MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1242 products
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72/2020 - 11/07/2020
Belli E.; Vantini S.
Measure Inducing Classification and Regression Trees for Functional Data | Abstract | | We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing generalization error while retaining the interpretability of a tree. This is achieved by learning a weighted functional L2 space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the input functions, in order to determine the binary split for each internal node of the tree. The approach is designed to manage multiple functional inputs and/or outputs, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with scalar and categorical data, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar-valued functional inputs defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real world applications. |
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71/2020 - 11/07/2020
Belli E; Vantini S.
Ridge regression with adaptive additive rectangles and other piecewise functional templates | Abstract | | We propose an L2-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template ?, which is constrained to belong to a class of piecewise functions by restricting its basis expansion. In particular, we focus on the case where ? can be expressed as a sum of q rectangles that are adaptively positioned with respect to the regression error. As the problem of finding the optimal knot placement of a piecewise function is nonconvex, the proposed parametrization allows to reduce the number of variables in the global optimization scheme, resulting in a fitting algorithm that alternates between approximating a suitable template and solving a convex ridge-like problem. The predictive power and interpretability of our method is shown on multiple simulations and two real world case studies. |
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70/2020 - 11/07/2020
Belli E.
Smoothly Adaptively Centered Ridge Estimator | Abstract | | With a focus on linear models with smooth functional covariates, we propose a penalization framework (SACR) based on the nonzero centered ridge, where the center of the penalty is optimally reweighted in a supervised way, starting from the ordinary ridge solution as the initial centerfunction. In particular, we introduce a convex formulation that jointly estimates the model's coefficients and the weight function, with a roughness penalty on the centerfunction and constraints on the weights in order to recover a possibly smooth and/or sparse solution. This allows for a non-iterative and continuous variable selection mechanism, as the weight function can either inflate or deflate the initial center, in order to target the penalty towards a suitable center, with the objective to reduce the unwanted shrinkage on the nonzero coefficients, instead of uniformly shrinking the whole coefficient function. As empirical evidence of the interpretability and predictive power of our method, we provide a simulation study and two real world spectroscopy applications with both classification and regression. |
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69/2020 - 11/07/2020
Galvani, M.; Torti, A.; Menafoglio, A.; Vantini S.
FunCC: a new bi-clustering algorithm for functional data with misalignment | Abstract | | The problem of bi-clustering functional data, which has recently been addressed in literature, is considered. A definition of ideal functional bi-cluster is given and a novel bi-clustering method, called Functional Cheng and Church (FunCC), is developed. The introduced algorithm searches for non-overlapping and non-exhaustive bi-clusters in a set of functions which are naturally ordered in matrix structure through a non-parametric deterministic iterative procedure.
Moreover, the possible misalignment of the data, which is a common problem when dealing with functions, is taken into account. Hence, the FunCC algorithm is extended obtaining a model able to jointly bi-cluster and align curves.
Different simulation studies are performed to show the potential of the introduced method and to compare it with state-of-the-art methods. The model is also applied on a real case study allowing to discover the spatio-temporal patterns of a bike-sharing system infrastructure.
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67/2020 - 11/07/2020
Caramenti, L.; Menafoglio, A.; Sgobba, S.; Lanzano, G.
Multi-Source Geographically Weighted Regression for Regionalized Ground-Motion Models | Abstract | | This work proposes a novel approach to the calibration of regionalized regression models, with particular reference to ground-motion models (GMMs), which are key for probabilistic seismic hazard analysis and earthquake engineering applications. A novel methodology, named multi-source geographically-weighted regression (MS-GWR), is developed, allowing one to (i) estimate regionalized regression models depending on multiple sources of non-stationarity (such as site- and event-dependent non-stationarities in GMMs), and (ii) make inference on the significance and stationarity of the regression coefficients. Unlike previous approaches to the problem, the proposed framework is fully non-parametric, the inference being based on a permutation scheme. MS-GWR is here used to calibrate a new regionalized ground-motion model for predicting peak ground acceleration in Italy, based on a large scale database of waveforms and metadata made available by the Italian Institute for Geophysics and Vulcanology (INGV). |
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66/2020 - 10/29/2020
Didkovsky, O.; Ivanov, V.; Papini, M.; Longoni, L.; Menafoglio, A.
