All Years Seminars
[INMA] 2020-12-08 (14h) : Intrinsic Wavelet Smoothing of Curves of Hermitian Positive Definite Matrices
At MS Teams
Speaker :
Rainer von Sachs (UCLouvain)
Abstract :
In multivariate time series analysis, non-degenerate autocovariance and spectral density matrices are necessarily Hermitian and positive definite, and it is important to preserve these properties in any estimation procedure. Our main contribution is the development of intrinsic wavelet transforms and nonparametric wavelet regression for curves in the non-Euclidean space of Hermitian positive definite matrices. The primary focus is on the construction of intrinsic average-interpolation wavelet transforms in the space equipped with a natural invariant Riemannian metric. In addition, we derive the wavelet coefficient decay and linear wavelet thresholding convergence rates of intrinsically smooth curves of Hermitian positive definite matrices. The intrinsic wavelet transforms are computationally fast, and nonlinear wavelet thresholding captures localised features, such as cups or kinks, in the matrix-valued curves. In the context of nonparametric spectral estimation, the intrinsic (linear or nonlinear) wavelet spectral estimator satisfies the important property that it is equivariant under a change of basis of the time series, in contrast to most existing approaches. The finite-sample performance of the intrinsic wavelet spectral estimator based on nonlinear tree-structured trace thresholding is demonstrated by some simulated and real data examples.
All details of this work can be found in Chau, J., von Sachs, R. Intrinsic wavelet smoothing of curves of Hermitian positive definite matrices. Journal American Statistical Association 2020, to appear (available on https://arxiv.org/pdf/1701.03314.pdf).
[INMA] 2020-12-01 (14h) : Applications of Convex Restriction Techniques to Electric Power System Optimization Problems
At MS Teams
Speaker :
Daniel Molzahn (Georgia Institute of Technology, USA)
Abstract :
Electric power systems are critical infrastructure that underlie almost all aspects of modern society. With rapidly increasing quantities of renewable generation and the continuing expansion of electricity markets, electric power systems are undergoing significant changes. New algorithms for optimizing the design and operation of electric power systems are needed in order to enable these transformational changes.
Power system optimization problems are constrained by the so-called “power flow” equations which relate the voltages and power injections. Due to the nonlinearity of these equations, power system optimization problems are nonconvex, resulting in a variety of algorithmic and theoretical challenges. Over the last decade, the research community has developed many new techniques for addressing the nonlinearities associated with the power flow equations. These techniques can be categorized as approximations, convex relaxations (outer approximations of the feasible space), and convex restrictions (inner approximations of the feasible space). After overviewing each of these categories of techniques, this presentation details recent progress in the development of convex restrictions of power system optimization problems. This presentation then describes two algorithms that use convex restrictions to 1) compute paths between operating points such that all points on the paths are feasible with respect to both the power flow equations and the operational constraints, and 2) solve robust optimization problems that ensure constraint satisfaction despite uncertain perturbations from renewable generators.
This is joint work with Dongchan Lee, Line Roald, and Kostya Turitsyn.
[INMA] 2020-11-24 (14h) : Can we use network analysis and tools from graph theory to radically transform clinical psychology?
At MS Teams
Speaker :
Alexandre Heeren (UCLouvain)
Abstract :
For decades, science has attempted to understand the world by boiling concepts down to their simplest components in a quest for reductionism, but there is now a general scientific move to map the world's complexities. Clinical psychology has recently started to embrace this perspective, as well. To do so, researchers have begun to conceptualize symptoms of mental disorders as network systems using computational tools from graph theory and network analysis. In this talk, Alexandre Heeren will introduce the theoretical conjectures, methodological approaches, and levels of evidence of this "network takeover" currently transforming clinical psychology. He will also discuss the theoretical and methodological challenges and the potential translational value of this radically new approach to clinical psychology.
[INMA] 2020-11-17 (14h) : Large system limit of convolutional neural networks for image denoising
At MS Teams
Speaker :
Tachella, Julián
Abstract :
Convolutional Neural Networks (CNNs) are now a well-established tool for solving computer vision and imaging problems, and modern CNNs often obtain state-of-the-art performance. Perhaps surprisingly, it has been recently shown that, despite being highly overparameterized, such networks can be trained with a single corrupted image and still perform as well as fully trained networks - a phenomenon encapsulated in the deep image prior (DIP). Here we attempt to explain what might be going on in terms of recent advances of Neural Tangent Kernel (NTK) theory, which characterizes the large system limit of neural networks. We identify strong links between CNN architectures and well-known signal processing techniques such as non-local means, showing that the function associated with a CNN to a given image can be obtained in closed form without need to train the network. Although our analysis shows that the NTK still does not fully explain the DIP phenomenon, we argue it suggests that CNN's inductive bias is better characterized by images with non-local self-similar structure.
[INMA] 2020-11-10 (14h) : Algorithms for Nonnegative Matrix Factorization
At MS Teams
Speaker :
Leplat, Valentin
Abstract :
The low-rank approximation of a matrix is a key problem in data analysis, and is equivalent to linear dimensionality reduction (LDR). LDR techniques such as principal component analysis are powerful tools for the analysis of high-dimensional data. In this talk, we consider a particular low-rank approximation model, namely nonnegative matrix factorization (NMF). NMF is the problem of approximating a given nonnegative matrix, V, with the product of two nonnegative matrices, W and H. The nonnegativity constraint on W and H allows us to extract easily interpretable and meaningful information from the input data. However, they make the problem much more difficult to solve (NP-hard). This talk focuses on the algorithmic aspect to compute an NMF for an input matrix. First, we introduce NMF models and algorithms. Second, we introduce a general framework to design algorithms (namely multiplicative updates) for NMF problems minimizing the β-divergence between V and WH, with disjoint equality constraints and penalty terms in the objective function. Finally, we introduce a novel framework using tools from conic optimization in order to compute an NMF which is exact, that is, with V = WH.
The content of this talk contains joint works with Nicolas Gillis (UMons), Jérôme Idier (Ecole Centrale de Nantes), Yurii Nesterov (UCLouvain) and François Glineur (UCLouvain).
Keywords : nonnegative matrix factorization (NMF), β-divergences, disjoint constraints, exact NMF, conic programming, successive approximations.
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