Counterfactual decision-making in the face of uncertainty involves selecting the optimal action from several alternatives using causal reasoning. Decision-makers often rank expected potential outcomes (or their corresponding utility and desirability) to compare the preferences of candidate actions. In this paper, we study new counterfactual decision-making rules by introducing two new metrics: the probabilities of potential outcome ranking (PoR) and the probability of achieving the best potential outcome (PoB). PoR reveals the most probable ranking of potential outcomes for an individual, and PoB indicates the action most likely to yield the top-ranked outcome for an individual. We then establish identification theorems and derive bounds for these metrics, and present estimation methods. Finally, we perform numerical experiments to illustrate the finite-sample properties of the estimators and demonstrate their application to a real-world dataset.

This paper is concerned with the data collaboration (DC) analysis, a privacy-preserving method for analyzing decentralized datasets held by multiple parties. In this method, privacy-preserving intermediate representations of original datasets are collected from multiple parties and then converted into collaboration representations for collaborative data analysis. However, conventional methods for creating collaboration representations suffer from several challenges; namely, the optimization problem being considered is not well defined, and the process of solving it is very difficult to understand. We thus propose a new solution for creating high-quality collaboration representations for the DC analysis. Specifically, we formulate a revised optimization problem for creating collaboration representations and then transform this optimization problem into a generalized eigenvalue problem. We also propose a reduction of the generalized eigenvalue problem to a singular value decomposition through the QR decomposition. Computational experiments using publicly available datasets demonstrate that our method can outperform the conventional methods for the DC analysis in terms of both prediction accuracy and computational efficiency. • Privacy-preserving data collaboration for analyzing decentralized datasets. • Generalized eigenvalue problem for high-quality collaboration representations. • Reduction of the generalized eigenvalue problem to a singular value decomposition. • Superiority of our method evaluated through computational experiments.

Probabilities of causation (PoC) offer valuable insights for informed decision-making. This paper introduces novel variants of PoC-controlled direct, natural direct, and natural indirect probability of necessity and sufficiency (PNS). These metrics quantify the necessity and sufficiency of a treatment for producing an outcome, accounting for different causal pathways. We develop identification theorems for these new PoC measures, allowing for their estimation from observational data. We demonstrate the practical application of our results through an analysis of a real-world psychology dataset.

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments, including covariance and correlation, reveal the relationships between multiple random variables. On the other hand, the primary focus of causal inference is the evaluation of causal effects, which are defined as the difference between two potential outcomes. While traditional causal effect assessment focuses on the average causal effect, this work provides definitions, identification theorems, and bounds for moments and product moments of causal effects to analyze their distribution and relationships. We conduct experiments to illustrate the estimation of the moments of causal effects from finite samples and demonstrate their practical application using a real-world medical dataset.

Mediation analysis for probabilities of causation (PoC) provides a fundamental framework for evaluating the necessity and sufficiency of treatment in provoking an event through different causal pathways. One of the primary objectives of causal mediation analysis is to decompose the total effect into path-specific components. In this study, we investigate the path-specific probability of necessity and sufficiency (PNS) to decompose the total PNS into path-specific components along distinct causal pathways between treatment and outcome, incorporating two mediators. We define the path-specific PNS for decomposition and provide an identification theorem. Furthermore, we conduct numerical experiments to assess the properties of the proposed estimators from finite samples and demonstrate their practical application using a real-world educational dataset.

*Probabilities of causation* (PoC) are valuable concepts for explainable artificial intelligence and practical decision-making. PoC are originally defined for scalar binary variables. In this paper, we extend the concept of PoC to continuous treatment and outcome variables, and further generalize PoC to capture causal effects between multiple treatments and multiple outcomes. In addition, we consider PoC for a sub-population and PoC with multi-hypothetical terms to capture more sophisticated counterfactual information useful for decision-making. We provide a nonparametric identification theorem for each type of PoC we introduce. Finally, we illustrate the application of our results on a real-world dataset about education.

