Event Calendar

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  • Event CalendarGeneral Relativity Seminar
    09:30 -10:30
    2023-02-02
    Event Calendar

    General Relativity Seminar

    Speaker: Chiara Toldo (Harvard)

    Title: Near extremal de Sitter black holes and JT gravity

    Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

  • Event CalendarColloquia
    12:30 -13:30
    2023-02-02
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    Speaker: Max Reppen (Boston University)

    Title: Neural Optimal Stopping Boundary

    Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

  • Event CalendarActive Matter Seminar
    13:00 -14:00
    2023-02-02
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar
    Active Matter Seminar

    Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

    Title: Interacting Active Matter

    Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

  • Event CalendarYip Lecture Series
    Yip Lecture Series Event
    Third Annual Yip Lecture
    19:00 -20:00
    2023-02-02
    1 Oxford Street, Cambridge MA 02138
    Event Calendar

    Event Calendar

    Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

    Time: 7:00-8:00 pm ET

    Location: Harvard Science Center Hall A

    Registration is required.

    In-person Registration

    Zoom Webinar Registration

    Title: Black Holes: The Most Mysterious Objects in the Universe

    Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

    Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

    Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

    Moderator: Daniel Kapec (Harvard CMSA)

    The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

     


    The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

  • More events
    • Event CalendarGeneral Relativity Seminar
      09:30 -10:30
      2023-02-02
      Event Calendar

      General Relativity Seminar

      Speaker: Chiara Toldo (Harvard)

      Title: Near extremal de Sitter black holes and JT gravity

      Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

    • Event CalendarColloquia
      12:30 -13:30
      2023-02-02
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Event Calendar

      Speaker: Max Reppen (Boston University)

      Title: Neural Optimal Stopping Boundary

      Abstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

    • Event CalendarActive Matter Seminar
      13:00 -14:00
      2023-02-02
      CMSA, 20 Garden Street, Cambridge, MA 02138 USA
      Event Calendar
      Active Matter Seminar

      Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen

      Title: Interacting Active Matter

      Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

    • Event CalendarYip Lecture Series
      Yip Lecture Series Event
      Third Annual Yip Lecture
      19:00 -20:00
      2023-02-02
      1 Oxford Street, Cambridge MA 02138
      Event Calendar

      Event Calendar

      Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.

      Time: 7:00-8:00 pm ET

      Location: Harvard Science Center Hall A

      Registration is required.

      In-person Registration

      Zoom Webinar Registration

      Title: Black Holes: The Most Mysterious Objects in the Universe

      Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.

      Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.

      Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)

      Moderator: Daniel Kapec (Harvard CMSA)

      The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

       


      The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

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  • Event CalendarQuantum Matter
    10:30 -11:30
    2023-02-03
    Event Calendar

    Quantum Matter Seminar

    Speaker: Han Yan (Rice U)

    Title: Fracton orders in hyperbolic space and its excitations with fractal mobility

    Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.

    Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

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  • Event CalendarMember Seminar
    12:00 -13:00
    2023-02-07
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA

    Member Seminar

    Speaker: Chuck Doran

    Title: Motivic Geometry of Two-Loop Feynman Integrals

    Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

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  • Event CalendarColloquia
    12:30 -13:30
    2023-02-08
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    Speaker: David Gamarnik (MIT)

    Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property

    Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap.

    In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.

    We will specifically illustrate how to use this property to obtain stronger (exponential) than the state of the art (quasi-polynomial) lower bounds on the depth of Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.

    Joint work with Aukosh Jagannath and Alex Wein.

  • Probability Seminar
    15:30 -16:30
    2023-02-08

    Probability Seminar

    Speaker: Roland Bauerschmidt (Cambridge)
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  • Event CalendarGeneral Relativity Seminar
    13:30 -14:30
    2023-02-09
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    General Relativity Seminar

    Speaker: Maciej Zworski, UC Berkeley

    Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective

    Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

  • Workshop
    15:30 -17:00
    2023-02-09
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    The CMSA will host a series of three 90-minute lectures on the subject of machine learning for protein folding.

