Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.

There is a growing interest in estimating heterogeneous treatment effects across individuals using their high-dimensional feature attributes. Achieving high performance in such high-dimensional heterogeneous treatment effect estimation is challenging because in this setup, it is usual that some features induce sample selection bias while others do not but are predictive of potential outcomes. To avoid losing such predictive feature information, existing methods learn separate feature representations using inverse probability weighting (IPW). However, due to their numerically unstable IPW weights, these methods suffer from estimation bias under a finite sample setup. To develop a numerically robust estimator by weighted representation learning, we propose a differentiable Pareto-smoothed weighting framework that replaces extreme weight values in an end-to-end fashion. Our experimental results show that by effectively correcting the weight values, our proposed method outperforms the existing ones, including traditional weighting schemes. Our code is available at [this https URL](https://github.com/ychika/DPSW).

Finding the features relevant to the difference in treatment effects is essential to unveil the underlying causal mechanisms. Existing methods seek such features by measuring how greatly the feature attributes affect the degree of the {\it conditional average treatment effect} (CATE). However, these methods may overlook important features because CATE, a measure of the average treatment effect, cannot detect differences in distribution parameters other than the mean (e.g., variance). To resolve this weakness of existing methods, we propose a feature selection framework for discovering {\it distributional treatment effect modifiers}. We first formulate a feature importance measure that quantifies how strongly the feature attributes influence the discrepancy between potential outcome distributions. Then we derive its computationally efficient estimator and develop a feature selection algorithm that can control the type I error rate to the desired level. Experimental results show that our framework successfully discovers important features and outperforms the existing mean-based method.

Machine learning is used to make decisions for individuals in various fields, which require us to achieve good prediction accuracy while ensuring fairness with respect to sensitive features (e.g., race and gender). This problem, however, remains difficult in complex real-world scenarios. To quantify unfairness under such situations, existing methods utilize path-specific causal effects. However, none of them can ensure fairness for each individual without making impractical functional assumptions about the data. In this paper, we propose a far more practical framework for learning an individually fair classifier. To avoid restrictive functional assumptions, we define the probability of individual unfairness (PIU) and solve an optimization problem where PIU’s upper bound, which can be estimated from data, is controlled to be close to zero. We elucidate why our method can guarantee fairness for each individual. Experimental results show that our method can learn an individually fair classifier at a slight cost of accuracy.

Causal inference in time series is an important problem in many fields. Traditional methods use regression models for this problem. The inference accuracies of these methods depend greatly on whether or not the model can be well fitted to the data, and therefore we are required to select an appropriate regression model, which is difficult in practice. This paper proposes a supervised learning framework that utilizes a classifier instead of regression models. We present a feature representation that employs the distance between the conditional distributions given past variable values and show experimentally that the feature representation provides sufficiently different feature vectors for time series with different causal relationships. Furthermore, we extend our framework to multivariate time series and present experimental results where our method outperformed the model-based methods and the supervised learning method for i.i.d. data.

MOTIVATION: The Systems Biology Markup Language (SBML) is currently supported by >230 software tools, among which 160 support numerical integration of ordinary differential equation (ODE) models. Although SBML is a widely accepted standard within this field, there is still no language-neutral library that supports all features of SBML for simulating ODE models. Therefore, a demand exists for a simple portable implementation of a numerical integrator that supports SBML to enhance the development of a computational platform for systems biology. RESULTS: We implemented a library called libSBMLSim, which supports all the features of SBML and confirmed that the library passes all tests in the SBML test suite including those for SBML Events, AlgebraicRules, 'fast' attribute on Reactions and Delay. LibSBMLSim is implemented in the C programming language and does not depend on any third-party library except libSBML, which is a library to handle SBML documents. For the numerical integrator, both explicit and implicit methods are written from scratch to support all the functionality of SBML features in a straightforward implementation. We succeeded in implementing libSBMLSim as a platform-independent library that can run on most common operating systems (Windows, MacOSX and Linux) and also provides several language bindings (Java, C#, Python and Ruby). AVAILABILITY: The source code of libSBMLSim is available from http://fun.bio.keio.ac.jp/software/libsbmlsim/. LibSBMLSim is distributed under the terms of LGPL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.