A comparison between machine learning and functional geostatistics approaches for data-driven analyses of solid transport in a pre-Alpine stream | Abstract | | We address the problem of providing data-driven models for sediment transport in a pre-Alpine stream in Italy. We base our study on a large set of measurements collected from real pebbles, traced along the stream through Radio Frequency IDentificator (RFID) tags after precipitation events. We propose and evaluate two classes of data-driven models -- based on machine learning and functional geostatistics approaches respectively -- to predict the probability of movement of single pebbles within the stream. The first class is built upon gradient boosting decision trees, and allows one to estimate the probability of movement of a pebble, based on the pebbles’ geometrical features, river flow rate, locations, and subdomain types. The second class is built upon functional kriging, a recent geostatistical technique which allows one to predict a functional profile --i.e., the movement probability of a pebble, as a function of the pebbles geometrical features or of the stream's flow rate-- at unsampled locations in the study area.
Although grounded on different perspectives, both these models aim to account for two main sources of uncertainty, namely (i) the complexity of river’s morphological structure, and (ii) the highly-nonlinear dependence between probability of movement, pebble’s size and shape, and the stream’s flow rate.
We extensively compare the performances of the two methods in terms of classification accuracy, and show that, although these techniques are grounded on different perspectives, an overall consistency appears between the methods suggesting that both approaches may provide valuable modeling frameworks for the problem at hand. We finally discuss on the use of the developed models in a bottom-up strategy, which starts with the prediction/classification of a single pebble and then integrates the results into a forecast of the grain-size distribution of mobilized sediments. |
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64/2020 - 10/16/2020
Fiz, F.; Viganò, L.; Gennaro, N.; Costa, G.; La Bella, L.; Boichuk A.; Cavinato, L.; Sollini, M.; Politi, L. S.; Chiti, A.; Torzilli, G.
Radiomics of Liver Metastases: A Systematic Review | Abstract | | Patients with liver metastases can be scheduled for different therapies
(e.g., chemotherapy, surgery, radiotherapy, and ablation). The choice of the most appropriate treatment should rely on adequate understanding of tumor biology and prediction of survival, but reliable biomarkers are lacking. Radiomics is an innovative approach to medical imaging: it identifies invisible-to-the-human-eye radiological patterns that can predict tumor aggressiveness and patients outcome. We reviewed the available literature to elucidate the role of radiomics in patients with liver metastases. Thirty-two papers were analyzed, mostly (56%) concerning metastases from colorectal cancer. Even if available studies are still preliminary, radiomics provided effective prediction of response to chemotherapy and of survival, allowing more accurate and earlier prediction than standard predictors. Entropy and homogeneity were the radiomic features with the strongest clinical impact. In the next few years, radiomics is expected to give a consistent contribution to the precision medicine approach to patients with liver metastases. |
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63/2020 - 09/30/2020
Tuveri, M.; Milani, E.; Marchegiani, G.; Landoni, L.; Torresani, E.; Capelli, P.; Sperandio, N.; D’Onofrio, M.; Salvia, R.; Vergara, C.; Bassi, C.
HEMODYNAMICS AND REMODELING OF THE PORTAL CONFLUENCE IN PATIENTS WITH CANCER OF THE PANCREATIC HEAD: A PILOT STUDY | Abstract | | We designed a computational study to evaluate the effects of hemodynamics on portal confluence remodeling in cancer of the pancreatic head. The importance of this study is the finding that altered flow conditions due to tumor growth can disrupt the balance between eutrophic remodeling and degradative process of the vein wall, leading to the complete substitution of the three-layered vein wall and the opportunity to perform a total pancreatectomy with en-bloc resection of the portal confluence. |
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