Playlist: 23 videos
Quantum Physics and Statistical Causal Models
0:47:35
James Robins (Harvard University)
https://simons.berkeley.edu/talks/tbd-383
Quantum Physics and Statistical Causal Models
We give a simple proof of Bell's inequality in quantum mechanics using theory from causal interaction, which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between treatments.
Joint work with Tyler VanderWeele, Richard Gill and Thomas Richardson.
Visit talk page
https://simons.berkeley.edu/talks/tbd-383
Quantum Physics and Statistical Causal Models
We give a simple proof of Bell's inequality in quantum mechanics using theory from causal interaction, which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between treatments.
Joint work with Tyler VanderWeele, Richard Gill and Thomas Richardson.
0:45:45
Pascal Vontobel (The Chinese University of Hong Kong)
https://simons.berkeley.edu/talks/polytopes-and-convex-sets-associated-graphical-models-classical-and-quantum-information
Quantum Physics and Statistical Causal Models
Graphical models haven proven very beneficial for modeling classical and quantum information setups. This presentation consists of two parts. In the first part, we talk about graphical models for classical information processing. In particular, we show how certain polytopes associated with graphical models can be used to understand efficient, suboptimal algorithms like loopy belief propagation. (Such algorithms are, for example, used to decode low-density parity-check codes, a class of codes that appears in the recent 5G telecommunications standard.) In the second part, we talk about a class of graphical models suitable for quantum information processing. Certain polytopes and convex sets associated with these graphical models help to understand the difference between classical and quantum information processing, thereby generalizing Bell's theorem. Finally, we point out some surprising connections between the polytopes in the first part and the polytopes in the second part.
Visit talk page
https://simons.berkeley.edu/talks/polytopes-and-convex-sets-associated-graphical-models-classical-and-quantum-information
Quantum Physics and Statistical Causal Models
Graphical models haven proven very beneficial for modeling classical and quantum information setups. This presentation consists of two parts. In the first part, we talk about graphical models for classical information processing. In particular, we show how certain polytopes associated with graphical models can be used to understand efficient, suboptimal algorithms like loopy belief propagation. (Such algorithms are, for example, used to decode low-density parity-check codes, a class of codes that appears in the recent 5G telecommunications standard.) In the second part, we talk about a class of graphical models suitable for quantum information processing. Certain polytopes and convex sets associated with these graphical models help to understand the difference between classical and quantum information processing, thereby generalizing Bell's theorem. Finally, we point out some surprising connections between the polytopes in the first part and the polytopes in the second part.
0:43:51
Robin Evans (University of Oxford)
https://simons.berkeley.edu/talks/marginal-dag-models-equivalent-another-dag
Quantum Physics and Statistical Causal Models
A marginal DAG model is the model induced by the observed variables in a DAG with latent nodes, where we make no assumption about the state-space of the unobserved variables. A question that arises in this context is when such a model is reducible to another DAG model. We show that this occurs if and only if the model does not induce any non-trivial inequality constraints. This has a few interesting consequences: for instance, both maximal ancestral graph models and nested Markov models (that are not Markov equivalent to a DAG model) are shown to be strictly larger than the corresponding marginal model. The proof relies on a series of reductions to smaller classes, including so-called arid and ancestral graphs, which we will define and present as part of the talk. [NOTE: I'm hoping that it would be of interest to expose the Quantum people to ancestral graphs and arid graphs, which are part of the proof.]
Visit talk page
https://simons.berkeley.edu/talks/marginal-dag-models-equivalent-another-dag
Quantum Physics and Statistical Causal Models
A marginal DAG model is the model induced by the observed variables in a DAG with latent nodes, where we make no assumption about the state-space of the unobserved variables. A question that arises in this context is when such a model is reducible to another DAG model. We show that this occurs if and only if the model does not induce any non-trivial inequality constraints. This has a few interesting consequences: for instance, both maximal ancestral graph models and nested Markov models (that are not Markov equivalent to a DAG model) are shown to be strictly larger than the corresponding marginal model. The proof relies on a series of reductions to smaller classes, including so-called arid and ancestral graphs, which we will define and present as part of the talk. [NOTE: I'm hoping that it would be of interest to expose the Quantum people to ancestral graphs and arid graphs, which are part of the proof.]
