4,119 research outputs found
A Theory of the Risk for Optimization with Relaxation and its Application to Support Vector Machines
No full textIn this paper we consider optimization with relaxation, an ample paradigm to
make data-driven designs. This approach was previously considered by the same
authors of this work in Garatti and Campi (2019), a study that revealed a
deep-seated connection between two concepts: risk (probability of not
satisfying a new, out-of-sample, constraint) and complexity (according to a
definition introduced in paper Garatti and Campi (2019)). This connection was
shown to have profound implications in applications because it implied that the
risk can be estimated from the complexity, a quantity that can be measured from
the data without any knowledge of the data-generation mechanism. In the present
work we establish new results. First, we expand the scope of Garatti and Campi
(2019) so as to embrace a more general setup that covers various algorithms in
machine learning. Then, we study classical support vector methods - including
SVM (Support Vector Machine), SVR (Support Vector Regression) and SVDD (Support
Vector Data Description) - and derive new results for the ability of these
methods to generalize. All results are valid for any finite size of the data
set. When the sample size tends to infinity, we establish the unprecedented
result that the risk approaches the ratio between the complexity and the
cardinality of the data sample, regardless of the value of the complexity.Comment: https://www.jmlr.org/papers/v22/21-0641.htm
New results on the scenario design approach
No full textThe scenario optimization method developed by Calafiore and Campi (2006) is a theoretically sound and practically effective technique for solving in a probabilistic setting robust convex optimization problems arising in systems and control design, that would otherwise be hard to tackle via standard deterministic techniques. In this note, we further explore some aspects of the scenario methodology, and present two results pertaining to the tightness of the sample complexity bounds. We also state a new theorem that enables the user to make a-priori probabilistic claims on the scenario solution, with one level of probability only
A theory of the risk for optimization with relaxation and its application to support vector machines
No full textIn this paper we consider optimization with relaxation, an ample paradigm to make data-driven designs. This approach was previously considered by the same authors of this work in Garatti and Campi (2019), a study that revealed a deep-seated connection between two concepts: risk (probability of not satisfying a new, out-of-sample, constraint) and complexity (according to a definition introduced in paper Garatti and Campi, 2019). This connection was shown to have profound implications in applications because it implied that the risk can be estimated from the complexity, a quantity that can be measured from the data without any knowledge of the data-generation mechanism. In the present work we establish new results. First, we expand the scope of Garatti and Campi (2019) so as to embrace a more general setup that covers various algorithms in machine learning. Then, we study classical support vector methods – including SVM (Support Vector Machine), SVR (Support Vector Regression) and SVDD (Support Vector Data Description) – and derive new results for the ability of these methods to generalize. All results are valid for any finite size of the data set. When the sample size tends to infinity, we establish the unprecedented result that the risk approaches the ratio between the complexity and the cardinality of the data sample, regardless of the value of the complexity
Attenuation and velocity structure in the area of Pozzuoli-Solfatara (Campi Flegrei, Italy) for the estimate of local site response
No full textIn the present work I infer the 1D shear-wave velocity model in the volcanic area of Pozzuoli-Solfatara using the dispersion properties of both Rayleigh waves generated by artificial explosions and microtremor. The group-velocity dispersion curves are retrieved from application of the Multiple Filter Technique (MFT) to single-station recordings of air-gun sea shots. Seismic signals are filtered in different frequency bands and the dispersion curves are obtained by evaluating the arrival times of the envelope maxima of the filtered signals. Fundamental and higher modes are carefully recognized and separated by using a Phase Matched Filter (PMF). The obtained dispersion curves indicate Rayleigh-wave fundamental-mode group velocities ranging from about 0.8 to 0.6 km/sec over the 1-12 Hz frequency band.
I also propose a new approach based on the autoregressive analysis, to recover group velocity dispersion. I first present a numerical example on a synthetic test signal and then I apply the technique to the data recorded in Solfatara, in order to compare the obtained results with those inferred from the MF analysis
Moreover, I analyse ambient noise data recorded at a dense array, by using Aki’s correlation technique (SAC) and an extended version of this method (ESAC) The obtained phase velocities range from 1.5 km/s to 0.3 km/s over the 1-10 Hz frequency band.
