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Nina Miolane

Bio: Nina Miolane is an academic researcher from Stanford University. The author has contributed to research in topics: Computer science & Manifold. The author has an hindex of 8, co-authored 24 publications receiving 189 citations. Previous affiliations of Nina Miolane include French Institute for Research in Computer Science and Automation.

Papers
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Journal Article
TL;DR: It is shown that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications.
Abstract: We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at http://geomstats.ai.

70 citations

Posted Content
TL;DR: Geomstats as discussed by the authors is a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations.
Abstract: We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively unit-tested implementations of these manifolds, together with useful Riemannian metrics and associated Exponential and Logarithm maps. The corresponding geodesic distances provide a range of intuitive choices of Machine Learning loss functions. We also give the corresponding Riemannian gradients. The operations implemented in geomstats are available with different computing backends such as numpy, tensorflow and keras. We have enabled GPU implementation and integrated geomstats manifold computations into keras deep learning framework. This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.

48 citations

Book ChapterDOI
16 Sep 2018
TL;DR: This work proposes a new metric for linear spaces that does not take into account the Lie group structure of SE(3) that is applicable to pose estimation and regression.
Abstract: Pose estimation, i.e. predicting a 3D rigid transformation with respect to a fixed co-ordinate frame in, SE(3), is an omnipresent problem in medical image analysis. Deep learning methods often parameterise poses with a representation that separates rotation and translation. As commonly available frameworks do not provide means to calculate loss on a manifold, regression is usually performed using the L2-norm independently on the rotation’s and the translation’s parameterisations. This is a metric for linear spaces that does not take into account the Lie group structure of SE(3).

24 citations

Posted Content
TL;DR: A Long-Term Recurrent Convolutional Network using Numerical Weather Predictions (NWP) to predict, in turn, PV production in the 24-hour and 48-hour forecast horizons, and compared to the persistence model and state-of-the-art methods.
Abstract: Photovoltaic (PV) power generation has emerged as one of the lead renewable energy sources. Yet, its production is characterized by high uncertainty, being dependent on weather conditions like solar irradiance and temperature. Predicting PV production, even in the 24-hour forecast, remains a challenge and leads energy providers to left idling - often carbon emitting - plants. In this paper, we introduce a Long-Term Recurrent Convolutional Network using Numerical Weather Predictions (NWP) to predict, in turn, PV production in the 24-hour and 48-hour forecast horizons. This network architecture fully leverages both temporal and spatial weather data, sampled over the whole geographical area of interest. We train our model on an NWP dataset from the National Oceanic and Atmospheric Administration (NOAA) to predict spatially aggregated PV production in Germany. We compare its performance to the persistence model and state-of-the-art methods.

17 citations

Proceedings ArticleDOI
14 Jun 2020
TL;DR: A Riemannian variational autoencoder with an intrinsic generative model of manifold-valued data is formulates and its performances on synthetic and real datasets are evaluated, by introducing the formalism of weighted RiemANNian submanifolds.
Abstract: Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their functional Magnetic Resonance Imaging (fMRI) time series – an object thus constrained by construction to belong to the manifold of symmetric positive definite matrices. One of the challenges that naturally arises in these studies consists in finding a lower-dimensional subspace for representing such manifold-valued and typically high-dimensional data. Traditional techniques, like principal component analysis, are ill-adapted to tackle non-Euclidean spaces and may fail to achieve a lower-dimensional representation of the data – thus potentially pointing to the absence of lower-dimensional representation of the data. However, these techniques are restricted in that: (i) they do not leverage the assumption that the connectomes belong on a pre-specified manifold, therefore discarding information; (ii) they can only fit a linear subspace to the data. In this paper, we are interested in variants to learn potentially highly curved submanifolds of manifold-valued data. Motivated by the brain connectomes example, we investigate a latent variable generative model, which has the added benefit of providing us with uncertainty estimates – a crucial quantity in the medical applications we are considering. While latent variable models have been proposed to learn linear and nonlinear spaces for Euclidean data, or geodesic subspaces for manifold data, no intrinsic latent variable model exists to learn non-geodesic subspaces for manifold data. This paper fills this gap and formulates a Riemannian variational autoencoder with an intrinsic generative model of manifold-valued data. We evaluate its performances on synthetic and real datasets, by introducing the formalism of weighted Riemannian submanifolds.

15 citations


Cited by
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Journal ArticleDOI
TL;DR: This study reviews recent advances in UQ methods used in deep learning and investigates the application of these methods in reinforcement learning (RL), and outlines a few important applications of UZ methods.
Abstract: Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

809 citations

Posted Content
TL;DR: From smart grids to disaster management, high impact problems where existing gaps can be filled by ML are identified, in collaboration with other fields, to join the global effort against climate change.
Abstract: Climate change is one of the greatest challenges facing humanity, and we, as machine learning experts, may wonder how we can help. Here we describe how machine learning can be a powerful tool in reducing greenhouse gas emissions and helping society adapt to a changing climate. From smart grids to disaster management, we identify high impact problems where existing gaps can be filled by machine learning, in collaboration with other fields. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the machine learning community to join the global effort against climate change.

441 citations

Journal ArticleDOI
TL;DR: In this article, a review of the recent developments in medical image analysis with deep learning can be found and a critical review of related major aspects is provided. But the authors do not assume prior knowledge of deep learning and make a significant contribution in explaining the core deep learning concepts to the non-experts in the Medical Community.
Abstract: Medical image analysis is currently experiencing a paradigm shift due to deep learning. This technology has recently attracted so much interest of the Medical Imaging Community that it led to a specialized conference in “Medical Imaging with Deep Learning” in the year 2018. This paper surveys the recent developments in this direction and provides a critical review of the related major aspects. We organize the reviewed literature according to the underlying pattern recognition tasks and further sub-categorize it following a taxonomy based on human anatomy. This paper does not assume prior knowledge of deep learning and makes a significant contribution in explaining the core deep learning concepts to the non-experts in the Medical Community. This paper provides a unique computer vision/machine learning perspective taken on the advances of deep learning in medical imaging. This enables us to single out “lack of appropriately annotated large-scale data sets” as the core challenge (among other challenges) in this research direction. We draw on the insights from the sister research fields of computer vision, pattern recognition, and machine learning, where the techniques of dealing with such challenges have already matured, to provide promising directions for the Medical Imaging Community to fully harness deep learning in the future.

148 citations

Journal ArticleDOI
TL;DR: Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of uncertainties during both optimization and decision making processes as mentioned in this paper, and have been applied to solve a variety of real-world problems in science and engineering Bayesian approximation and ensemble learning techniques are two widely-used types of uncertainty quantification.

77 citations