离散分数匹配实现从计数数据进行因果发现
Discrete Score Matching Enables Causal Discovery from Count Data
- Seoul National University（首尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对计数数据因果发现中导数不可用的问题，提出基于条件曲率分数（CCS）和非对角曲率分数（OCS）的DISCO算法，实现半参数GLM DAG的识别与恢复，实验验证了多种分布下的准确性和可扩展性。
AI中文摘要：
计数数据对基于分数匹配的因果发现构成挑战：导数不可用，简单地用有限差分替代通常不足以进行因果发现。我们通过以节点值为条件来推广SCORE的常曲率准则（Rolland等人，2022），从而得到用于排序的条件曲率分数（CCS）。我们还通过非对角曲率分数（OCS）扩展了基于曲率的父节点恢复，使得有向无环图（DAG）恢复能够使用从连续数据的分数函数和计数的具体分数构建的两种分数。在双变量设置中，零CCS精确刻画了半参数广义线性模型（GLM）的条件形式，其中条件族无需预先指定，这与经典GLM不同。对于满足我们正则条件下的双变量半参数GLM DAG，典范参数非线性是识别性的充分必要条件。在多变量DAG中，这种非线性通过CCS和OCS实现DAG恢复。我们的框架识别了一类新的半参数GLM DAG，它严格包含SCORE识别的非线性高斯ANM类。我们引入了DISCO（离散分数），一种使用离散扩散估计CCS和OCS的计数DAG恢复算法。实验表明，在泊松、负二项、二项和混合族设置中，DAG恢复准确，并且可在单个GPU上扩展到1000节点的DAG。
英文摘要：
Count data pose a challenge for score-matching-based causal discovery: derivatives are unavailable, and simply replacing them with finite differences does not generally suffice for causal discovery. We generalize SCORE's constant-curvature criterion (Rolland et al., 2022) by conditioning on the node's value, yielding the conditional curvature score (CCS) for ordering. We also extend curvature-based parent recovery through the off-diagonal curvature score (OCS), enabling directed acyclic graph (DAG) recovery with both scores constructed from score functions for continuous data and concrete scores for counts. In the bivariate setting, zero CCS exactly characterizes a semiparametric generalized linear model (GLM) conditional form in which the conditional family need not be specified in advance, unlike in classical GLMs. For bivariate semiparametric GLM DAGs under our regularity condition, canonical-parameter nonlinearity is necessary and sufficient for identifiability. In multivariate DAGs, this nonlinearity enables DAG recovery through CCS and OCS. Our framework identifies a new class of semiparametric GLM DAGs that strictly contains the nonlinear Gaussian ANM class identified by SCORE. We introduce DISCO (DIscrete SCOre), a count-DAG recovery algorithm that estimates CCS and OCS using discrete diffusion. Experiments demonstrate accurate DAG recovery across Poisson, negative binomial, binomial, and mixed-family settings, as well as scalability to 1,000-node DAGs on a single GPU.