The group velocity dispersion curves are then inverted to infer a shallow shear-wave velocity model down to a depth of about 250 m, for the area of Pozzuoli-Solfatara. The shear-wave velocities thus obtained are compatible with those derived both from cross- and down-hole measurements in neighbour wells and from laboratory experiments. These data are eventually interpreted in the light of the geological setting of the area.
I perform an attenuation study on array recordings of the signals generated by the shots. The attenuation curve was retrieved by analysing the amplitude spectral decay of Rayleigh waves with the distance, in different frequency bands. The attenuation curve was then inverted to infer the shallow Q inverse model.
Using the obtained velocity and attenuation model, I calculate the theoretical ground response to a vertically-incident SH-wave obtaining two main amplification peaks centered at frequencies of 2.1 and 5.4 Hz. The transfer function was compared with that obtained experimentally from the application of Nakamura’s technique to microtremor data, artificial explosions and local earthquakes. Agreement between the two transfer functions is observed only for the amplification peak of frequency 5.4 Hz.
Finally, as a complementary contribution that might be used to the assessment of seismic risk in the investigated area, I evaluate the peak ground acceleration (PGA) for the whole Campi Flegrei caldera and locally for the Pozzuoli-Solfatara area, by performing stochastic simulation of ground motion partially constrained by the previously described results. Two different methods (Random Vibration Theory (RVT) and ground motion generated from a Gaussian distribution (GMG)) are used, providing the PGA values of 0.04 g and 0.097 g for Campi Flegrei and Pozzuoli-Solfatara, respectively
On a class of interval predictor models with universal reliability
No full textAn Interval Predictor Model (IPM) is a rule by which some observable variables (system inputs) are mapped into an interval that is used to predict an inaccessible variable (system output). IPMs have been studied in Campi et al. (2009), where the problem of fitting an IPM on a set of observations has been considered. In the same paper, upper-bounds on the probability that a future system output will fall outside the predicted interval (misprediction) have also been derived in a stationary and independent framework. While these bounds have the notable property of being valid independently of the unknown mechanism that has generated the data, in general the actual probability distribution of the misprediction does depend on the data generation mechanism and, hence, these bounds may introduce conservatism when applied to a specific case. In this paper, we study the reliability of an important class of IPMs, called minimax layers, and show that this class exhibits the special property that the probability distribution of the misprediction is known exactly and is universal, i.e., is always the same irrespective of the data generation mechanism. This result carries important consequences on the use of minimax layers in practice. (C) 2019 Published by Elsevier Ltd
Strategie di Differenziazione di Prodotto: Una rassegna Critica. La differenziazione orizzontale.
No full textGeochemical study of the Solchiaro (Procida Island,Campi Flegrei) eruptive products by microthermometry and microanalyses of fluid and melt inclusions.
No full textThis study presents the work I have done during the 4 years of a PhD program that was part of the internationalization programme of the Italian research system approved by the Ministero della Ricerca e dell’Università (MIUR) between the Università degli Studi di Napoli “Federico II”, (Dipartimento di Scinze della Terra) and the Virginia Polytechnic Institute and State University (Department of Geosciences).
