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Cooling quantum systems with quantum information processing
Nayeli Azucena Rodríguez Briones Technische Universität Wien
Panel Discussion
Elias Bareinboim (Columbia University), Frederick Eberhardt (Caltech), Kun Zhang (Carnegie Mellon University), and Uri Shalit (Technion - Israel Institute of Technology)Online Reinforcement Learning With The Help Of Confounded Offline Data
Uri Shalit (Technion - Israel Institute of Technology)Learning & Reasoning With Soft Interventions
Elias Bareinboim (Columbia University)Learning Causal Representations From Unknown Interventions
Kun Zhang (Carnegie Mellon University)Causal Emergence: When Distortions In A Map Obscure The Territory
Frederick Eberhardt (Caltech)Measurement-induced criticality and charge-sharpening transitions
Romain Vasseur University of Massachusetts Amherst
Nonparametric Density Estimation and Convergence of GANs under Besov IPMs
Ananya Uppal (University of Texas Austin)Teamwork Makes The Von Neumann Work: Two Team Zero Sum Games
Emmanouil Vlatakis (Columbia University)Causal Inference For Socio-Economic & Engineering Systems
Anish Agarwal (MIT EECS)Learning In The Presence Of Strategic Agents: Dynamics, Equilibria, And Convergence
Eric Mazumdar (Caltech)
Counterfactual Inference For Sequential Experiment Design
Raaz Dwivedi (MIT)We consider the problem of counterfactual inference in sequentially designed experiments wherein a collection of units undergo a sequence of interventions based on policies adaptive over time, and outcomes are observed based on the assigned interventions. Our goal is counterfactual inference, i.e., estimate what would have happened if alternate policies were used, a problem that is inherently challenging due to the heterogeneity in the outcomes across users and time. In this work, we identify structural assumptions that allow us to impute the missing potential outcomes in sequential experiments, where the policy is allowed to adapt simultaneously to all users' past data. We prove that under suitable assumptions on the latent factors and temporal dynamics, a variant of the nearest neighbor strategy allows us to impute the missing information using the observed outcome across time and users. Under mild assumptions on the adaptive policy and the underlying latent factor model, we prove that using data till time t for N users in the study, our estimate for the missing potential outcome at time t+1 admits a mean squared-error that scales as t^{-1/2+\delta} + N^{-1+\delta} for any \delta>0, for any fixed user. We also provide an asymptotic confidence interval for each outcome under suitable growth conditions on N and t, which can then be used to build confidence intervals for individual treatment effects. Our work extends the recent literature on inference with adaptively collected data by allowing for policies that pool across users, the matrix completion literature for missing at random settings by allowing for adaptive sampling mechanisms, and missing data problems in multivariate time series by allowing for a generic non-parametric model.Cooling quantum systems with quantum information processing
Nayeli Azucena Rodríguez Briones Technische Universität Wien
The field of quantum information provides fundamental insight into central open questions in quantum thermodynamics and quantum many-body physics, such as the characterization of the influence of quantum effects on the flow of energy and information. These insights have inspired new methods for cooling physical systems at the quantum scale using tools from quantum information processing. These protocols not only provide an essentially different way to cool, but also go beyond conventional cooling techniques, bringing important applications for quantum technologies. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using quantum correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. Finally, I will present a recently fully characterized quantum property of quantum many-body systems, in which entanglement in low-energy eigenstates can obstruct local outgoing energy flows.
