The paper tackles individualized decision-making under unmeasured confounding, providing a novel minimax solution and a paradox.
problem Unmeasured confounding in causal inference leads to biased estimates and affects individualized decision-making.
method The authors establish a formal link between individualized decision-making under partial identification and classical decision theory, providing a minimax solution and a paradox.
result A novel minimax solution for individualized decision-making/policy assignment is provided, and an interesting paradox is drawn.
Aggregated variables can mask causal effects, turning unconfounded into confounded relations.
problem Aggregated variables can mask causal effects, leading to paradoxical confounding.
method Analysis of how aggregated variables can change the definition of causality and the feasibility of causal relations.
result Macro causal relations are defined by micro states, not just aggregated variables.
This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to one conclusion (such as 'drug is effective') for every possible combination of t…
The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.
New pricing theory solves St. Petersburg paradox.
problem St. Petersburg Paradox unresolved for 280 years.
method Proposes new pricing theory with fair pricing rules.
result New pricing theory resolves the paradox.
Paper revisits five IF paradoxes using differential geometry.
problem Five paradoxes of Instantaneous Frequency in three-phase systems.
method Geometric interpretation of frequency to explain IF paradoxes.
result Revisits and explains five IF paradoxes through a common framework.
Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg paradox.
This paper develops a cohomological hierarchy for bistable visual paradoxes.
problem Understanding the hierarchy of visual paradoxes built from bistable elements.
method Develops a cohomological hierarchy using Z2 coefficients and a discrete Stokes theorem. result Reveals a hierarchy of paradox classes from H0 through H2, refined at each degree by the relative/absolute distinction. Siegel's paradox is a fundamental question in international finance about exchange rates for futures contracts and has puzzled many scholars for over forty years. The unorthodox approach presented in this article leads to an arbitrage-free solution which is invariant under currency re-denominations and is symmetric, as…
In this article, I will present a paradox whose purpose is to draw your attention to an important topic in finance, concerning the non-independence of the financial returns (non-ergodic hypothesis). In this paradox, we have two people sitting at a table separated by a black sheet so that they cannot see each other and …
The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathemat…
Thompson Sampling shows polynomial regret for combinatorial semi-bandits with subgaussian rewards.
problem Finding optimal solutions in combinatorial semi-bandits with suboptimal sampling.
method Proposes Thompson Sampling with polynomial regret for linear combinatorial semi-bandits.
result Demonstrates 'mismatched sampling paradox' where knowing distributions can lead to worse performance.
A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is …
A mathematical paradox shows secant planes don't always form a tangent plane, but some analogies hold with a specific vector product.
problem Secant planes of a two-variable smooth function do not always form a tangent plane, even for simple polynomials.
method Analogies with the one-variable case are explored, using Clifford's geometric vector product.
result Some analogies with the one-variable case still hold in the multi-variable context with a specific vector product.
We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between "put" and "call" in the portfolio such that the average gain is almost always positive for a generic Black and Scholes model. This gain is zero if and only if the market price of ris…
New methods resolve conflicting treatment effect estimates in health tech assessments.
problem Conflicting conclusions from different sponsors analyzing the same data.
method Arbitrated indirect treatment comparisons (ArMAIC) targeting a common target population.
result Estimates treatment effects in a common target population, resolving the MAIC paradox.
Partial covariance factorizes in path diagrams, simplifying analysis.
problem Understanding partial covariance in complex diagrams.
method Factorization of partial covariance over nodes and edges.
result Simpson's paradox cannot occur in singly-connected diagrams.
Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for every trade, there is a buy side and a sell side, the total amount of asset and …
The paper proposes a method to precisely decompose confounders and estimate treatment effects.
problem Estimating treatment effects from observational data with confounder identification and balancing.
method Learning decomposed representations to identify and balance confounders and non-confounders.
result The method achieves more precise treatment effect estimation than existing methods.
Researchers solved a geometry paradox for creased tubes.
problem Resolving the paradox of Gaussian curvature in creased tubes.
method Calculated Gaussian curvature in terms of rate of change of solid angle, dependent on fold angle and curvature.
result Gaussian curvature is zero overall despite the surface being doubly-curved.
Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions are considered. The solution of the paradox lies in the non-constant nature of re…
Research shows continual learning challenges in confounded datasets.
problem Challenges in mitigating confounders in continual learning settings.
method Formal description of continual confounders, construction of ConCon dataset.
result Standard continual learning methods fail to ignore confounders.
Statistical learning on biological data can be challenging due to confounding variables in sample collection and processing. Confounders can cause models to generalize poorly and result in inaccurate prediction performance metrics if models are not validated thoroughly. In this paper, we propose methods to control for …
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive way by exploiting useful information about the system. In order to determine fr…
Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treat…
Detect hidden confounding in observational data using multiple environments.
problem Detect hidden confounding in observational data.
method Theoretical framework and simulation studies to test for hidden confounding.
result The proposed procedure correctly predicts hidden confounding, especially when bias is large.
Machine learning confound removal biases results, leading to misleading predictions.
problem Common confound removal methods in machine learning lead to misleading predictions.
method Featurewise removal of confound variance by linear regression before applying ML.
result This common deconfounding approach can leak information, amplifying null or moderate effects.
