Dario Piga

Marco Forgione, Manas Mejari, Dario Piga

In recent years, several algorithms for system identification with neural state-space models have been introduced. Most of the proposed approaches are aimed at reducing the computational complexity of the learning problem, by splitting the optimization over short sub-sequences extracted from a longer training dataset. Different sequences are then processed simultaneously within a minibatch, taking advantage of modern parallel hardware for deep learning. An issue arising in these methods is the need to assign an initial state for each of the sub-sequences, which is required to run simulations and thus to evaluate the fitting loss. In this paper, we provide insights for calibration of neural state-space training algorithms based on extensive experimentation and analyses performed on two recognized system identification benchmarks. Particular focus is given to the choice and the role of the initial state estimation. We demonstrate that advanced initial state estimation techniques are really required to achieve high performance on certain classes of dynamical systems, while for asymptotically stable ones basic procedures such as zero or random initialization already yield competitive performance.

Alessio Benavoli, Dario Azzimonti, Dario Piga

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not able to select a single most preferred object. To address these situations, we need a choice-model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice-data. The proposed model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.

Marco Forgione, Dario Piga

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.

Francesca Venturini, Silvan Fluri, Manas Mejari et al.

This work systematically investigates the oxidation of extra virgin olive oil (EVOO) under accelerated storage conditions with UV absorption and total fluorescence spectroscopy. With the large amount of data collected, it proposes a method to monitor the oil's quality based on machine learning applied to highly-aggregated data. EVOO is a high-quality vegetable oil that has earned worldwide reputation for its numerous health benefits and excellent taste. Despite its outstanding quality, EVOO degrades over time owing to oxidation, which can affect both its health qualities and flavour. Therefore, it is highly relevant to quantify the effects of oxidation on EVOO and develop methods to assess it that can be easily implemented under field conditions, rather than in specialized laboratories. The following study demonstrates that fluorescence spectroscopy has the capability to monitor the effect of oxidation and assess the quality of EVOO, even when the data are highly aggregated. It shows that complex laboratory equipment is not necessary to exploit fluorescence spectroscopy using the proposed method and that cost-effective solutions, which can be used in-field by non-scientists, could provide an easily-accessible assessment of the quality of EVOO.

Le Anh Dao, Loris Roveda, Marco Maccarini et al.

Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to access the optimization problem is through performing physical experiments with the available outcomes being the preference of one candidate with respect to one or many others. Accordingly, the algorithm so-called Active Preference Learning has been developed to exploit this specific information in constructing a surrogate function based on standard radial basis functions, and then forming an easy-to-solve acquisition function which repetitively suggests new decision vectors to search for the optimal solution. Based on this idea, our approach aims to extend the algorithm in such a way that can exploit further information effectively, which can be obtained in reality such as: 5-point Likert type scale for the outcomes of the preference query (i.e., the preference can be described in not only "this is better than that" but also "this is much better than that" level), or multiple outcomes for a single preference query with possible additive information on how certain the outcomes are. The validation of the proposed algorithm is done through some standard benchmark functions, showing a promising improvement with respect to the state-of-the-art algorithm.

Marco Forgione, Filippo Pura, Dario Piga

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this paper. In response to this query, we introduce a novel paradigm for system identification, addressing two primary tasks: one-step-ahead prediction and multi-step simulation. Unlike conventional methods, we do not directly estimate a model for the specific system. Instead, we learn a meta model that represents a class of dynamical systems. This meta model is trained on a potentially infinite stream of synthetic data, generated by simulators whose settings are randomly extracted from a probability distribution. When provided with a context from a new system-specifically, an input/output sequence-the meta model implicitly discerns its dynamics, enabling predictions of its behavior. The proposed approach harnesses the power of Transformers, renowned for their \emph{in-context learning} capabilities. For one-step prediction, a GPT-like decoder-only architecture is utilized, whereas the simulation problem employs an encoder-decoder structure. Initial experimental results affirmatively answer our foundational question, opening doors to fresh research avenues in system identification.

