Eventi
This talk considers a testing problem that is associated with principal component analysis and that may be of interest whenever dimension reduction is considered, as it is the case, e.g., when analyzing high-dimensional data in life sciences or environmental sciences. More specifically, in a triangular array framework where n observations are randomly sampled from a p-dimensional elliptical distribution with shape matrix V_n, we consider the problem of testing the null hypothesis H_0: theta=theta_0, where theta is the (fixed) leading unit eigenvector of V_n and theta_0 is a given unit p-vector. The dependence of the shape matrix on the sample size allows us to consider challenging asymptotic scenarios in which the parameter of interest theta is unidentified in the limit, because the ratio between both leading eigenvalues of V_n converges to one. We study the corresponding limiting experiments under such weak identifiability, and we show that these may be LAN or non-LAN. While earlier work in the framework was strictly limited to Gaussian distributions, where the study of local log-likelihood ratios could simply rely on explicit expressions, our asymptotic investigation allows for essentially arbitrary elliptical distributions. Even in non-LAN experiments, our results enable us to investigate the asymptotic null and non-null properties of multivariate rank tests. These nonparametric tests are shown to exhibit an excellent behavior under weak identifiability: not only do they maintain the target nominal size irrespective of the amount of weak identifiability, but they also keep their uniform efficiency properties under such non-standard scenarios. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk. Contatti: laura.sangalli@polimi.it
Linkage has been used for over a century to study and classify curves in projective three-space and, more generally, varieties in projective space or homogeneous ideals in polynomial rings. Of particular importance have been licci ideals, ideals that can be linked to a complete intersection in a finite number of steps. It is known that the Castelnuovo-Mumford regularity of a licci ideal forces a very strict upper bound for the initial degree of the ideal. Now, in joint work with Craig Huneke and Bernd Ulrich, we conjecture that it also bounds the number of generators of the ideal, and we prove this conjecture in many cases. In addition, we provide new sufficient conditions for an ideal to be licci, for classes of ideals of height three and for ideals containing a maximal regular sequence of quadrics. The talk will also explain connections with recent work by Guerrieri, Ni, Weyman and by Jelisiejew, Ramkumar, Sammartano.
Electricity load forecasting is a necessary capability for power system operators and electricity market participants. Both demand and supply characteristics evolve over time. On the demand side, unexpected events as well as longer-term changes in consumption habits affect demand patterns. On the production side, the increasing penetration of intermittent power generation significantly changes the forecasting needs. We address this challenge in two ways. First, our setting is adaptive; our models take into account the most recent observations available to automatically respond to changes in the underlying process. Second, we consider probabilistic rather than point forecasting; indeed, uncertainty quantification is required to operate electricity systems efficiently and reliably. Our methodology relies on the Kalman filter, previously used successfully for adaptive point load forecasting. The probabilistic forecasts are obtained by quantile regressions on the residuals of the point forecasting model. We achieve adaptive quantile regressions using the online gradient descent; we avoid the choice of the gradient step size considering multiple learning rates and aggregation of experts. We apply our methodology to the regional net-load in Great Britain; by net-load we denote the difference between the consumption and the embedded generation (mainly wind and solar energy). Indeed, as the production of new renewables increases, that quantity is becoming more popular.
The presentation is based on a joint work with J. Browell, M. Fasiolo, Y. Goude and O. Wintenberger (ieeexplore.ieee.org/document/10234679).
I will present a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the observed data directly to account for all sources of uncertainty, instead of relying on prior estimation of the underlying densities in a two-step approach, which can be inaccurate if small or heterogeneous numbers of samples per density are available. To account for the constrained nature of densities, we base our approach on Bayes spaces, which extend the Aitchison geometry for compositional data to density functions. For modeling, we exploit the isometric isomorphism between the Bayes space and the L2 subspace L2_0 with integration-to-zero constraint through the centered log-ratio transformation. As only discrete draws from each density are observed, we treat the underlying functional densities as latent variables within a maximum likelihood framework and employ a Monte Carlo Expectation Maximization (MCEM) algorithm for model estimation. Resulting estimates are useful for exploratory analyses of density data, for dimension reduction in subsequent analyses, as well as for improved preprocessing of sparsely sampled density data compared to existing methods. The proposed method is applied to analyze the distribution of maximum daily temperatures in Berlin during the summer months for the last 70 years, as well as the distribution of rental prices in the districts of Munich.
The talk is based on joint work wit Lisa Steyer, available at arxiv.org/abs/2309.11352
This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk. Contatti: laura.sangalli@polimi.it, alessandra.menafoglio@polimi.it, piercesare.secchi@polimi.it, simone.vantini@polimi.it.
We characterize concavity properties preserved by the Dirichlet heat flow in convex domains of the Euclidean space. (This is a joint work with Paolo Salani and Asuka Takatsu.)
Next, we show that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain. (This is a joint work with Asuka Takatsu and Haruto Tokunaga.)
