This work characterize structural misspecification as a perturbed factor analysis problem, and establishes subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity.
Abstract
The presence of noise that depends on the latent variables poses a fundamental challenge to identifiability. Existing results rely on conditional independence among the observations given the latent variables. We study a more general \emph{misspecified structure}, where this conditional factorization does not hold, and establish both precise and approximate identifiability guarantees. We characterize structural misspecification as a perturbed factor analysis problem. For precise identifiability, we establish subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity. When the precise condition is not guaranteed, we derive an approximate subspace-identifiability theorem. Based on these results, we develop an unsupervised variational estimator for recovering latent variables. Experiments demonstrate the effectiveness of the proposed framework.
Understanding when neural networks learn interpretable representations is central to mechanistic interpretability. We study this through identifiability: when can supervised learning recover the true latent variables underlying the data? We introduce two data generating processes distinguished by their causal direction...
Learning the structure of latent factor models involves two central challenges: (1) estimating the number of latent factors and (2) learning the support of the mapping from latent variables to observed variables. This is especially challenging for nonparametric regimes and nonlinear settings. We propose a method for la...
A condition called the cross-Hessian Rank Constraint (HRC), which serves as a primitive rank-based tool for nonlinear latent causal discovery, shows that a rank-based property arises from the cross-Hessian of the observed-data log-density in the nonlinear case, revealing information about the latent variables.
Zi-Jian Li, Rui-Chu Cai, Feng Xie et al.· 0 citations
A theory is developed that connects a computationally tractable nonconvex procedure directly to statistical inference for nonlinear latent factor models with exponential-family links and partially observed entries with severe missingness, weak low-rank signals, and diminishing local curvature.
Principal component analysis and factor analysis are foundational to the study of high-dimensional data, yet their efficacy depends entirely on correctly identifying the latent dimension $r$. While parallel analysis (PA) is widely regarded as the gold standard for this task, its performance suffers in high-dimensional...
We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: paramet...
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
MIT News · Artificial Intelligence· news.mit.eduOct 13, 2026
Machine-learning networks can learn without detailed instructions from a designer. Those that do may offer insight into how the brain reorganizes itself during learning.
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