    Thursday Feb. 9, Thursday Feb. 16, & Thursday March 9, 2023, 3:30-5:00 pm ET

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    These special lectures will be hybrid:  they will be both in-person and online.

    Registration is required.

    In-person registration

    Zoom webinar registration form: Zoom Webinar.

     

    Event Calendar

    Speaker: Nazim Bouatta, Harvard Medical School

    Abstract: AlphaFold2, a neural network-based model which predicts protein structures from amino acid sequences, is revolutionizing the field of structural biology. This lecture series, given by a leader of the OpenFold project which created an open-source version of AlphaFold2, will explain the protein structure problem and the detailed workings of these models, along with many new results and directions for future research.

    Thursday, Feb. 9, 2023

    Thursday, Feb. 9, 2023

    3:30–5:00 pm ET

    Lecture 1: A brief intro to protein biology. AlphaFold2 impacts on experimental structural biology. Co-evolutionary approaches. Space of ‘algorithms’ for protein structure prediction. Proteins as images (CNNs for protein structure prediction). End-to-end differentiable approaches. Attention and long-range dependencies. AlphaFold2 in a nutshell.

     

    Thursday, Feb. 16, 2023

    3:30–5:00 pm ET

    Lecture 2: AlphaFold2 architecture. Turning the co-evolutionary principle into an algorithm: EvoFormer. Structure module and symmetry principles (equivariance and invariance). OpenFold: retraining AlphaFol2 and insights into its learning mechanisms and capacity for generalization. Applications of variants of AlphaFold2 beyond protein structure prediction: AlphaFold Multimer for protein complexes, RNA structure prediction.

     

    Thursday, March 9, 2023

    3:30–5:00 pm ET

    Lecture 3: Limitations of AlphaFold2 and evolutionary ML pipelines. Current single sequence models. Protein language models (LM): single sequence + LM embeddings. Combining LM models with Frenet-Serret construction for protein structure prediction. Applying AlphaFold2 and OpenFold for language models.

     

     

    Biography: Nazim Bouatta received his doctoral training in high-energy theoretical physics, and transitioned to systems biology at Harvard Medical School, where he received training in cellular and molecular biology in the group of Prof. Judy Lieberman. He is currently a Senior Research Fellow in the Laboratory of Systems Pharmacology led by Prof. Peter Sorger at Harvard Medical School, and an affiliate of the Department of Systems Biology at Columbia, in the group of Prof. Mohammed AlQuraishi. He is interested in applying machine learning, physics, and mathematics to biology at multiple scales. He recently co-supervised the OpenFold project, an optimized, trainable, and completely open-source version of AlphaFold2. OpenFold has paved the way for many breakthroughs in biology, including the release of the ESM Metagenomic Atlas containing over 600 million predicted protein structures.

     

    Chair: Michael Douglas (Harvard CMSA)

    Moderators: Farzan Vafa & Sergiy Verstyuk (Harvard CMSA)

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  • Workshop
    15:30 -17:00
    2023-02-16
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    The CMSA will host a series of three 90-minute lectures on the subject of machine learning for protein folding.

    Thursday Feb. 9, Thursday Feb. 16, & Thursday March 9, 2023, 3:30-5:00 pm ET

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    Directions and Recommended Lodging

    These special lectures will be hybrid:  they will be both in-person and online.

    Registration is required.

    In-person registration

    Zoom webinar registration form: Zoom Webinar.

     

    Event Calendar

    Speaker: Nazim Bouatta, Harvard Medical School

    Abstract: AlphaFold2, a neural network-based model which predicts protein structures from amino acid sequences, is revolutionizing the field of structural biology. This lecture series, given by a leader of the OpenFold project which created an open-source version of AlphaFold2, will explain the protein structure problem and the detailed workings of these models, along with many new results and directions for future research.

    Thursday, Feb. 9, 2023

    Thursday, Feb. 9, 2023

    3:30–5:00 pm ET

    Lecture 1: A brief intro to protein biology. AlphaFold2 impacts on experimental structural biology. Co-evolutionary approaches. Space of ‘algorithms’ for protein structure prediction. Proteins as images (CNNs for protein structure prediction). End-to-end differentiable approaches. Attention and long-range dependencies. AlphaFold2 in a nutshell.

