# Effect estimation with proxies {% hint style="info" %} You probably need some knowledge of Causal Inference to understand all the details in this post. If you're interested, [*The Book of Why*](https://dl.acm.org/doi/10.5555/3238230) (Judea Pearl) and [*Causal Inference: What If*](https://miguelhernan.org/whatifbook) (Hernán and Robins) are a good place to start. {% endhint %} Estimating the causal effect of a treatment on an outcome is somewhat straightforward when all relevant variables are observed. Of these, the most important are the [confounders](https://en.wikipedia.org/wiki/Confounding): third variables that affect both treatment and outcome and that, if unobserved, distort their true relationship. In practice, it is very common that we cannot observe confounders directly, but only have access to them through a noisy measurement, called a *proxy.* This is the problem that our colleagues at the [University of Copenhagen](https://www.ku.dk/en) studied in their recent 2026 paper ["Identifying Causal Effects Using a Single Proxy Variable"](https://arxiv.org/abs/2604.09135) by [Silvan Vollmer](https://silvanvollmer.github.io/), [Niklas Pfister](https://niklaspfister.github.io/), and [Sebastian Weichwald](https://sweichwald.de/). With a novel result, they extend the settings in which the causal effect between treatment and outcome is identifiable, and develop an algorithm to estimate it.

Silvan Vollmer, the first author of the paper, presenting his work at EuroCIM.

### Validation on a real physical experiment The authors encountered the *other* fundamental problem in causal inference: finding real-world datasets suitable to validate your algorithms 🤓. This is where the [Chambers](/the-chambers/how-they-work.md) come in. The authors used our [Light Tunnel Mk2](/the-chambers/light-tunnel-mk2.md) to create a real, physical experiment that matched their problem formulation. By running the tunnel in its [`linked_leds`](https://cchamber-box.s3.eu-central-2.amazonaws.com/config_doc_lt_mk2_linked_leds.pdf) configuration, the causal graph of the chamber (C) resembled the single-proxy scenario:

Overview of the setup used in the paper and the resulting causal graph. You can find a detailed description of all variables in the documentation of the hardware configuration.

Let's break this down. In this particular [hardware configuration](/the-chambers/how-they-work.md#hardware-configurations), the brightness of the UV LED atop the second light-intensity sensor (`ir_2`) is [set by the chamber](https://cchamber-box.s3.eu-central-2.amazonaws.com/config_doc_lt_mk2_linked_leds.pdf) as a linear function of the measurement of the first sensor (`ir_1`). In this setup, `ir_1` serves as the **treatment** and `ir_2` as the **outcome**, with the `green` brightness[^1] of the main light source acting as the **confounder** between both sensor measurements. As **proxy**, we take `current_ls_raw`: a noisy measurement of the electrical current drawn by the light source, which depends on its brightness. There are two additional variables: the sensor parameters `sps_` and `offset_current_ls`, which control the [oversampling rate](https://www.microchip.com/en-us/about/media-center/blog/2024/what-is-oversampling) and reference voltage of the current sensor. By changing their values, the authors were able to test their method under different proxies. The values for all the variables are given in [Appendix K](https://arxiv.org/pdf/2604.09135#page=44) of the paper. ### Additional resources You can find the [datasets](https://github.com/juangamella/causal-chamber/tree/main/datasets/lt_spice_v1) collected by the authors, as well as the code to collect them using the [Remote Lab](/remote-lab/quickstart.md), in our open-source [dataset repository](https://github.com/juangamella/causal-chamber). ### References * \[[PDF](https://arxiv.org/pdf/2604.09135)] Vollmer, Silvan, Niklas Pfister, and Sebastian Weichwald. "Identifying Causal Effects Using a Single Proxy Variable." [*arXiv preprint arXiv:2604.09135*](https://arxiv.org/abs/2604.09135#page=44) (2026). [^1]: the same setup would also work with the `red` or `blue` channels of the light source --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://docs.causalchamber.ai/case-studies/causal-inference/effect-estimation-with-proxies.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.