Gabriele Maroni, Loris Cannelli, Dario Piga

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l2-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that our multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.

Raffaele Giuseppe Cestari, Gabriele Maroni, Loris Cannelli et al.

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and the onset of overfitting in the face of a small amount of data. In this framework, we propose an innovative training strategy for feed-forward architectures - called split-boost - that improves performance and automatically includes a regularizing behaviour without modeling it explicitly. Such a novel approach ultimately allows us to avoid explicitly modeling the regularization term, decreasing the total number of hyperparameters and speeding up the tuning phase. The proposed strategy is tested on a real-world (anonymized) dataset within a benchmark medical insurance design problem.

Milad Banitalebi Dehkordi, Manas Mejari, Dario Piga

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters including process and measurement noise covariances are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. We prove a theoretical consistency result by bounding the impact of the SVGD approximated parameter posterior on state estimates, relating the divergence between the true and approximate parameter posteriors to the total variation distance between the resulting state marginals. Performance of the proposed filter is validated on two case studies: a bioreactor with Haldane kinetics and a neural-network-augmented dynamic system. The latter demonstrates the filter's capacity for online neural network training within a dynamical model, showcasing its potential for fully adaptive, data-driven system identification.

Dario Piga, Marco Forgione

Over the years, research in system identification has provided a rich set of methods for learning dynamical models, together with well-established theoretical guarantees. In practice, however, the choice of model class, training algorithm, and hyperparameter tuning is still largely left to empirical trial-and-error, requiring substantial expert time and domain experience. Motivated by recent advances in agentic artificial intelligence, we present ASIA, a framework that delegates this iterative search to a large language model acting as an autonomous coding agent. Building on existing agentic platforms, ASIA closes the loop between hypothesis, implementation, and evaluation without human intervention, requiring only a plain-English description of the identification problem. We conduct an empirical study of ASIA on two system identification benchmarks and analyse the agent's search behaviour, the architectures and training strategies it discovers, and the quality of the resulting models. We also discuss the potential of the approach and its current limitations, including implicit test leakage, reduced methodological transparency, and reproducibility concerns.

Angelo Moroncelli, Vishal Soni, Marco Forgione et al.

Recently, generative AI and reinforcement learning (RL) have been redefining what is possible for AI agents that take information flows as input and produce intelligent behavior. As a result, we are seeing similar advancements in embodied AI and robotics for control policy generation. Our review paper examines the integration of generative AI models with RL to advance robotics. Our primary focus is on the duality between generative AI and RL for robotics downstream tasks. Specifically, we investigate: (1) The role of prominent generative AI tools as modular priors for multi-modal input fusion in RL tasks. (2) How RL can train, fine-tune and distill generative models for policy generation, such as VLA models, similarly to RL applications in large language models. We then propose a new taxonomy based on a considerable amount of selected papers. Lastly, we identify open challenges accounting for model scalability, adaptation and grounding, giving recommendations and insights on future research directions. We reflect on which generative AI models best fit the RL tasks and why. On the other side, we reflect on important issues inherent to RL-enhanced generative policies, such as safety concerns and failure modes, and what are the limitations of current methods. A curated collection of relevant research papers is maintained on our GitHub repository, serving as a resource for ongoing research and development in this field: https://github.com/clmoro/Robotics-RL-FMs-Integration.

Loddo Fabio, Dario Piga, Michelucci Umberto et al.

