Modern causal inference methods allow machine learning to be used to weaken parametric modeling assumptions. However, the use of machine learning may result in bias and incorrect inferences due to overfitting. Cross-fit estimators have been proposed to eliminate this bias and yield better statistical properties. We conducted a simulation study to assess the performance of several different estimators for the average causal effect (ACE). The data generating mechanisms for the simulated treatment and outcome included log-transforms, polynomial terms, and discontinuities. We compared singly-robust estimators (g-computation, inverse probability weighting) and doubly-robust estimators (augmented inverse probability weighting, targeted maximum likelihood estimation). Nuisance functions were estimated with parametric models and ensemble machine learning, separately. We further assessed cross-fit doubly-robust estimators. With correctly specified parametric models, all of the estimators were unbiased and confidence intervals achieved nominal coverage. When used with machine learning, the cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage. Due to the difficulty of properly specifying parametric models in high dimensional data, doubly-robust estimators with ensemble learning and cross-fitting may be the preferred approach for estimation of the ACE in most epidemiologic studies. However, these approaches may require larger sample sizes to avoid finite-sample issues.

In their article, "Egalitarianism under Severe Uncertainty", Philosophy and Public Affairs, 46:3, 2018, Thomas Rowe and Alex Voorhoeve develop an original moral decision theory for cases under uncertainty, called "pluralist egalitarianism under uncertainty". In this paper, I firstly sketch their views and arguments. I then elaborate on their moral decision theory by discussing how it applies to choice scenarios in health ethics. Finally, I suggest a new two-stage Ellsberg thought experiment challenging the core of the principle of their theory. In such an experiment pluralist egalitarianism seems to suggest the wrong, morally and rationally speaking, course of action -- no matter whether I consider my thought experiment in a simultaneous or a sequential setting.

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for guiding decisions. However, many interesting models are intractable with standard Bayesian methods, as they lack a closed-form likelihood function or the likelihood is computationally too expensive to evaluate. With this work, we propose a novel method for performing Bayesian model comparison using specialized deep learning architectures. Our method is purely simulation-based and circumvents the step of explicitly fitting all alternative models under consideration to each observed dataset. Moreover, it involves no hand-crafted summary statistics of the data and is designed to amortize the cost of simulation over multiple models and observable datasets. This makes the method applicable in scenarios where model fit needs to be assessed for a large number of datasets, so that per-dataset inference is practically infeasible. Finally, we propose a novel way to measure epistemic uncertainty in model comparison problems. We argue that this measure of epistemic uncertainty provides a unique proxy to quantify absolute evidence even in a framework which assumes that the true data-generating model is within a finite set of candidate models.

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and antisymmetric for a better behaved groupoidal semantics over the set of roughly equivalent objects by the first author. Another distinct algebraic semantics over the set of approximations, and a new knowledge interpretation are also invented in this research by her. Because of minimal conditions imposed on the relations, neighborhood granulations are used in the construction of all approximations (granular and pointwise). Necessary and sufficient conditions for the lattice of local upper approximations to be completely distributive are proved by the second author. These results are related to formal concept analysis. Applications to student centered learning and decision making are also outlined.

Scientific analyses often rely on slow, but accurate forward models for observable data conditioned on known model parameters. While various emulation schemes exist to approximate these slow calculations, these approaches are only safe if the approximations are well understood and controlled. This workshop submission reviews and updates a previously published method, which has been used in cosmological simulations, to (1) train an emulator while simultaneously estimating posterior probabilities with MCMC and (2) explicitly propagate the emulation error into errors on the posterior probabilities for model parameters. We demonstrate how these techniques can be applied to quickly estimate posterior distributions for parameters of the $\Lambda$CDM cosmology model, while also gauging the robustness of the emulator approximation.

The concept of free energy has its origins in 19th century thermodynamics, but has recently found its way into the behavioral and neural sciences, where it has been promoted for its wide applicability and has even been suggested as a fundamental principle of understanding intelligent behavior and brain function. We argue that there are essentially two different notions of free energy in current models of intelligent agency, that can both be considered as applications of Bayesian inference to the problem of action selection: one that appears when trading off accuracy and uncertainty based on a general maximum entropy principle, and one that formulates action selection in terms of minimizing an error measure that quantifies deviations of beliefs and policies from given reference models. The first approach provides a normative rule for action selection in the face of model uncertainty or when information-processing capabilities are limited. The second approach directly aims to formulate the action selection problem as an inference problem in the context of Bayesian brain theories, also known as Active Inference in the literature. We elucidate the main ideas and discuss critical technical and conceptual issues revolving around these two notions of free energy that both claim to apply at all levels of decision-making, from the high-level deliberation of reasoning down to the low-level information-processing of perception.

It is based on the representation of elementary pieces of evidence by belief functions (defined as completely monotone set functions) and on their combination by an operator called the product-intersection rule, or Dempster's rule of combination. A belief function can be constructed by comparing a piece evidence to a scale of canonical examples such as randomly coded messages, whose meanings are determined by chance [40]. A belief function on a set Θ can be seen as being induced by a multi-valued mapping from a probability space to Ω; it is mathematically equivalent to a random set [5, 34]. As rational beliefs are essentially determined by evidence, the Dempster-Shafer (DS) theory can be regarded as a general framework for reasoning with uncertainty [11]. Shortly after the introduction of DS theory, Zadeh independently proposed another formalism, called Possibility Theory [54], in which the concept of "fuzzy restriction" plays a

Papers published at the Neural Information Processing Systems Conference.

Papers published at the Neural Information Processing Systems Conference.

As a response to the increasing linkages between the macroeconomy and the financial sector, as well as the expanding interconnectedness of the global economy, empirical macroeconomic models have increased both in complexity and size. For that reason, estimation of modern models that inform macroeconomic decisions - such as linear and nonlinear versions of dynamic stochastic general equilibrium (DSGE) and vector autoregressive (VAR) models - many times relies on Bayesian inference via powerful Markov chain Monte Carlo (MCMC) methods. 1 However, existing posterior simulation algorithms cannot scale up to very high-dimensions due to the computational inefficiency and the larger numerical error associated with repeated sampling via Monte Carlo; see Angelino et al. (2016) for a thorough review of such computational issues from a machine learning and high-dimensional data perspective. In that respect, while Bayesian inference is a natural probabilistic framework for learning about parameters by utilizing all information in the data likelihood and prior, computational restrictions might make it less suitable for supporting real-time decision-making in very high dimensions. This paper introduces to the econometric literature the framework of factor graphs (Kschischang et al., 2001) for the purpose of designing computationally efficient, and easy to maintain, Bayesian estimation algorithms. The focus is not only on "faster" posterior inference broadly interpreted, but on designing algorithms that have such low complexity that are future-proof and can be used in high-dimensional econometric problems with possibly thousands or millions of coefficients.