There has been considerable recent interest in estimating heterogeneous causal effects. In this paper, we study conditional average partial causal effects (CAPCE) to reveal the heterogeneity of causal effects with continuous treatment. We provide conditions for identifying CAPCE in an instrumental variable setting. Notably, CAPCE is identifiable under a weaker assumption than required by a commonly used measure for estimating heterogeneous causal effects of continuous treatment. We develop three families of CAPCE estimators: sieve, parametric, and reproducing kernel Hilbert space (RKHS)-based, and analyze their statistical properties. We illustrate the proposed CAPCE estimators on synthetic and real-world data.

We propose novel identification conditions and a statistical estimation method for the probabilities of potential outcome types using covariate information in randomized trials in which the treatment assignment is randomized but subject compliance is not perfect. Different from existing studies, the proposed identification conditions do not require strict assumptions such as the assumption of monotonicity. When the probabilities of potential outcome types are identifiable through the proposed conditions, the problem of estimating the probabilities of potential outcome types is reduced to that of singular models. Thus, the probabilities cannot be evaluated using standard statistical likelihood-based estimation methods. Rather, the proposed identification conditions show that we can derive consistent estimators of the probabilities of potential outcome types via the method of moments, which leads to the asymptotic normality of the proposed estimators through the delta method under regular conditions. We also propose a new statistical estimation method based on the bounded constrained augmented Lagrangian method to derive more efficient estimators than can be derived through the method of moments.

Instrumental variable (IV) analysis is a powerful tool widely used to elucidate causal relationships. We study the problem of estimating the average partial causal effect (APCE) of a continuous treatment in an IV setting. Specifically, we develop new methods for estimating APCE based on a recent identification condition via an integral equation. We develop two families of methods, nonparametric and parametric - the former uses the Picard iteration to solve the integral equation; the latter parameterizes APCE using a linear basis function model. We analyze the statistical and computational properties of the proposed methods and illustrate them on synthetic and real data.

This paper deals with the identification problem of causal effects in randomized trials with noncompliance. In this problem, generally, causal effects are not identifiable and thus have been evaluated under some strict assumptions, or through the bounds. Different from existing studies, we propose novel identification conditions of joint probabilities of potential outcomes, which allow us to derive a consistent estimator of the causal effect. Regarding the identification conditions of joint probabilities of potential outcomes, the assumptions of monotonicity (Pearl, 2009), independence between potential outcomes (Robins & Richardson, 2011), gain equality (Li & Pearl, 2019) and specific functional relationships between cause and effect (Pearl, 2009) have been utilized. In contrast, without such assumptions, the proposed conditions enable us to evaluate joint probabilities of potential outcomes using an instrumental variable and a proxy variable of potential outcomes. The results of this paper extend the range of solvable identification problems in causal inference.

The detection of human and spoofed (synthetic/converted) speech has started to receive more attention. In this study, relative phase information extracted from a Fourier spectrum is used to detect human and spoofed speech. Because original/natural phase information is almost entirely lost in spoofed speech using current synthesis/conversion techniques, a modified group delay based feature, the frequency derivative of the phase spectrum, has been shown effective for detecting human speech and spoofed speech. The modified group delay based phase contains both the magnitude spectrum and phase information. Therefore, the relative phase information, which contains only phase information, is expected to achieve a better spoofing detection performance. In this study, the relative phase information is also combined with the Mel-Frequency Cepstral Coefficient (MFCC) and modified group delay. The proposed method was evaluated using the “ASVspoof 2015: Automatic Speaker Verification Spoofing and Countermeasures Challenge” dataset. The results show that the proposed relative phase information significantly outperforms the MFCC and modified group delay. The equal error rate (EER) was reduced from 1.74% of MFCC, 0.83% of modified group delay to 0.013% of relative phase. By combining the relative phase with MFCC and modified group delay, the EER was reduced to 0.002%. Index Terms: Spoofing detection, relative phase information, group delay, GMM, countermeasures