0:43:36
Joris Mooij (University of Amsterdam)
https://simons.berkeley.edu/talks/causal-reductions
Quantum Physics and Statistical Causal Models
We propose a parsimonious parameterization for causal models using a ``causal reduction'' technique. This technique: - shows that the observational distribution p(x,y) and the interventional distributions (p(y|do(x)) in Pearl's notation, {p(y(x))} in potential outcome notation) are not variationally independent objects; - allows to derive bounds on the (conditional) causal effect in terms of the observational distribution; - inspires estimators of the (conditional) causal effect that use a combination of observational and interventional data that do not suffer from bias due to unobserved confounding in the observed regime. We consider two cases in more detail. In the discrete case, we analyze maximum likelihood estimation and discuss simple settings in which the observational data is helpful for estimating the causal effect. In the continuous case we show empirically that non-parametric estimators based on normalizing flows may obtain more accurate estimates of causal effects from a combination of observational and interventional data than what could be obtained from the interventional data alone Joint work with Maximilian Ilse, Patrick Forré and Max Welling https://arxiv.org/abs/2103.04786v2
Visit talk page
https://simons.berkeley.edu/talks/causal-reductions
Quantum Physics and Statistical Causal Models
We propose a parsimonious parameterization for causal models using a ``causal reduction'' technique. This technique: - shows that the observational distribution p(x,y) and the interventional distributions (p(y|do(x)) in Pearl's notation, {p(y(x))} in potential outcome notation) are not variationally independent objects; - allows to derive bounds on the (conditional) causal effect in terms of the observational distribution; - inspires estimators of the (conditional) causal effect that use a combination of observational and interventional data that do not suffer from bias due to unobserved confounding in the observed regime. We consider two cases in more detail. In the discrete case, we analyze maximum likelihood estimation and discuss simple settings in which the observational data is helpful for estimating the causal effect. In the continuous case we show empirically that non-parametric estimators based on normalizing flows may obtain more accurate estimates of causal effects from a combination of observational and interventional data than what could be obtained from the interventional data alone Joint work with Maximilian Ilse, Patrick Forré and Max Welling https://arxiv.org/abs/2103.04786v2
0:52:6
Désiré Kédagni (Iowa State University)
https://simons.berkeley.edu/talks/marginal-treatment-effects-misclassified-treatment
Quantum Physics and Statistical Causal Models
This paper studies identification of the marginal treatment effect (MTE) when a binary treatment variable is misclassified. We show under standard assumptions that the MTE is identified as the derivative of the conditional expectation of the observed outcome given the true propensity score, which is partially identified. We characterize the identified set for this propensity score, and then for the MTE. We show under some mild regularity conditions that the sign of the MTE is locally identified. We use our MTE bounds to derive bounds on other commonly used parameters in the literature. We show that our bounds are tighter than the existing bounds for the local average treatment effect. We illustrate the practical relevance of our derived bounds through some numerical and empirical results.
Visit talk page
https://simons.berkeley.edu/talks/marginal-treatment-effects-misclassified-treatment
Quantum Physics and Statistical Causal Models
This paper studies identification of the marginal treatment effect (MTE) when a binary treatment variable is misclassified. We show under standard assumptions that the MTE is identified as the derivative of the conditional expectation of the observed outcome given the true propensity score, which is partially identified. We characterize the identified set for this propensity score, and then for the MTE. We show under some mild regularity conditions that the sign of the MTE is locally identified. We use our MTE bounds to derive bounds on other commonly used parameters in the literature. We show that our bounds are tighter than the existing bounds for the local average treatment effect. We illustrate the practical relevance of our derived bounds through some numerical and empirical results.
