Tree with Instrumental Variable (CT-IV). As compared to CT, the main strength of CT-IV is that it can deal more efficiently with the heterogeneity of causal effects, as demonstrated by a series of numerical results obtained on synthetic data. Then, the proposed algorithm is used to evaluate a public policy implemented by the Tuscan Regional Administration (Italy), which aimed at easing the access to credit for small firms. In this context, CT-IV breaks fresh ground for target-based policies, identifying interesting heterogeneous causal effects.

cs.LG↗

arXiv2018

Complex frequency band structure of periodic thermo-diffusive materials by Floquet-Bloch theory

This work deals with the micromechanical study of periodic thermo-diffusive elastic multi-layered materials, which are of interest for the fabrication of solid oxide fuel cells (SOFCs). The focus is on the dynamic regime, that is investigating the dispersive wave propagation within the periodic material. In this framework, a generalization of the Floquet-Bloch theory is adopted, able to determine the complex band structure of such materials. The infinite algebraic linear system, obtained by exploiting both bilateral Laplace transform and Fourier transform, is replaced by its finite counterpart, resulting from a proper truncation at a finite number of considered equations. A regularization technique is herein useful to get rid of the Gibbs phenomenon. The solution of the problem is, finally, found in terms of complex angular frequencies, corresponding to a finite sequence of eigenvalue problems for given values of the wave vector. The paper is complemented by numerical examples taking into account thermo-mechanical coupling. The overall behaviour is found to be strongly influenced by the interaction between thermal and mechanical phenomena.

physics.app-ph↗

arXiv2018

Parameters estimation in a 3-parameters p-star model

An important issue in social network analysis refers to the development of algorithms for estimating optimal parameters of a social network model, using data available from the network itself. This entails solving an optimization problem. In the paper, we propose a new method for parameters estimation in a specific social network model, namely, the so-called p-star model with three parameters. The method is based on the mean-field approximation of the moments associated with the three subgraphs defining the model, namely: the mean numbers of edges, two-stars, and triangles. A modified gradient ascent method is applied to maximize the log-likelihood function of the p-star model, in which the components of the gradient are computed using approximate values of the moments. Compared to other existing iterative methods for parameters estimation, which are computationally very expensive when the number of vertices becomes large, such as gradient ascent applied to maximum log-pseudo- likelihood estimation, the proposed approach has the advantage of a much cheaper cost per iteration, which is practically independent of the number of vertices.

math.ST↗

arXiv2016

LQG Online Learning

Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with the classical Linear Quadratic Gaussian (LQG) optimal control problem, of which the proposed learning paradigm is a non-trivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman-filter estimate of the parameter vector to be learned. It is shown that the proposed algorithm is less sensitive to outliers with respect to the Kalman estimate (thanks to the presence of the regularization term), thus providing smoother estimates with respect to time. The basic formulation of the proposed online-learning framework refers to a discrete-time setting with a finite learning horizon and a linear model. Various extensions are investigated, including the infinite learning horizon and, via the so-called "kernel trick", the case of nonlinear models.

math.OC↗

arXiv2016

Symmetric and antisymmetric properties of solutions to kernel-based machine learning problems

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations (Herbrich et al., 1998). In these cases, one may want to embed additional prior knowledge into the optimization problem associated with the training of the learning machine, modeled, respectively, by the symmetry of its optimal solution with respect to an exchange of order between the two objects, and by its antisymmetry. Extending the approach proposed in (Brunner et al., 2012) (where the only symmetric case was considered), we show, focusing on support vector binary classification, how such embedding is possible through the choice of a suitable pairwise kernel, which takes as inputs the individual feature vectors and also the group feature vectors associated with the two objects. We also prove that the symmetry/antisymmetry constraints still hold when considering the sequence of suboptimal solutions generated by one version of the Sequential Minimal Optimization (SMO) algorithm, and we present numerical results supporting the theoretical findings. We conclude discussing extensions of the main results to support vector regression, to transductive support vector machines, and to several kinds of graph kernels, including diffusion kernels.

cs.LG↗

arXiv2016

Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials

The elastic wave propagation is investigated in the beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, a nonlinear optimization problem is formulated. The maximum of the largest band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the optimal solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and resonators. The optimization problems related to full and partial band gaps are solved independently, by means of a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized.

cond-mat.mtrl-sci↗

arXiv2016

Design of acoustic metamaterials through nonlinear programming

The dispersive wave propagation in a periodic metamaterial with tetrachiral topology and inertial local resonators is investigated. The Floquet-Bloch spectrum of the metamaterial is compared with that of the tetrachiral beam lattice material without resonators. The resonators can be designed to open and shift frequency band gaps, that is, spectrum intervals in which harmonic waves do not propagate. Therefore, an optimal passive control of the frequency band structure can be pursued in the metamaterial. To this aim, a suitable constrained nonlinear optimization problem on a compact set of admissible geometrical and mechanical parameters is stated. According to functional requirements, the particular set of parameters which determines the largest low-frequency band gap between a pair of consecutive branches of the Floquet-Bloch spectrum is obtained. The optimization problem is successfully solved by means of a version of the method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique.

cond-mat.mtrl-sci↗