     

    Thursday, Feb. 16, 2023

    3:30–5:00 pm ET

    Lecture 2: AlphaFold2 architecture. Turning the co-evolutionary principle into an algorithm: EvoFormer. Structure module and symmetry principles (equivariance and invariance). OpenFold: retraining AlphaFol2 and insights into its learning mechanisms and capacity for generalization. Applications of variants of AlphaFold2 beyond protein structure prediction: AlphaFold Multimer for protein complexes, RNA structure prediction.

     

    Thursday, March 9, 2023

    3:30–5:00 pm ET

    Lecture 3: Limitations of AlphaFold2 and evolutionary ML pipelines. Current single sequence models. Protein language models (LM): single sequence + LM embeddings. Combining LM models with Frenet-Serret construction for protein structure prediction. Applying AlphaFold2 and OpenFold for language models.

     

     

    Biography: Nazim Bouatta received his doctoral training in high-energy theoretical physics, and transitioned to systems biology at Harvard Medical School, where he received training in cellular and molecular biology in the group of Prof. Judy Lieberman. He is currently a Senior Research Fellow in the Laboratory of Systems Pharmacology led by Prof. Peter Sorger at Harvard Medical School, and an affiliate of the Department of Systems Biology at Columbia, in the group of Prof. Mohammed AlQuraishi. He is interested in applying machine learning, physics, and mathematics to biology at multiple scales. He recently co-supervised the OpenFold project, an optimized, trainable, and completely open-source version of AlphaFold2. OpenFold has paved the way for many breakthroughs in biology, including the release of the ESM Metagenomic Atlas containing over 600 million predicted protein structures.

     

    Chair: Michael Douglas (Harvard CMSA)

    Moderators: Farzan Vafa & Sergiy Verstyuk (Harvard CMSA)

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  • Conference
    09:00 -17:00
    2023-02-27-2023-03-01
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    This conference will be held in person. Directions and Recommended Lodging

    Registration is required.

    Register here to attend in-person.

    Organizing Committee:
    Stephan Huckemann (Georg-August-Universität Göttingen)
    Ezra Miller (Duke University)
    Zhigang Yao (Harvard CMSA and Committee Chair)

    Scientific Advisors:
    Horng-Tzer Yau (Harvard CMSA)
    Shing-Tung Yau (Harvard CMSA)

    Speakers:

    • Tamara Broderick (MIT)
    • David Donoho (Stanford)
    • Ian Dryden (Florida International University in Miami)
    • David Dunson (Duke)
    • Charles Fefferman (Princeton)
    • Susan Holmes (Stanford)
    • Stefanie Jegelka (MIT)
    • Sebastian Kurtek (OSU)
    • Lizhen Lin (Notre Dame)
    • Steve Marron (U North Carolina)
    • Ezra Miller (Duke)
    • Hans-Georg Mueller (UC Davis)
    • Wolfgang Polonik (UC Davis)
    • Amit Singer (Princeton)
    • Zhigang Yao (Harvard CMSA)
    • Bin Yu (Berkeley)

    Moderator: Michael Simkin (Harvard CMSA)

     

    SCHEDULE

    Monday, Feb. 27, 2023 (Eastern Time)

    8:45-8:55 amZhigang YaoWelcome Remarks
    8:55-9:00 amShing-Tung YauRemarks
    Morning Session Chair: Zhigang Yao
    9:00-10:00 amDavid DonohoTitle

    Abstract

    10:00-10:10 amBreak
    10:10-11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

    Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

    11:10-11:20 amBreak
    11:20 am-12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. The first half of the talk discusses the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. When the manifold is unknown, one has to estimate it with certain theoretical guarantees. The second half of the talk concerns the problem of manifold fitting along with its recent progress.

