MOTIVATION: Channel interference in mass cytometry can cause spillover and may result in miscounting of protein markers. Chevrier et al. introduce an experimental and computational procedure to estimate and compensate for spillover implemented in their R package CATALYST. They assume spillover can be described by a spillover matrix that encodes the ratio between the signal in the unstained spillover receiving and stained spillover emitting channel. They estimate the spillover matrix from experiments with beads. We propose to skip the matrix estimation step and work directly with the full bead distributions. We develop a nonparametric finite mixture model and use the mixture components to estimate the probability of spillover. Spillover correction is often a pre-processing step followed by downstream analyses, and choosing a flexible model reduces the chance of introducing biases that can propagate downstream. RESULTS: We implement our method in an R package spillR using expectation-maximization to fit the mixture model. We test our method on simulated, semi-simulated, and real data from CATALYST. We find that our method compensates low counts accurately, does not introduce negative counts, avoids overcompensating high counts, and preserves correlations between markers that may be biologically meaningful. AVAILABILITY AND IMPLEMENTATION: Our new R package spillR is on bioconductor at bioconductor.org/packages/spillR. All experiments and plots can be reproduced by compiling the R markdown file spillR_paper.Rmd at github.com/ChristofSeiler/spillR_paper.

Additive Noise Models (ANMs) are a common model class for causal discovery from observational data. Due to a lack of real-world data for which an underlying ANM is known, ANMs with randomly sampled parameters are commonly used to simulate data for the evaluation of causal discovery algorithms. While some parameters may be fixed by explicit assumptions, fully specifying an ANM requires choosing all parameters. Reisach et al. (2021) show that, for many ANM parameter choices, sorting the variables by increasing variance yields an ordering close to a causal order and introduce ‘var-sortability’ to quantify this alignment. Since increasing variances may be unrealistic and cannot be exploited when data scales are arbitrary, ANM data are often rescaled to unit variance in causal discovery benchmarking. We show that synthetic ANM data are characterized by another pattern that is scale-invariant and thus persists even after standardization: the explainable fraction of a variable’s variance, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. The result is high ‘$R^2$-sortability’, meaning that sorting the variables by increasing $R^2$ yields an ordering close to a causal order. We propose a computationally efficient baseline algorithm termed ‘$R^2$-SortnRegress’ that exploits high $R^2$-sortability and that can match and exceed the performance of established causal discovery algorithms. We show analytically that sufficiently high edge weights lead to a relative decrease of the noise contributions along causal chains, resulting in increasingly deterministic relationships and high $R^2$. We characterize $R^2$-sortability on synthetic data with different simulation parameters and find high values in common settings. Our findings reveal high $R^2$-sortability as an assumption about the data generating process relevant to causal discovery and implicit in many ANM sampling schemes. It should be made explicit, as its prevalence in real-world data is an open question. For causal discovery benchmarking, we provide implementations of $R^2$-sortability, the $R^2$-SortnRegress algorithm, and ANM simulation procedures in our library CausalDisco at https://causaldisco.github.io/CausalDisco/.

Simulated DAG models may exhibit properties that, perhaps inadvertently, render their structure identifiable and unexpectedly affect structure learning algorithms. Here, we show that marginal variance tends to increase along the causal order for generically sampled additive noise models. We introduce varsortability as a measure of the agreement between the order of increasing marginal variance and the causal order. For commonly sampled graphs and model parameters, we show that the remarkable performance of some continuous structure learning algorithms can be explained by high varsortability and matched by a simple baseline method. Yet, this performance may not transfer to real-world data where varsortability may be moderate or dependent on the choice of measurement scales. On standardized data, the same algorithms fail to identify the ground-truth DAG or its Markov equivalence class. While standardization removes the pattern in marginal variance, we show that data generating processes that incur high varsortability also leave a distinct covariance pattern that may be exploited even after standardization. Our findings challenge the significance of generic benchmarks with independently drawn parameters. The code is available at https://github.com/Scriddie/Varsortability.