Satellites equipped with optical sensors capture high-resolution imagery, providing valuable insights into various environmental phenomena. In recent years, there has been a surge of research focused on addressing some challenges in remote sensing, ranging from water detection in diverse landscapes to the segmentation of mountainous and terrains. Ongoing investigations goals to enhance the precision and efficiency of satellite imagery analysis. Especially, there is a growing emphasis on developing methodologies for accurate water body detection, snow and clouds, important for environmental monitoring, resource management, and disaster response. Within this context, this paper focus on the cloud segmentation from remote sensing imagery. Accurate remote sensing data analysis can be challenging due to the presence of clouds in optical sensor-based applications. The quality of resulting products such as applications and research is directly impacted by cloud detection, which plays a key role in the remote sensing data processing pipeline. This paper examines seven cutting-edge semantic segmentation and detection algorithms applied to clouds identification, conducting a benchmark analysis to evaluate their architectural approaches and identify the most performing ones. To increase the model's adaptability, critical elements including the type of imagery and the amount of spectral bands used during training are analyzed. Additionally, this research tries to produce machine learning algorithms that can perform cloud segmentation using only a few spectral bands, including RGB and RGBN-IR combinations. The model's flexibility for a variety of applications and user scenarios is assessed by using imagery from Sentinel-2 and Landsat-8 as datasets. This benchmark can be reproduced using the material from this github link: https://github.com/toelt-llc/cloud_segmentation_comparative.

Marco Forgione, Manas Mejari, Dario Piga

With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which feature linear dynamical blocks as key constituent components, offer high predictive performance. However, the learned representations often suffer from excessively large model orders, which render them unsuitable for control design purposes. The current paper addresses this challenge by means of system-theoretic model order reduction techniques that target the linear dynamical blocks of SSMs. We introduce two regularization terms which can be incorporated into the training loss for improved model order reduction. In particular, we consider modal $\ell_1$ and Hankel nuclear norm regularization to promote sparsity, allowing one to retain only the relevant states without sacrificing accuracy. The presented regularizers lead to advantages in terms of parsimonious representations and faster inference resulting from the reduced order models. The effectiveness of the proposed methodology is demonstrated using real-world ground vibration data from an aircraft.

Matteo Cercola, Michele Lomuscio, Dario Piga et al.

Human-in-the-loop calibration is often addressed via preference-based optimization, where algorithms learn from pairwise comparisons rather than explicit cost evaluations. While effective, methods such as Preferential Bayesian Optimization or Global optimization based on active preference learning with radial basis functions (GLISp) treat the system as a black box and ignore informative sensor measurements. In this work, we introduce a sensor-guided regularized extension of GLISp that integrates measurable descriptors into the preference-learning loop through a physics-informed hypothesis function and a least-squares regularization term. This injects grey-box structure, combining subjective feedback with quantitative sensor information while preserving the flexibility of preference-based search. Numerical evaluations on an analytical benchmark and on a human-in-the-loop vehicle suspension tuning task show faster convergence and superior final solutions compared to baseline GLISp.

Dario Piga, Filippo Pura, Marco Forgione

In-context system identification aims at constructing meta-models to describe classes of systems, differently from traditional approaches that model single systems. This paradigm facilitates the leveraging of knowledge acquired from observing the behaviour of different, yet related dynamics. This paper discusses the role of meta-model adaptation. Through numerical examples, we demonstrate how meta-model adaptation can enhance predictive performance in three realistic scenarios: tailoring the meta-model to describe a specific system rather than a class; extending the meta-model to capture the behaviour of systems beyond the initial training class; and recalibrating the model for new prediction tasks. Results highlight the effectiveness of meta-model adaptation to achieve a more robust and versatile meta-learning framework for system identification.

Dario Piga, Matteo Rufolo, Gabriele Maroni et al.

This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized by data scarcity. Central to the proposed methodology is the concept of knowledge transfer from systems within the same class. Specifically, synthetic data is generated through a pre-trained meta-model that describes a broad class of systems to which the system of interest is assumed to belong. Training data serves a dual purpose: firstly, as input to the pre-trained meta model to discern the system's dynamics, enabling the prediction of its behavior and thereby generating synthetic output sequences for new input sequences; secondly, in conjunction with synthetic data, to define the loss function used for model estimation. A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data in the definition of the loss function. The same validation set can be also used for other purposes, such as early stopping during the training, fundamental to avoid overfitting in case of small-size training datasets. The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process.

Marco Forgione, Ankush Chakrabarty, Dario Piga et al.