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmBin YuTitle: Interpreting Deep Neural Networks towards Trustworthiness

    Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

    2:50-3:00 pmBreak
    3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

    Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

    These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

    4:00-4:10 pmBreak
    4:10-5:10 pmStefanie JegelkaTitle

    Abstract

     

    Tuesday, Feb. 28, 2023 (Eastern Time)

    Morning Session Chair: Zhigang Yao
    9:00-10:00 amCharles FeffermanTitle: Lipschitz Selection on Metric Spaces

    Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

    10:00-10:10 amBreak
    10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

    Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance.

    Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

    11:10-11:20 amBreak
    11:20 am-12:20 pmWolfgang PolonikTitle

    Abstract

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

    Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics.

    Joint work with Jonathan Mattingly and Do Tran.

    2:50-3:00 pmBreak
    3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

    Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking . We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session 

     

    6:30 pmBanquet (TBA)

     

    Wednesday, March 1, 2023 (Eastern Time)

    Morning Session Chair: Ezra Miller
    9:00-10:00 amAmit SingerTitle: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

    Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

    10:00-10:10 amBreak
    10:10-11:10 amIan DrydenTitle

    Abstract

    11:10-11:20 amBreak
    11:20 am-12:20 pmTamara BroderickTitle

    Abstract

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Ezra Miller
    1:50-2:50 pmSusan HolmesTitle

    Abstract

    2:50-3:00 pmBreak
    3:00-4:00 pmSebastian KurtekTitle

    Abstract

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session 

     

    5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

     


     

28
  • Conference
    09:00 -17:00
    2023-02-28-2023-03-01
    CMSA, 20 Garden Street, Cambridge, MA 02138 USA
    Event Calendar

    On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

    Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138

    This conference will be held in person. Directions and Recommended Lodging

    Registration is required.

    Register here to attend in-person.

    Organizing Committee:
    Stephan Huckemann (Georg-August-Universität Göttingen)
    Ezra Miller (Duke University)
    Zhigang Yao (Harvard CMSA and Committee Chair)

    Scientific Advisors:
    Horng-Tzer Yau (Harvard CMSA)
    Shing-Tung Yau (Harvard CMSA)

    Speakers:

    • Tamara Broderick (MIT)
    • David Donoho (Stanford)
    • Ian Dryden (Florida International University in Miami)
    • David Dunson (Duke)
    • Charles Fefferman (Princeton)
    • Susan Holmes (Stanford)
    • Stefanie Jegelka (MIT)
    • Sebastian Kurtek (OSU)
    • Lizhen Lin (Notre Dame)
    • Steve Marron (U North Carolina)
    • Ezra Miller (Duke)
    • Hans-Georg Mueller (UC Davis)
    • Wolfgang Polonik (UC Davis)
    • Amit Singer (Princeton)
    • Zhigang Yao (Harvard CMSA)
    • Bin Yu (Berkeley)

    Moderator: Michael Simkin (Harvard CMSA)

     

    SCHEDULE

    Monday, Feb. 27, 2023 (Eastern Time)

    8:45-8:55 amZhigang YaoWelcome Remarks
    8:55-9:00 amShing-Tung YauRemarks
    Morning Session Chair: Zhigang Yao
    9:00-10:00 amDavid DonohoTitle

    Abstract

    10:00-10:10 amBreak
    10:10-11:10 amSteve MarronTitle: Modes of Variation in Non-Euclidean Spaces

    Abstract: Modes of Variation provide an intuitive means of understanding variation in populations, especially in the case of data objects that naturally lie in non-Euclidean spaces. A variety of useful approaches to finding useful modes of variation are considered in several non-Euclidean contexts, including shapes as data objects, vectors of directional data, amplitude and phase variation and compositional data.

    11:10-11:20 amBreak
    11:20 am-12:20 pmZhigang YaoTitle: Manifold fitting: an invitation to statistics

    Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. The first half of the talk discusses the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. When the manifold is unknown, one has to estimate it with certain theoretical guarantees. The second half of the talk concerns the problem of manifold fitting along with its recent progress.

