Ultralocality and the robustness of slow contraction to cosmic initial conditions
Anna Ijjas Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
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Panel Discussion
Arnab Bhattacharyya (National University of Singapore, Singapore), Christopher Harshaw (Yale University), and Liam Solus (KTH)Balancing Covariates In Randomized Experiments: The Gram--Schmidt Walk Design
Christopher Harshaw (Yale University)Learning And Testing Causal Models: A Property Testing Viewpoint
Arnab Bhattacharyya (National University of Singapore, Singapore)Panel Discussion
Chiara Sabatti (Stanford University), Jennifer Listgarten (UC Berkeley), and Peng Ding (UC Berkeley)Comments on Euclidean wormholes and holography
Panagiotis Betzios University of British Columbia
Searching For Causal Genetic Mechanisms Across Human Populations
Chiara Sabatti (Stanford University)
Ultralocality and the robustness of slow contraction to cosmic initial conditions
Anna Ijjas Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
I will discuss the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, I will show that the geometry first rapidly converges to an inhomogeneous, spatially-curved, and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat, and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.
Zoom Link: https://pitp.zoom.us/j/95441238892?pwd=TUh4Mjh1MHJ6TDNCL0V1NUk5WWFZQT09
Panel Discussion
Arnab Bhattacharyya (National University of Singapore, Singapore), Christopher Harshaw (Yale University), and Liam Solus (KTH)No abstract available.Balancing Covariates In Randomized Experiments: The Gram--Schmidt Walk Design
Christopher Harshaw (Yale University)The design of experiments involves an inescapable compromise between covariate balance and robustness. In this talk, we describe a formalization of this trade-off and introduce a new style of experimental design that allows experimenters to navigate it. The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect. Subject to the experimenter’s desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates. The achieved level of balance is better than previously known possible, considerably better than what a fully random assignment would produce, and close to optimal given the desired level of robustness. We show that the mean squared error of the estimator is bounded by the minimum of the loss function of an implicit ridge regression of the potential outcomes on the covariates. The estimator does not itself conduct covariate adjustment, so one can interpret the approach as regression adjustment by design. Finally, we provide non-asymptotic tail bounds for the estimator, which facilitate the construction of conservative confidence intervals.Some Staged Tree Models For Learning From Interventions
Liam Solus (KTH)A well-known limitation of modeling causal systems via DAGs is their inability to encode context-specific information. Among the several proposed representations for context-specific causal information are the staged tree models, which are colored probability trees capable of expressing highly diverse context-specific information. The expressive power of staged trees comes at the cost of easy interpretability and the admittance of desirable properties useful in the development of causal discovery algorithms. In this talk, we consider a subfamily of staged trees, which we call CStrees, that admit an alternative representation via a sequence of DAGs. This alternate representation allows us to prove a Verma-Pearl-type characterization of model equivalence for CStrees which extends to the interventional setting, providing a graphical characterization of interventional CStree model equivalence. We will discuss these results and their potential applications to causal discovery algorithms for context-specific models based on interventional and observational data.Learning And Testing Causal Models: A Property Testing Viewpoint
Arnab Bhattacharyya (National University of Singapore, Singapore)We consider testing and learning problems on causal Bayesian networks where the variables take values from a bounded domain. We address two problems: (i) Given access to observations and experiments on two unknown environments X and Y, test whether X=Y or X is far from Y. Here, two environments are equal if no intervention can distinguish between them. (ii) Given access to observations and experiments on an unknown environment X, learn a DAG that admits a causal model M such that X is close to M. For problem (i), we show that under natural sparsity assumptions on the underlying DAG, only O(log n) interventions and O~(n) samples/intervention is sufficient. This is joint work with Jayadev Acharya, Constantinos Daskalakis and Saravanan Kandasamy. For problem (ii), we consider the setting where there are two variables, and the goal is to learn whether X causes Y, Y causes X, or there is a hidden variable confounding the two. Under natural assumptions, we obtain a nearly tight characterization of the sample complexity that is sublinear in k. Moreover, there is a tradeoff between the number of observational samples and interventional samples. This is joint work with Jayadev Acharya, Sourbh Bhadane, Saravanan Kandasamy, and Ziteng Sun.Panel Discussion
Chiara Sabatti (Stanford University), Jennifer Listgarten (UC Berkeley), and Peng Ding (UC Berkeley)Comments on Euclidean wormholes and holography
Panagiotis Betzios University of British Columbia
Euclidean wormholes are exotic types of gravitational solutions that we still don't understand completely. In the first part of the talk, I will analyze asymptotically AdS wormhole solutions from a gravitational point of view. By studying correlation functions of local and non-local operators, the universal properties that any putative holographic dual should exhibit, become manifest. In the second part, I will describe some concrete field theoretic models (both effective and microscopic) that share these properties.
