Minimizing error in prevalence estimates and diagnostic classifiers remains a
challenging task in serology. In theory, these problems can be reduced to
modeling class-conditional probability densities (PDFs) of measurement
outcomes, which control all downstream analyses. However, this task quickly
succumbs to the curse of dimensionality, even for assay outputs with only a few
dimensions (e.g. target antigens). To address this problem, we propose a
technique that uses empirical training data to classify samples and estimate
prevalence in arbitrary dimension without direct access to the conditional
PDFs. We motivate this method via a lemma that relates relative conditional
probabilities to minimum-error classification boundaries. This leads us to
formulate an optimization problem that: (i) embeds the data in a parameterized,
curved space; (ii) classifies samples based on their position relative to a
coordinate axis; and (iii) subsequently optimizes the space by minimizing the
empirical classification error of pure training data, for which the classes are
known. Interestingly, the solution to this problem requires use of a
homotopy-type method to stabilize the optimization. We then extend the analysis
to the case of impure training data, for which the classes are unknown. We find
that two impure datasets suffice for both prevalence estimation and
classification, provided they satisfy a linear independence property. Lastly,
we discuss how our analysis unifies discriminative and generative learning
techniques in a common framework based on ideas from set and measure theory.
Throughout, we validate our methods in the context of synthetic data and a
research-use SARS-CoV-2 enzyme-linked immunosorbent (ELISA) assay.

在血清学中，我们提出了一种用于分类样本和估计未知维度中流行率的技术，通过将数据嵌入参数化的曲线空间，并通过最小化纯训练数据的经验分类误差来优化空间。

最优血清分类的最小假设：理论及对多维环境和杂质训练数据的启示

Minimal Assumptions for Optimal Serology Classification: Theory and  Implications for Multidimensional Settings and Impure Training Data

Inferring the causal structure that links n observables is usually based upon
detecting statistical dependences and choosing simple graphs that make the
joint measure Markovian. Here we argue why causal inference is also possible
when only single observations are present.
We develop a theory how to generate causal graphs explaining similarities
between single objects. To this end, we replace the notion of conditional
stochastic independence in the causal Markov condition with the vanishing of
conditional algorithmic mutual information and describe the corresponding
causal inference rules.
We explain why a consistent reformulation of causal inference in terms of
algorithmic complexity implies a new inference principle that takes into
account also the complexity of conditional probability densities, making it
possible to select among Markov equivalent causal graphs. This insight provides
a theoretical foundation of a heuristic principle proposed in earlier work.
We also discuss how to replace Kolmogorov complexity with decidable
complexity criteria. This can be seen as an algorithmic analog of replacing the
empirically undecidable question of statistical independence with practical
independence tests that are based on implicit or explicit assumptions on the
underlying distribution.

本文介绍了一种基于单个观测数据进行因果推断的方法，使用条件算法互信息代替因果马尔科夫条件中的条件随机独立性，解释了单个对象之间相似性的因果图生成，并使用可判定复杂度标准替代 Kolmogorov 复杂度，提出了一种新的因果推断原则，从而可以在 Markov 等价因果图之间进行选择。