Disentangling Mixtures of Unknown Causal Interventions

Abhinav Kumar; Gaurav Sinha

Home/Archive/arXiv

arXiv · 2210.03242

Disentangling Mixtures of Unknown Causal Interventions

Abhinav Kumar·Gaurav Sinha

View original source ↗Read source document ↗Export metadata ↓

Abstract

In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

Explore related subjects

stat.ML cs.AI cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Abhinav Kumar, Gaurav Sinha. 2022-10-01. Disentangling Mixtures of Unknown Causal Interventions. https://arxiv.org/abs/2210.03242

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Attack-Resistant Uniform Fairness for Linear and Smooth Contextual Bandits

Modern digital platforms use contextual bandits to allocate valuable exposure and opportunities among competing participants. Fair treatment is therefore an important concern, yet reward maximization alone does not ensure that preferential allocation reflects participants' merits. We develop algorithms for linear and smooth contextual bandits under uniform merit-based fairness, requiring the reward ordering to justify preferential allocation across all contexts and rounds, and study how these guarantees are affected by adversarial reward corruption. Our algorithms achieve $(1-\widetilde O(1/T))$-fairness, with regret that is minimax optimal among fair policies for linear rewards and nearly minimax optimal for smooth rewards. In the linear setting, matching lower bounds identify the price of fairness exactly: minimax regret increases from $\log T$ to $\log^2 T$. For smooth rewards, the cost of fairness is at most polylogarithmic. We further establish a separation between regret and fairness robustness: an $\widetilde O(1)$ corruption budget can cause substantial fairness violations without worsening the regret order. We therefore develop robust algorithms that adapt sampling, estimation, and fairness certification to corruption, which preserve uniform fairness and achieve minimax-optimal and nearly optimal regrets for linear and smooth rewards, respectively. Numerical and semi-synthetic experiments illustrate these findings.

stat.ML↗

arXiv2026

The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy

We study the minimax cost of $(\varepsilon,δ)$-differential privacy for mean estimation and Gaussian linear regression in low and high dimensions. For low-dimensional mean estimation, a resampling reduction to fingerprinting yields the privacy contribution $d^2\log(1/δ)/(n^2\varepsilon^2)$ in the stated polynomial-$δ$ regime. For low-dimensional regression, a tracing argument gives the contribution $d^2/(n^2\varepsilon^2)$ under an explicit approximate-DP remainder condition. For sparse mean estimation and sparse regression, a constant-weight packing and a private Fano lemma produce an effective privacy entropy of order $\min\{s\log(ed/s),[\log((e^\varepsilon-1)/δ)]_+\}$ for $δ>0$, up to universal constants and a fixed threshold; for pure DP it is $s\log(ed/s)$. Thus, when $δ$ is polynomially smaller than $\varepsilon$, the pure-DP dependence is retained up to polylogarithmic factors whenever the effective dimension is polylogarithmic in $n$, including regimes with $\varepsilon=o(1)$. Coordinatewise-clipping estimators for means and split-sample noisy-gradient estimators for regression attain the lower bounds up to explicit logarithmic factors. Simulations and data examples illustrate related implementations.

stat.ML↗

arXiv2026

Robust Mixture Models for Algorithmic Fairness Under Latent Heterogeneity

Machine learning models optimized for average performance can perform poorly on vulnerable subpopulations. Existing approaches often rely on groups specified in advance, yet fairness-relevant subgroup structure may be latent, intersectional, and driven by complex interactions among continuous and discrete attributes. We introduce \textbf{ROME} (\textbf{\underline{RO}}bust \textbf{\underline{M}}ixture \textbf{\underline{E}}nsemble), a framework that learns latent group structure while optimizing worst-group predictive performance. ROME connects latent-variable modeling with distributionally robust optimization (DRO) through two complementary approaches: an Expectation-Maximization formulation with robust aggregation for linear models and a neural Mixture-of-Experts formulation for nonlinear settings. Across simulations and three real-world regression datasets, ROME improves worst-group performance while maintaining competitive overall accuracy, including in comparisons with established group-aware and group-label-free robust learning methods. ROME provides a flexible approach to robust prediction when fairness-relevant attributes are available for subgroup discovery but their direct use in group-specific outcome models is restricted.

stat.ML↗