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmBin YuTitle: Interpreting Deep Neural Networks towards Trustworthiness

    Abstract: Recent deep learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This lecture first defines interpretable machine learning in general and introduces the agglomerative contextual decomposition (ACD) method to interpret neural networks. Extending ACD to the scientifically meaningful frequency domain, an adaptive wavelet distillation (AWD) interpretation method is developed. AWD is shown to be both outperforming deep neural networks and interpretable in two prediction problems from cosmology and cell biology. Finally, a quality-controlled data science life cycle is advocated for building any model for trustworthy interpretation and introduce a Predictability Computability Stability (PCS) framework for such a data science life cycle.

    2:50-3:00 pmBreak
    3:00-4:00 pmHans-Georg MuellerTitle: Exploration of Random Objects with Depth Profiles and Fréchet Regression

    Abstract: Random objects, i.e., random variables that take values in a separable metric space, pose many challenges for statistical analysis, as vector operations are not available in general metric spaces. Examples include random variables that take values in the space of distributions, covariance matrices or surfaces, graph Laplacians to represent networks, trees and in other spaces. The increasing prevalence of samples of random objects has stimulated the development of metric statistics, an emerging collection of statistical tools to characterize, infer and relate samples of random objects. Recent developments include depth profiles, which are useful for the exploration of random objects. The depth profile for any given object is the distribution of distances to all other objects (with P. Dubey, Y. Chen 2022).

    These distributions can then be subjected to statistical analysis. Their mutual transports lead to notions of transport ranks, quantiles and centrality. Another useful tool is global or local Fréchet regression (with A. Petersen 2019) where random objects are responses and scalars or vectors are predictors and one aims at modeling conditional Fréchet means. Recent theoretical advances for local Fréchet regression provide a basis for object time warping (with Y. Chen 2022). These approaches are illustrated with distributional and other data.

    4:00-4:10 pmBreak
    4:10-5:10 pmStefanie JegelkaTitle

    Abstract

     

    Tuesday, Feb. 28, 2023 (Eastern Time)

    Morning Session Chair: Zhigang Yao
    9:00-10:00 amCharles FeffermanTitle: Lipschitz Selection on Metric Spaces

    Abstract: The talk concerns the problem of finding a Lipschitz map F from a given metric space X into R^D, subject to the constraint that F(x) must lie in a given compact convex “target” K(x) for each point x in X. Joint work with Pavel Shvartsman and with Bernat Guillen Pegueroles.

    10:00-10:10 amBreak
    10:10-11:10 amDavid DunsonTitle: Inferring manifolds from noisy data using Gaussian processes

    Abstract: In analyzing complex datasets, it is often of interest to infer lower dimensional structure underlying the higher dimensional observations. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the original data with lower dimensional coordinates without providing an estimate of the manifold in the observation space or using the manifold to denoise the original data. This article proposes a new methodology for addressing these problems, allowing interpolation of the estimated manifold between fitted data points. The proposed approach is motivated by novel theoretical properties of local covariance matrices constructed from noisy samples on a manifold. Our results enable us to turn a global manifold reconstruction problem into a local regression problem, allowing application of Gaussian processes for probabilistic manifold reconstruction. In addition to theory justifying the algorithm, we provide simulated and real data examples to illustrate the performance.

    Joint work with Nan Wu – see https://arxiv.org/abs/2110.07478

    11:10-11:20 amBreak
    11:20 am-12:20 pmWolfgang PolonikTitle

    Abstract

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Stephan Huckemann
    1:50-2:50 pmEzra MillerTitle: Geometric central limit theorems on non-smooth spaces

    Abstract: The central limit theorem (CLT) is commonly thought of as occurring on the real line, or in multivariate form on a real vector space. Motivated by statistical applications involving nonlinear data, such as angles or phylogenetic trees, the past twenty years have seen CLTs proved for Fréchet means on manifolds and on certain examples of singular spaces built from flat pieces glued together in combinatorial ways. These CLTs reduce to the linear case by tangent space approximation or by gluing. What should a CLT look like on general non-smooth spaces, where tangent spaces are not linear and no combinatorial gluing or flat pieces are available? Answering this question involves figuring out appropriate classes of spaces and measures, correct analogues of Gaussian random variables, and how the geometry of the space (think “curvature”) is reflected in the limiting distribution. This talk provides an overview of these answers, starting with a review of the usual linear CLT and its generalization to smooth manifolds, viewed through a lens that casts the singular CLT as a natural outgrowth, and concluding with how this investigation opens gateways to further advances in geometric probability, topology, and statistics.