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep learning models often require large datasets and significant computational resources at training and inference due to their high-dimensional parameterizations. To address this challenge, we propose a meta-learning framework that discovers a low-dimensional manifold within the parameter space of an over-parameterized neural network architecture. This manifold is learned from a meta-dataset of input-output sequences generated by a class of related dynamical systems, enabling efficient model training while preserving the network's expressive power for the considered system class. Unlike bilevel meta-learning approaches, our method employs an auxiliary neural network to map datasets directly onto the learned manifold, eliminating the need for costly second-order gradient computations during meta-training and reducing the number of first-order updates required in inference, which could be expensive for large models. We validate our approach on a family of Bouc-Wen oscillators, which is a well-studied nonlinear system identification benchmark. We demonstrate that we are able to learn accurate models even in small-data scenarios.

Alessio Benavoli, Dario Piga, Marco Forgione et al.

In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.

Matteo Rufolo, Dario Piga, Marco Forgione

Meta learning aims at learning how to solve tasks, and thus it allows to estimate models that can be quickly adapted to new scenarios. This work explores distributionally robust minimization in meta learning for system identification. Standard meta learning approaches optimize the expected loss, overlooking task variability. We use an alternative approach, adopting a distributionally robust optimization paradigm that prioritizes high-loss tasks, enhancing performance in worst-case scenarios. Evaluated on a meta model trained on a class of synthetic dynamical systems and tested in both in-distribution and out-of-distribution settings, the proposed approach allows to reduce failures in safety-critical applications.

Riccardo Busetto, Manas Mejari, Marco Forgione et al.

When gradient-based methods are impractical, black-box optimization (BBO) provides a valuable alternative. However, BBO often struggles with high-dimensional problems and limited trial budgets. In this work, we propose a novel approach based on meta-learning to pre-compute a reduced-dimensional manifold where optimal points lie for a specific class of optimization problems. When optimizing a new problem instance sampled from the class, black-box optimization is carried out in the reduced-dimensional space, effectively reducing the effort required for finding near-optimal solutions.

Marco Forgione, Aneri Muni, Dario Piga et al.

This paper presents a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network (RNN) models of dynamical systems. A nominal RNN model is first identified using available measurements. The system dynamics are then assumed to change, leading to an unacceptable degradation of the nominal model performance on the perturbed system. To cope with the mismatch, the model is augmented with an additive correction term trained on fresh data from the new dynamic regime. The correction term is learned through a Jacobian Feature Regression (JFR) method defined in terms of the features spanned by the model's Jacobian with respect to its nominal parameters. A non-parametric view of the approach is also proposed, which extends recent work on Gaussian Process (GP) with Neural Tangent Kernel (NTK-GP) to the RNN case (RNTK-GP). This can be more efficient for very large networks or when only few data points are available. Implementation aspects for fast and efficient computation of the correction term, as well as the initial state estimation for the RNN model are described. Numerical examples show the effectiveness of the proposed methodology in presence of significant system variations.

Alessio Benavoli, Dario Azzimonti, Dario Piga

In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension $n_e$ which embeds the options into the real vector space of dimension n, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.

Umberto Michelucci, Michela Sperti, Dario Piga et al.

This paper presents the intrinsic limit determination algorithm (ILD Algorithm), a novel technique to determine the best possible performance, measured in terms of the AUC (area under the ROC curve) and accuracy, that can be obtained from a specific dataset in a binary classification problem with categorical features {\sl regardless} of the model used. This limit, namely the Bayes error, is completely independent of any model used and describes an intrinsic property of the dataset. The ILD algorithm thus provides important information regarding the prediction limits of any binary classification algorithm when applied to the considered dataset. In this paper the algorithm is described in detail, its entire mathematical framework is presented and the pseudocode is given to facilitate its implementation. Finally, an example with a real dataset is given.