Panel Discussion
Elias Bareinboim (Columbia University), Frederick Eberhardt (Caltech), Kun Zhang (Carnegie Mellon University), and Uri Shalit (Technion - Israel Institute of Technology)Online Reinforcement Learning With The Help Of Confounded Offline Data
Uri Shalit (Technion - Israel Institute of Technology)I will present recent work exploring how and when can confounded offline data be used to improve online reinforcement learning. We will explore conditions of partial observability and distribution shifts between the offline and online environments, and present results for contextual bandits, imitation learning and reinforcement learning.Learning & Reasoning With Soft Interventions
Elias Bareinboim (Columbia University)In this talk, I will discuss recent work on reasoning and learning with soft interventions, including the problem of identification, extrapolation/transportability, and structural learning. I will also briefly discuss a new calculus, which generalizes the do-calculus, as well as algorithmic and graphical conditions. Supporting material: General Transportability of Soft Interventions: Completeness Results . J. Correa, E. Bareinboim. In Proceedings of the 34th Annual Conference on Neural Information Processing Systems (NeurIPS), 2020. https://causalai.net/r68.pdf Causal Discovery from Soft Interventions with Unknown Targets: Characterization & Learning. A. Jaber, M. Kocaoglu, K. Shanmugam, E. Bareinboim. In Proceedings of the 34th Annual Conference on Neural Information Processing Systems (NeurIPS), 2020. https://causalai.net/r67.pdf A Calculus For Stochastic Interventions: Causal Effect Identification and Surrogate Experiments J. Correa, E. Bareinboim. In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), 2019. https://causalai.net/r55.pdfLearning Causal Representations From Unknown Interventions
Kun Zhang (Carnegie Mellon University)Learning causal representations from observational data can be viewed as a task of identifying where and how the interventions were applied--this reveals information of the causal representations at the same time. Given that this learning task is a typical inverse problem, an essential issue is the establishment of identifiability results: one has to guarantee that the learned representations are consistent with the underlying causal process. Dealing with this issue generally involves appropriate assumptions. In this talk, I focus on learning latent causal variables and their causal relations, together with their relations with the measured variables, from observational data. I show what assumptions, together with instantiations of the "minimal change" principle, render the underlying causal representations identifiable across several settings. Specifically, in the i.i.d. case, the identifiability benefits from appropriate parametric assumptions on the causal relations and a certain type of "minimality" assumption. Temporal dependence makes it possible to recover latent temporally causal processes from time series data without parametric assumptions, and nonstationarity further improves the identifiability. I then draw the connection between recent advances in nonlinear independent component analysis and the minimal change principle. Finally, concerning the nonparametric setting with changing instantaneous causal relations, I show how to learn the latent variables with changing causal relations in light of the minimal change principle.Causal Emergence: When Distortions In A Map Obscure The Territory
Frederick Eberhardt (Caltech)We provide a critical assessment of the account of causal emergence presented in Hoel (2017). The account integrates causal and information theoretic concepts to explain under what circumstances there can be causal descriptions of a system at multiple scales of analysis. We show that the causal macro variables implied by this account result in interventions with significant ambiguity, and that the operations of marginalization and abstraction do not commute. Both of these are desiderata that, we argue, any account of multi-scale causal analysis should be sensitive to. The problems we highlight in Hoel's definition of causal emergence derive from the use of various averaging steps and the introduction of a maximum entropy distribution that is extraneous to the system under investigation. (This is joint work with Lin Lin Lee.)Measurement-induced criticality and charge-sharpening transitions
Romain Vasseur University of Massachusetts Amherst
Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics and effective field theory approaches to such charge-sharpening transitions.
Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO
Nonparametric Density Estimation and Convergence of GANs under Besov IPMs
Ananya Uppal (University of Texas Austin)Since their introduction in Goodfellow et al. (2014) as sampling algorithms, Generative Adversarial Networks (GANs) have evolved to produce remarkable results in several tasks e.g. image generation, text-to-image translation, etc. Statistically, a GAN may be viewed as a density estimate constructed by optimizing over an Integral Probability Metric (IPM) encoded by its discriminator. I will present our work on estimating a nonparametric density under IPMs defined by Besov spaces. Such IPMs are a rich class of losses and include, e.g., Lp distances, the total variation distance, and generalizations of both the Wasserstein and the Kolmogorov-Smirnov distances. Our results generalize, unify, or improve several results, both recent and classical. Consequently, we imply bounds on the statistical error of a GAN, showing that GANs are minimax optimal and in some cases, strictly outperform the best linear estimator (e.g. the empirical estimator, kernel density estimator). Further, we study the above framework of nonparametric density estimation under the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide a minimax optimal estimator that adapts to both an unknown contamination proportion and the unknown smoothness of the true density. We use this to imply that certain GAN architectures are robustly minimax optimal.Teamwork Makes The Von Neumann Work: Two Team Zero Sum Games
Emmanouil Vlatakis (Columbia University)Motivated by recent advances in both theoretical and applied aspects of multiplayer games, spanning from e-sports to multi-agent generative adversarial networks, we focus on min-max optimization in team zero-sum games. In this class of games, players are split into two teams with payoffs equal within the same team and of opposite sign across the opponent team. Unlike the textbook two-player zero-sum games, finding a Nash equilibrium in our class can be shown to be CLS-hard, i.e., it is unlikely to have a polynomial-time algorithm for computing Nash equilibria. Moreover, in this generalized framework, we establish that even asymptotic last iterate or time average convergence to a Nash Equilibrium is not possible using Gradient Descent Ascent (GDA), its optimistic variant, and extra gradient. Specifically, we present a family of team games whose induced utility is \emph{non} multi-linear with \emph{non} attractive \emph{per-se} mixed Nash Equilibria, as strict saddle points of the underlying optimization landscape. Leveraging techniques from control theory, we complement these negative results by designing a modified GDA that converges locally to Nash equilibria. Finally, we discuss connections of our framework with AI architectures with team competition structures like multi-agent generative adversarial networks.Causal Inference For Socio-Economic & Engineering Systems
Anish Agarwal (MIT EECS)What will happen to Y if we do A? A variety of meaningful socio-economic and engineering questions can be formulated this way. To name a few: What will happen to a patient's health if they are given a new therapy? What will happen to a country's economy if policy-makers legislate a new tax? What will happen to a data center's latency if a new congestion control protocol is used? In this talk, we will explore how to answer such counterfactual questions using observational data---which is increasingly available due to digitization and pervasive sensors---and/or very limited experimental data. The two key challenges in doing so are: (i) counterfactual prediction in the presence of latent confounders; (ii) estimation with modern datasets which are high-dimensional, noisy, and sparse. Towards this goal, the key framework we introduce is connecting causal inference with tensor completion, a very active area of research across a variety of fields. In particular, we show how to represent the various potential outcomes (i.e., counterfactuals) of interest through an order-3 tensor. The key theoretical results presented are: (i) Formal identification results establishing under what missingness patterns, latent confounding, and structure on the tensor is recovery of unobserved potential outcomes possible. (ii) Introducing novel estimators to recover these unobserved potential outcomes and proving they are finite-sample consistent and asymptotically normal. The efficacy of the proposed estimators is shown on high-impact real-world applications. These include working with: (i) TaurRx Therapeutics to propose novel clinical trial designs to reduce the number of patients recruited for a trial and to correct for bias from patient dropouts; (ii) Uber Technologies on evaluating the impact of certain driver engagement policies without having to run an A/B test.Learning In The Presence Of Strategic Agents: Dynamics, Equilibria, And Convergence
Eric Mazumdar (Caltech)The ability to learn from data and make decisions in real-time has led to the rapid deployment of machine learning algorithms across many aspects of everyday life. While this has enabled new services and technologies, the fact that algorithms are increasingly interacting with people and other algorithms marks a distinct shift away from the traditional machine learning paradigm. Indeed, little is known about how these algorithms--- that were designed to operate in isolation--- behave when confronted with strategic behaviors on the part of people, and the extent to which strategic agents can game the algorithms to achieve better outcomes. In this talk, I will give an overview of my work on learning games and in the presence of strategic agents and multi-agent reinforcement learning.