    Joint work with Jonathan Mattingly and Do Tran.

    2:50-3:00 pmBreak
    3:00-4:00 pmLizhen LinTitle: Statistical foundations of deep generative models

    Abstract: Deep generative models are probabilistic generative models where the generator is parameterized by a deep neural network. They are popular models for modeling high-dimensional data such as texts, images and speeches, and have achieved impressive empirical success. Despite demonstrated success in empirical performance, theoretical understanding of such models is largely lacking . We investigate statistical properties of deep generative models from a nonparametric distribution estimation viewpoint. In the considered model, data are assumed to be observed in some high-dimensional ambient space but concentrate around some low-dimensional structure such as a lower-dimensional manifold structure. Estimating the distribution supported on this low-dimensional structure is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. We obtain convergence rates with respect to the Wasserstein metric of distribution estimators based on two methods: a sieve MLE based on the perturbed data and a GAN type estimator. Such an analysis provides insights into i) how deep generative models can avoid the curse of dimensionality and outperform classical nonparametric estimates, and ii) how likelihood approaches work for singular distribution estimation, especially in adapting to the intrinsic geometry of the data.

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session 

     

    6:30 pmBanquet (TBA)

     

    Wednesday, March 1, 2023 (Eastern Time)

    Morning Session Chair: Ezra Miller
    9:00-10:00 amAmit SingerTitle: Heterogeneity analysis in cryo-EM by covariance estimation and manifold learning

    Abstract: In cryo-EM, the 3-D molecular structure needs to be determined from many noisy 2-D tomographic projection images of randomly oriented and positioned molecules. A key assumption in classical reconstruction procedures for cryo-EM is that the sample consists of identical molecules. However, many molecules of interest exist in more than one conformational state. These structural variations are of great interest to biologists, as they provide insight into the functioning of the molecule. Determining the structural variability from a set of cryo-EM images is known as the heterogeneity problem, widely recognized as one of the most challenging and important computational problem in the field. Due to high level of noise in cryo-EM images, heterogeneity studies typically involve hundreds of thousands of images, sometimes even a few millions. Covariance estimation is one of the earliest methods proposed for heterogeneity analysis in cryo-EM. It relies on computing the covariance of the conformations directly from projection images and extracting the optimal linear subspace of conformations through an eigendecomposition. Unfortunately, the standard formulation is plagued by the exorbitant cost of computing the N^3 x N^3 covariance matrix. In the first part of the talk, we present a new low-rank estimation method that requires computing only a small subset of the columns of the covariance while still providing an approximation for the entire matrix. This scheme allows us to estimate tens of principal components of real datasets in a few minutes at medium resolutions and under 30 minutes at high resolutions. In the second part of the talk, we discuss a manifold learning approach based on the graph Laplacian and the diffusion maps framework for learning the manifold of conformations. If time permits, we will also discuss the potential application of optimal transportation to heterogeneity analysis. Based on joint works with Joakim Andén, Marc Gilles, Amit Halevi, Eugene Katsevich, Joe Kileel, Amit Moscovich, and Nathan Zelesko.

    10:00-10:10 amBreak
    10:10-11:10 amIan DrydenTitle

    Abstract

    11:10-11:20 amBreak
    11:20 am-12:20 pmTamara BroderickTitle

    Abstract

     

    12:20-1:50 pm

     

    Lunch
    Afternoon Session Chair: Ezra Miller
    1:50-2:50 pmSusan HolmesTitle

    Abstract

    2:50-3:00 pmBreak
    3:00-4:00 pmSebastian KurtekTitle

    Abstract

    4:00-4:10 pmBreak
    4:10-5:10 pmConversation session 

     

    5:10-5:20 pmStephan Huckemann, Ezra Miller, Zhigang YaoClosing Remarks

     


     

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