Dario Piga, Marco Forgione, Manas Mejari

This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units {by} exploiting standard deep learning software. Two relevant applications of the operator in system identification are presented. The first one consists in the integration of {prediction error methods} in deep learning. The dynamical operator is included as {the} last layer of a neural network in order to obtain the optimal one-step-ahead prediction error. The second one considers identification of general block-oriented models from quantized data. These block-oriented models are constructed by combining linear dynamical operators with static nonlinearities described as standard feed-forward neural networks. A custom loss function corresponding to the log-likelihood of quantized output observations is defined. For gradient-based optimization, the derivatives of the log-likelihood are computed by applying the back-propagation algorithm through the whole network. Two system identification benchmarks are used to show the effectiveness of the proposed methodologies.

Alessio Benavoli, Dario Azzimonti, Dario Piga

Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also represent asymmetric distributions. In a recent contribution we showed that SkewGP and probit likelihood are conjugate, which allows us to compute the exact posterior for non-parametric binary classification and preference learning. In this paper, we generalize previous results and we prove that SkewGP is conjugate with both the normal and affine probit likelihood, and more in general, with their product. This allows us to (i) handle classification, preference, numeric and ordinal regression, and mixed problems in a unified framework; (ii) derive closed-form expression for the corresponding posterior distributions. We show empirically that the proposed framework based on SkewGP provides better performance than Gaussian processes in active learning and Bayesian (constrained) optimization. These two tasks are fundamental for design of experiments and in Data Science.

Alessio Benavoli, Dario Azzimonti, Dario Piga

Preferential Bayesian optimisation (PBO) deals with optimisation problems where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or recommender systems). The state-of-the-art approach to PBO uses a Gaussian process to model the preference function and a Bernoulli likelihood to model the observed pairwise comparisons. Laplace's method is then employed to compute posterior inferences and, in particular, to build an appropriate acquisition function. In this paper, we prove that the true posterior distribution of the preference function is a Skew Gaussian Process (SkewGP), with highly skewed pairwise marginals and, thus, show that Laplace's method usually provides a very poor approximation. We then derive an efficient method to compute the exact SkewGP posterior and use it as surrogate model for PBO employing standard acquisition functions (Upper Credible Bound, etc.). We illustrate the benefits of our exact PBO-SkewGP in a variety of experiments, by showing that it consistently outperforms PBO based on Laplace's approximation both in terms of convergence speed and computational time. We also show that our framework can be extended to deal with mixed preferential-categorical BO, where binary judgments (valid or non-valid) together with preference judgments are available.

Marco Forgione, Dario Piga

This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system identification purposes. The back-propagation behavior of the linear dynamical operator with respect to both its parameters and its input sequence is defined. This enables end-to-end training of structured networks containing linear dynamical operators and other differentiable units, exploiting existing deep learning software. Examples show the effectiveness of the proposed approach on well-known system identification benchmarks. Examples show the effectiveness of the proposed approach against well-known system identification benchmarks.

Marco Forgione, Dario Piga

This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space models. The sequence of hidden states is optimized along with the neural network parameters in order to minimize the difference between measured and estimated outputs, and at the same time to guarantee that the optimized state sequence is consistent with the estimated system dynamics. The effectiveness of the approach is demonstrated through three case studies, including two public system identification benchmarks based on experimental data.

Alessio Benavoli, Dario Azzimonti, Dario Piga

Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate Unified Skew-Normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace's method or Expectation Propagation.

Marco Forgione, Dario Piga

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are fitted to measured data using different criteria including a computationally efficient approach minimizing a regularized multi-step ahead simulation error. In this approach, the neural network parameters are estimated along with the initial conditions used to simulate the output signal in small-size subsequences. A regularization term is included in the fitting cost in order to enforce these initial conditions to be consistent with the estimated system dynamics. Pitfalls and limitations of naive one-step prediction and simulation error minimization are also discussed.

Alberto Bemporad, Dario Piga

This paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as "this is better than that" between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. The surrogate is fit by means of radial basis functions, under the constraint of satisfying, if possible, the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is superior in that, within the same number of comparisons, it approaches the global optimum more closely and is computationally lighter. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/idwgopt.