# BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect

arXiv: https://arxiv.org/abs/2211.10793 · HTML: https://mlsanity.com/paper/2211.10793/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 100 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 30 of 48)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [An Attentive Survey of Attention Models](https://mlsanity.com/paper/1904.02874/) (2019)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Estimating heterogeneous treatment effects with right-censored data via causal survival forests](https://mlsanity.com/paper/2001.09887/) (2020)
- [On Locality of Local Explanation Models](https://mlsanity.com/paper/2106.14648/) (2021)
- [SurvITE: Learning Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2110.14001/) (2021)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Unbiased split variable selection for random survival forests using maximally selected rank statistics](https://mlsanity.com/paper/1605.03391/) (2016)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values](https://mlsanity.com/paper/1908.02337/) (2019)
- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Transfer Learning for Estimating Causal Effects using Neural Networks](https://mlsanity.com/paper/1808.07804/) (2018)
- [Multi-Source Causal Inference Using Control Variates](https://mlsanity.com/paper/2103.16689/) (2021)
- [Counterfactual Phenotyping with Censored Time-to-Events](https://mlsanity.com/paper/2202.11089/) (2022)

## Built on by (most cited first, 1 of 1)

- [Surv-IPTB: An Attention-Based Model for Estimating Individual Probability of Treatment Benefit with Survival Data](https://mlsanity.com/paper/2608.06288/) (2026)

## Abstract (arXiv)

A method for estimating the conditional average treatment effect under condition of censored time-to-event data called BENK (the Beran Estimator with Neural Kernels) is proposed. The main idea behind the method is to apply the Beran estimator for estimating the survival functions of controls and treatments. Instead of typical kernel functions in the Beran estimator, it is proposed to implement kernels in the form of neural networks of a specific form called the neural kernels. The conditional average treatment effect is estimated by using the survival functions as outcomes of the control and treatment neural networks which consists of a set of neural kernels with shared parameters. The neural kernels are more flexible and can accurately model a complex location structure of feature vectors. Various numerical simulation experiments illustrate BENK and compare it with the well-known T-learner, S-learner and X-learner for several types of the control and treatment outcome functions based on the Cox models, the random survival forest and the Nadaraya-Watson regression with Gaussian kernels. The code of proposed algorithms implementing BENK is available in https://github.com/Stasychbr/BENK.