KRCD detects unobserved confounders in nonlinear observational data.
problem Detecting unobserved confounders in nonlinear observational studies.
method Kernel Regression Confounder Detection (KRCD) using reproducing kernel Hilbert spaces.
result KRCD outperforms existing methods and achieves superior computational efficiency.
GenAI adoption paradoxically lowers ROE for U.S. banks, with spillovers but systemic risk concerns.
problem Productivity paradox and implementation costs in U.S. banking sector with AI adoption.
method Dynamic Spatial Durbin Models (DSDM) and Synthetic Difference-in-Differences (SDID) for causal inference.
result AI adoption leads to a 428-basis-point decline in ROE for banks, with spillovers but systemic risk implications.
Prior work finds a diversity paradox: diversity breeds innovation, and yet, underrepresented groups that diversify organizations have less successful careers within them. Does the diversity paradox hold for scientists as well? We study this by utilizing a near-population of ~1.2 million US doctoral recipients from 1977…
Study identifies conditions for proxy adjustment in confounded binary treatment outcomes.
problem Average causal effect estimation with a non-differentially mismeasured binary confounder.
method Identifies conditions for proxy adjustment in the presence of a non-differentially mismeasured binary confounder.
result Adjusting for a non-differentially mismeasured binary proxy can improve estimation of the average causal effect.
New method estimates policy performance under unobserved confounding.
problem Estimating policy performance when decisions depend on unobserved variables.
method Developed worst-case bounds for robust OPE under unobserved confounding.
result Efficient procedure for computing worst-case bounds, proving statistical consistency.
Consistent estimator derived for confounding strength in observational data.
problem Estimating confounding strength in observational data is challenging due to unobserved confounders.
method Derived and adapted a consistent estimator using tools from random matrix theory.
result The original estimator is not consistent, but an adapted one is.
A new method uses randomized trials to estimate the strength of unobserved confounding.
problem Unobserved confounding compromises causal conclusions from non-randomized studies.
method Designs a statistical test to detect unobserved confounding strength and estimates a lower bound.
result Estimates an asymptotically valid lower bound on unobserved confounding strength.
This paper tackles confounding biases in data augmentation.
problem Mitigating spurious correlations and confounding variables in training data.
method Formal analysis and counterfactual data augmentation.
result Removing confounding biases leads to invariant features and better generalization.
New method recovers latent confounders from high-dimensional proxy variables.
problem Detecting latent confounders from high-dimensional proxy variables.
method Proxy Confounder Factorization (PCF) framework using ICA-PCF and GD-PCF.
result ICA-PCF recovers confounders with high correlation and low error in synthetic and real-world data.
Proposes tests to control confounding bias in predictive models.
problem Lack of non-parametric tests for confounding bias in predictive modeling.
method Partial and full confounder tests for probing null hypotheses of unconfounded and fully confounded models.
result Reveals previously unreported or hard-to-correct confounders in machine learning models.
New method tackles confounded bandit problems with dual instrumental variables.
problem Confounded contextual bandit problems where noise affects both contexts and rewards.
method Dual instrumental variable regression applied to reproducing kernel Hilbert spaces.
result Near-optimal convergence rate and computationally efficient algorithms proved.
New approach for causal inference with interdependent, time-varying latent confounders.
problem Estimating causal effects with interdependent, time-varying latent confounders.
method Variational estimation with a representer theorem and random input space.
result Demonstrates effectiveness on various temporal datasets.
Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders, while some constraint-based methods can present them. This paper proposes a causal f…
This paper highlights the role of risk neutral investors in generating endogenous bubbles in derivatives markets. We find that a market for derivatives, which has all the features of a perfect market except completeness and has some risk neutral investors, can exhibit extreme price movements which represent a violation…
Estimating the individual treatment effect (ITE) from observational data is essential in medicine. A central challenge in estimating the ITE is handling confounders, which are factors that affect both an intervention and its outcome. Most previous work relies on the unconfoundedness assumption, which posits that all th…
CARE improves LLM aggregation by accounting for shared confounders.
problem LLM judges' correlated errors due to shared latent confounders.
method CARE explicitly models judges' scores as true quality and confounders.
result CARE reduces aggregation error by up to 26.8% across various benchmarks.
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers v…
Proposes BDCM to handle unmeasured confounders in causal inference.
problem Handling unmeasured confounders in causal inference.
method Backdoor criterion to find variables for diffusion model.
result Captures counterfactual distribution more precisely.
The paradox of the energy transition is that the low marginal costs of new renewable energy sources (RES) drag electricity prices down and discourage investments in flexible productions that are needed to compensate for the lack of dispatchability of the new RES. The energy transition thus discourages the investments t…
New methods prioritize acquiring confounding features for efficient treatment effect estimation.
problem Efficient treatment effect estimation from observational data with missing confounding information.
method Proposes two acquisition strategies: covariate balancing and reducing factual outcome error.
result Our proposed methods, especially reducing factual outcome error, improve sample efficiency for treatment effect estimation.
Valid causal inference with unobserved confounding in high-dimensional settings.
problem Estimating causal effects with unobserved confounders in high-dimensional data.
method Proposes methods to estimate causal effects with valid confidence intervals in the presence of unobserved confounders and high-dimensional nuisance models.
result Valid semiparametric inference can be obtained with unobserved confounding, and uncertainty intervals are proposed.