107 selected melt inclusion (MI), 77 open glasses, 80 olivines and 7 bulk rocks (from 4 representative samples of Solchiaro eruption) were analyzed for major/trace element and volatiles. Mostly, olivine compositions vary from Fo82 to Fo88 with one maximum value of Fo90. 2 group of MI were recognized based on major element composition: 1) K2O-rich MI with composition that is the same of bulk rock in the literature and 2) K2O-poor MI that instead have been never reported from previous study of the Phlegrean Volcanic District (PVD). The first group consists of 95% of the melt and relates mostly to within plate setting whereas the second group consists of around 5% of the melt and relates to subduction setting. Magma associated with Solchiaro eruption evolved under open system processes as suggested by petrographic evidence and glass compositions. H2O-CO2 concentrations dissolved in glass suggest that magma was saturated in volatiles at least at 12.5 km depth and continuously degassed during the Solchiaro eruption. Maximum depths are in agreement with other studies based on different approaches. Volatile correlations suggest that during closed system degassing, as the Solchiaro eruption progressed, maximum S contents decreased and minimum Cl and F contents increased. The major, trace and volatile evolution of crystals, glass, and MI is consistent with a model that involves either continuous or episodic recharge of the magma chamber ponded at least at 12.5 km depth
Localization of neural activity from neuromagnetic data using varying-support sources
No full textMagnetoencephalography (MEG) and Electroencephalography (EEG) measure in a non-invasive way the magnetic field and the electrical potential, respectively, induced by cerebral activity. These instruments have an outstanding temporal resolution and the recorded data could provide interesting insights of the dynamics of neural currents. In order to get reliable information on the unknown neural currents from the data, we need to solve a ill-posed inverse problem: the operator involved in the formulation of the model linking the neural activity and the measured data is such that the solution of the inversion problem is not unique and does not depend continuously on the data. Moreover, the choice of the model for the source deeply affects the representation of the solution: a distributed model for neural currents can encompass complex, spread brain activity but could be not accurate in the representation of focal brain activity, while the representation with dipolar sources could not represent properly the activity generated by patches of cortex. In this work we propose a modified version of the Particle Filter we employed so far for MEG data analysis: in this implementation the support of the sources is not more fixed to be a dipole but can change back and forth to be distributed, adapting itself among the time samples to the best configuration. We test the method with ad hoc synthetic data
Legge quadro sui campi elettromagnetici: prime osservazioni
No full textLa legge- quadro n. 36 del 2001 sui campi elettromagnetici ha espressamente introdotto nel nostro diritto positivo il richiamo al principio di precauzione, sancito dall’art. 174, par. 2 del Trattato CE, sviluppandolo in prospettiva dinamica, sia come criterio di tutela della salute, che come criterio diretto ad assicurare la tutela dell’ambiente. La riserva di competenza legislativa statale sulla tutela dell’ambiente e dell’ecosistema operata dalla Costituzione (art. 117, 2 comma, lett. s) esprime l’esigenza di una disciplina unitaria definita dallo Stato per la determinazione dei limiti di esposizione , dei valori di attenzione, degli obiettivi di qualità, mentre la competenza concorrente in materia di tutela della salute, governo del territorio, protezione civile, produzione e trasporto dell’energia (art. 117, c. 3) e quella residuale regionale in materia di produzione e trasporto dell’energia a livello locale (art. 117., c. 4) trovano riscontro nelle previsioni della legge-quadro che affida alle regioni l’attuazione dei principi e dei limiti fissati a livello statale. La devoluzione alle Regioni e ai Comuni delle competenze amministrative ex art. 118 Cost. in materia di localizzazione dei siti e dei tracciati, delle modalità di rilascio delle autorizzazioni, dei controlli sugli aspetti urbanistici ed edilizi, conferma un principio ineludibile nel campo del diritto ambientale: quello del necessario coinvolgimento di tutti i livelli di governo e della loro corresponsabilità nella garanzia del rispetto degli interessi sanitari e ambientali
On a class of interval predictor models with universal reliability
No full textAn Interval Predictor Model (IPM) is a rule by which some observable variables (system inputs) are mapped into an interval that is used to predict an inaccessible variable (system output). IPMs have been studied in Campi et al. (2009), where the problem of fitting an IPM on a set of observations has been considered. In the same paper, upper-bounds on the probability that a future system output will fall outside the predicted interval (misprediction) have also been derived in a stationary and independent framework. While these bounds have the notable property of being valid independently of the unknown mechanism that has generated the data, in general the actual probability distribution of the misprediction does depend on the data generation mechanism and, hence, these bounds may introduce conservatism when applied to a specific case. In this paper, we study the reliability of an important class of IPMs, called minimax layers, and show that this class exhibits the special property that the probability distribution of the misprediction is known exactly and is universal, i.e., is always the same irrespective of the data generation mechanism. This result carries important consequences on the use of minimax layers in practice
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