Machine Learning-Based Design Of Proteins
Jennifer Listgarten (UC Berkeley)Data-driven design is making headway into a number of application areas, including protein, small-molecule, and materials engineering. The design goal is to construct an object with desired properties, such as a protein that binds to a target more tightly than previously observed. To that end, costly experimental measurements are being replaced with calls to a high-capacity regression model trained on labeled data, which can be leveraged in an in silico search for promising design candidates. The aim then is to discover designs that are better than the best design in the observed data. This goal puts machine-learning based design in a much more difficult spot than traditional applications of predictive modelling, since successful design requires, by definition, some degree of extrapolation---a pushing of the predictive models to its unknown limits, in parts of the design space that are a priori unknown. In this talk, I will discuss our methodological approaches to this problem, as well as report on some recent success in designing gene therapy delivery (AAV) libraries, useful for general downstream directed evolution selections.Ionization of Gravitational Atoms
John Stout Harvard University
Superradiant instabilities may create clouds of ultralight bosons around black holes, forming so-called “gravitational atoms.” It was recently shown that the presence of a binary companion can induce resonant transitions between a cloud's bound states. When these transitions backreact on the binary's orbit, they lead to qualitatively distinct signatures in the gravitational waveform that can dominate the overall behavior of the inspiral. In this talk, I will show that the interaction with the companion can also trigger transitions from bound to unbound states of the cloud---a process which I will refer to as ``ionization,'' in analogy with the photoelectric effect in atomic physics. Here, too, there is a type of resonance with a similarly distinct signature, which may ultimately be used to detect any dark ultralight bosons that exist in our universe.
Zoom Link: https://pitp.zoom.us/j/97300299361?pwd=azhmVTR5VmpPQ1hwbkVHTUsrOGlJZz09
Searching For Causal Genetic Mechanisms Across Human Populations
Chiara Sabatti (Stanford University)Identifying which genetic variants influence medically relevant phenotypes is an important task both for therapeutic development and for risk prediction. In the last decade, genome wide association studies have been the most widely-used instrument to tackle this question. One challenge that they encounter is in the interplay between genetic variability and the structure of human populations. In this talk, we will focus on some opportunities that arise when one collects data from diverse populations and present statistical methods that allow us to leverage them. The presentation will be based on joint work with M. Sesia, S. Li, Z. Ren, Y. Romano and E. Candes.To Adjust Or Not To Adjust? Estimating The Average Treatment Effect In Randomized Experiments With Missing Covariates
Peng Ding (UC Berkeley)Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The unadjusted difference in means is always unbiased. The complete-covariate analysis adjusts for all completely observed covariates and improves the efficiency of the difference in means if at least one completely observed covariate is predictive of the outcome. Then what is the additional gain of adjusting for covariates subject to missingness? A key insight is that the missingness indicators act as fully observed pretreatment covariates as long as missingness is not affected by the treatment, and can thus be used in covariate adjustment to bring additional estimation efficiency. This motivates adding the missingness indicators to the regression adjustment, yielding the missingness-indicator method as a well-known but not so popular strategy in the literature of missing data. We recommend it due to its many advantages. We also propose modifications to the missingness-indicator method based on asymptotic and finite-sample considerations. To reconcile the conflicting recommendations in the missing data literature, we analyze and compare various strategies for analyzing randomized experiments with missing covariates under the design-based framework. This framework treats randomization as the basis for inference and does not impose any modeling assumptions on the outcome-generating process and missing-data mechanism.