Integrated Calendar

The typical approach towards drawing causal conclusions from observed data starts by defining a causal estimand, for example in terms of potential outcomes or the so-called do operator, and continues by providing conditions for identification of this estimand from the data, followed by statistical estimation and inference. One of the main assumptions is the no-interference assumption, meaning that the treatment assigned to one unit does not affect other units in the sample. However, in many domains such as in the social sciences and infectious disease epidemiology, this assumption is implausible in practice due to social interactions.
As an alternative to the no-interference assumption, an interference structure is often represented using a network. Ubiquitously, the network structure is assumed to be known and correctly specified. Nevertheless, correctly encoding the interference structure in a network can be challenging. For example, people may misreport their social connections, or report connections irrelevant to the specific combination of treatment and outcome.
Building on the exposure mapping framework, we derive the bias arising from estimating causal effects under a misspecified interference structure. To address this problem, we propose a novel estimator that uses multiple networks simultaneously and is unbiased if one of the networks correctly represents the interference structure, thus providing robustness to the network specification. Additionally, we propose a sensitivity analysis that quantifies the impact of a postulated misspecification mechanism on the causal estimates. Through simulation studies, we illustrate the bias from assuming an incorrect network and show the bias-variance tradeoff of our proposed network-misspecification-robust estimator. We further demonstrate the utility of our methods in two real examples.
Joint work with Bar Weinstein

A central goal of physics is to
understand the low-energy solutions of
quantum interactions between
particles. This talk will focus on the
complexity of describing low-energy
solutions; I will show that we can
construct quantum systems for which
the low-energy solutions are highly
complex and unlikely to exhibit succinct
classical descriptions. I will discuss the
implications these results have for robust
entanglement at constant temperature and the
quantum PCP conjecture. En route, I will
discuss our positive resolution of the No Lowenergy
Trivial States (NLTS) conjecture on the
existence of robust complex entanglement.
Mathematically, for an n-particle system, the
low-energy states are the eigenvectors
corresponding to small eigenvalues of an
exp(n)-sized matrix called the Hamiltonian,
which describes the interactions between the
particles. Low-energy states can be thought of
as approximate solutions to the local
Hamiltonian problem with ground-states
serving as the exact solutions. In this sense,
low-energy states are the quantum
generalizations of approximate solutions to
satisfiability problems, a central object of
study in theoretical computer science. I will
discuss the theoretical computer science
techniques used to prove circuit lower bounds
for all low-energy states. This morally
demonstrates the existence of Hamiltonian
systems whose entire low-energy subspace is
robustly entangled.

Perceivers experience the world around them as organized, with sensory impressions clearly separated into entities. What makes a perceptual object, and what framework relates it to its composing features? A key insight is that under natural conditions, feature and object information is acquired actively, via sensor movements. Motor and sensory variables affect one another reciprocally, forming a closed-loop system. I therefore hypothesize that percepts signifying an object emerge when the motor-sensory loop’s dynamics converge towards a stable attractor. Using snout and whisker tracking data from freely-moving behaving rats, I outline such an attractor for object detection. I demonstrate that whisker-object contact elicits robust signals on a motor-sensory phase-plane, comprised of the derivatives of whisker base-angle and base-curvature. Over consecutive contact epochs, trajectories on the phase-plane converge to a specific area. The area is characterized by a basin of attraction during contact, more so than in free-air whisking. Differences in head-movement behavior are associated with proximity to the attractor, suggesting that the animal makes use of this proposed coding-scheme. Finally, to build upon these insights, I present a novel paradigm for the study of volitional perceptual exploration, in both rewarded and unrewarded contexts. It supports high-resolution study of motor-sensory development starting at birth, throughout task-learning and until mastery. Taken together, these results highlight a novel framework for the study of the perception of features and objects as motor-sensory attractors.