0:42:30
Jonas Peters (University of Copenhagen)
https://simons.berkeley.edu/talks/instrumental-variables-sparse-and-dynamical-settings
Quantum Physics and Statistical Causal Models
Exogenous heterogeneity, for example in the form of instrumental variables, can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this talk, we discuss this idea in a setting in which the causal effect from covariates on the response is sparse and in a setting, where the variables follow a time dependence structure. If time allows, we also briefly discuss what can be done when identifiability conditions are not satisfied.
Visit talk page
https://simons.berkeley.edu/talks/instrumental-variables-sparse-and-dynamical-settings
Quantum Physics and Statistical Causal Models
Exogenous heterogeneity, for example in the form of instrumental variables, can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this talk, we discuss this idea in a setting in which the causal effect from covariates on the response is sparse and in a setting, where the variables follow a time dependence structure. If time allows, we also briefly discuss what can be done when identifiability conditions are not satisfied.
0:48:55
Manfred Warmuth (Google Brain)
https://simons.berkeley.edu/talks/bayesian-probability-calculus-density-matrices
Quantum Physics and Statistical Causal Models
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal.
We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar ``conventional'' probability calculus and always retains the latter as a special case when all matrices are diagonal.
Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance.
Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator.
It is natural to build an "information theory" for density matrices based on the calculus. We conclude with a number of other Bayes rules developed recently and the question of realizability in Physics/Biology.
This is joint work with Dima Kuzmin.
Visit talk page
https://simons.berkeley.edu/talks/bayesian-probability-calculus-density-matrices
Quantum Physics and Statistical Causal Models
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal.
We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar ``conventional'' probability calculus and always retains the latter as a special case when all matrices are diagonal.
Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance.
Surprisingly the bounds also generalize: as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator.
It is natural to build an "information theory" for density matrices based on the calculus. We conclude with a number of other Bayes rules developed recently and the question of realizability in Physics/Biology.
This is joint work with Dima Kuzmin.
0:50:45
Sonja Smets (University of Amsterdam)
https://simons.berkeley.edu/talks/dynamic-epistemic-approach-conditionals
Quantum Physics and Statistical Causal Models
In this talk, I look at a general logical framework to compare and analyse various "epistemic conditionals", as formal tools to represent different types of learning: standard epistemic-doxastic conditionals (for updating beliefs after Bayesian conditioning), dynamic-quantum conditionals (for updating information after quantum measurements), causal-intervention conditionals, and counterfactual conditionals. My aim is to provide a comparative analysis of these various forms of conditioning, centred around the idea of "action-based reasoning". I will focus in particular on the role of logical dynamics in this analysis, using formal techniques coming from propositional dynamic logic and quantum dynamic logic. We show how these techniques can be used to analyze the ontic and epistemic-informational aspects of quantum measurements and to compare them with other forms of learning.
Visit talk page
https://simons.berkeley.edu/talks/dynamic-epistemic-approach-conditionals
Quantum Physics and Statistical Causal Models
In this talk, I look at a general logical framework to compare and analyse various "epistemic conditionals", as formal tools to represent different types of learning: standard epistemic-doxastic conditionals (for updating beliefs after Bayesian conditioning), dynamic-quantum conditionals (for updating information after quantum measurements), causal-intervention conditionals, and counterfactual conditionals. My aim is to provide a comparative analysis of these various forms of conditioning, centred around the idea of "action-based reasoning". I will focus in particular on the role of logical dynamics in this analysis, using formal techniques coming from propositional dynamic logic and quantum dynamic logic. We show how these techniques can be used to analyze the ontic and epistemic-informational aspects of quantum measurements and to compare them with other forms of learning.
0:56:30
Jonathan Barrett (Oxford)
https://simons.berkeley.edu/talks/causal-influence-quantum-theory
Quantum Physics and Statistical Causal Models
Any account of causality in the physical world should answer questions such as the following. If A is a cause of B, then what sort of thing are A and B? What does it mean to say that A is a direct cause of B? Do causal concepts involve, in an essential way, interventions by agents? Are causal relations directed in time? What, in the overall picture, is ontic (i.e., factual and independent of the agent), and what is epistemic (i.e., relative to an agent’s knowledge or beliefs)? I will give an account of causality in quantum theory that answers these questions, leading to a formalism for quantum causal modelling. The classical formalism for causal modelling can be recovered from this account, as a special case when quantum channels are all diagonal. Towards the end I will make some more speculative remarks about a possible new direction in the interpretation of quantum theory that is suggested by the work. The talk is based on (bits of):
arXiv:1609.09487
arXiv:1906.10726
arXiv:2001.07774
arXiv:2002.12157
arXiv:2011.08120
Visit talk page
https://simons.berkeley.edu/talks/causal-influence-quantum-theory
Quantum Physics and Statistical Causal Models
Any account of causality in the physical world should answer questions such as the following. If A is a cause of B, then what sort of thing are A and B? What does it mean to say that A is a direct cause of B? Do causal concepts involve, in an essential way, interventions by agents? Are causal relations directed in time? What, in the overall picture, is ontic (i.e., factual and independent of the agent), and what is epistemic (i.e., relative to an agent’s knowledge or beliefs)? I will give an account of causality in quantum theory that answers these questions, leading to a formalism for quantum causal modelling. The classical formalism for causal modelling can be recovered from this account, as a special case when quantum channels are all diagonal. Towards the end I will make some more speculative remarks about a possible new direction in the interpretation of quantum theory that is suggested by the work. The talk is based on (bits of):
arXiv:1609.09487
arXiv:1906.10726
arXiv:2001.07774
arXiv:2002.12157
arXiv:2011.08120
0:54:50
Tim Maudlin (NYU & John Bell Institute)
https://simons.berkeley.edu/talks/fine-tuned-unfaithful-unnatural-abuse-terminology-causal-modeling
Quantum Physics and Statistical Causal Models
Many researchers have had the idea of using the methods employed in causal search programs to try to shed light on quantum theory, and more particularly on the significance of the particular way that quantum theory predicts violations of Bell's Inequality for distant experiments. The causal search literature, in turn, employs certain proprietary use of technical terminology: particular causal models, under specific circumstances, can violate a condition denominated "Faithfulness" or "Naturalness" or "No Fine Tuning". Such models are then regarded as objectionable via the rhetorical method of dropping the scare quotes and acting as if the technical terminology has the same meaning as the natural-language words that have been introduced. I will argue, using particular examples, that this rhetorical trope is illegitimate. In particular, Bohmian Mechanics, which according to the technical terminology, is "fine-tuned" or "unfaithful" or "unnatural", is none of these things in the usual sense of these terms. So the causal modeling technical terminology is counterproductive in this instance.
Visit talk page
https://simons.berkeley.edu/talks/fine-tuned-unfaithful-unnatural-abuse-terminology-causal-modeling
Quantum Physics and Statistical Causal Models
Many researchers have had the idea of using the methods employed in causal search programs to try to shed light on quantum theory, and more particularly on the significance of the particular way that quantum theory predicts violations of Bell's Inequality for distant experiments. The causal search literature, in turn, employs certain proprietary use of technical terminology: particular causal models, under specific circumstances, can violate a condition denominated "Faithfulness" or "Naturalness" or "No Fine Tuning". Such models are then regarded as objectionable via the rhetorical method of dropping the scare quotes and acting as if the technical terminology has the same meaning as the natural-language words that have been introduced. I will argue, using particular examples, that this rhetorical trope is illegitimate. In particular, Bohmian Mechanics, which according to the technical terminology, is "fine-tuned" or "unfaithful" or "unnatural", is none of these things in the usual sense of these terms. So the causal modeling technical terminology is counterproductive in this instance.