Environmental data science relies on some fundamental problems such as: 1) Spatial Gaussian likelihood inference; 2) Spatial kriging; 3) Gaussian random field simulations; 4) Multivariate Gaussian probabilities; and 5) Robust inference for spatial data. These problems develop into very challenging tasks when the number of spatial locations grows large. Moreover, they are the cornerstone of more sophisticated procedures involving non-Gaussian distributions, multivariate random fields, or space-time processes. Parallel computing becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications. In this talk, I will explain how high-performance computing can provide solutions to the aforementioned problems using tile-based linear algebra, tile low-rank approximations, as well as multi- and mixed-precision computational statistics. I will introduce ExaGeoStat, and its R version ExaGeoStatR, a powerful software that can perform exascale (10^18 flops/s) geostatistics by exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, i.e., supercomputers. I will then describe how ExaGeoStat can be used to design competitions on spatial statistics for large datasets and to benchmark new methods developed by statisticians and data scientists for large-scale environmental data science. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.
Contatti: laura.sangalli@polimi.it, piercesare.secchi@polimi.it
Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal modeling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with a parametric covariance structure. However, processes in real-world applications often exhibit non-Gaussianity and nonstationarity. Moreover, likelihood-based inference for GPs is computationally expensive and thus prohibitive for large datasets. In this paper, we propose a deep neural network (DNN) based two-stage model for spatio-temporal interpolation and forecasting. Interpolation is performed in the first step, which utilizes a dependent DNN with the embedding layer constructed with spatio-temporal basis functions. For the second stage, we use Long Short-Term Memory (LSTM) and convolutional LSTM to forecast future observations at a given location. We adopt the quantile-based loss function in the DNN to provide probabilistic forecasting. Compared to Kriging, the proposed method does not require specifying covariance functions or making stationarity assumptions and is computationally efficient. Therefore, it is suitable for large-scale prediction of complex spatio-temporal processes. We apply our method to monthly PM$_{2.5}$ data at more than 200,000 space–time locations for fast imputation of missing values and forecasts with uncertainties. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk. Contatti: laura.sangalli@polimi.it, simone.vantini@polimi.it, Piercesare.secchi@polimi.it
Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
Nel VI canto del Purgatorio Dante cita il gioco di dadi "zara". Sarà questo l'inizio di un "percorso matematico tra teoria ed esperienza", in cui si incontreranno persone intelligenti e curiose, tra le quali Galileo Galilei (analisi probabilistica del gioco della zara), Jacob Bernoulli (Legge dei grandi numeri) e Stan Ulam (Metodo Monte Carlo). Al termine si proporranno alcune attività legate al gioco della zara e al metodo Monte Carlo.
Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
Given a domain $\Omega \subset \mathbb{C}^n$ and $p>1$, let $A^p(\Omega)$ denote the $L^p$-Bergman space, the holomorphic subspace of $L^p(\Omega)$. When $\Omega$ is, for instance, smoothly bounded and strongly pseudoconvex, it is well known that the dual of $A^p(\Omega)$ can be naturally identified with $A^q(\Omega)$, where
$\tfrac{1}{p}+\tfrac{1}{q}=1$. This follows the established paradigm seen in ordinary $L^p$-spaces, and is closely linked to the $L^p$-mapping regularity of the Bergman projection. But the presence of boundary singularities can cause the above dual space characterization to fail. In this talk, we look at this problem on monomial polyhedra, a class of non-smooth and weakly pseudoconvex domains in $\mathbb C^n$ where the $L^p$-regularity of the Bergman projection and the $A^p$-$A^q$ duality paradigm both break down. We will construct a family of new projection operators with better $L^p$-mapping behavior than the Bergman projection, then use them to concretely characterize the duals of $A^p$-spaces on these domains.
Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
We address the global-in-time existence, uniqueness, and regularity of solutions to the Cauchy problem for the three-dimensional Navier-Stokes equation with the initial vorticity concentrated on a helix. More specifically, we establish a local-in-time well-posedness result for vortex filaments that are periodic in one spatial direction, following the approach of Bedrossian, Germain and Harrop-Griffiths for closed filaments. Then, we use local energy weak solutions and helical estimates to extend the solution uniquely and globally in time in the helical case.
Marc G. Genton is Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received the Ph.D. degree in Statistics (1996) from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), and is an elected member of the International Statistical Institute (ISI). In 2010, he received the El-Shaarawi award for excellence from the International Environmetrics Society (TIES) and the Distinguished Achievement award from the Section on Statistics and the Environment (ENVR) of the American Statistical Association (ASA). He received an ISI Service award in 2019 and the Georges Matheron Lectureship award in 2020 from the International Association for Mathematical Geosciences (IAMG). He led a Gordon Bell Prize finalist team with the ExaGeoStat software for Super Computing 2022. He received the Royal Statistical Society (RSS) 2023 Barnett Award for his outstanding research in environmental statistics. His research interests include statistical analysis, flexible modeling, prediction, and uncertainty quantification of spatio-temporal data, with applications in environmental and climate science, as well as renewable energies.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica