arXiv subjects

Gemma E. Moran

Publications and source records attributed to Gemma E. Moran.

11 recordsLinked to original sources

arXiv2026

Aggregated Posterior Predictive Checks for Generative Modeling

Latent variable generative models are commonly fit using simple priors over latent variables, but draws from these priors often fail to produce realistic data. This failure is due to a mismatch between the prior and the aggregated posterior, the distribution of latent variables induced by the fitted model and the data. This mismatch is often viewed as evidence that the prior is misspecified and should be replaced. Alternatively, in modern generative models, a two-stage strategy is increasingly used where first, the model is fit, and second, the aggregated posterior is estimated (van den Oord et al.,2017; Rombach et al., 2022.). Synthetic data are then obtained by sampling from this aggregated posterior instead of the prior. To check such procedures, we introduce the aggregated posterior predictive check (APPC). Theoretically, we establish sufficient conditions under which the APPC is asymptotically calibrated. For probabilistic principal component analysis, we show that the APPC can remain calibrated under a misspecified latent prior when pervasive factors permit recovery of the signal space. Experiments with variational autoencoders show that aggregated posterior sampling improves generation for heavy-tailed and clustered data relative to Gaussian prior sampling while performing comparably to models with more flexible latent priors.

stat.ME↗

arXiv2026

Holdout predictive checks for Bayesian model criticism

Bayesian modeling helps applied researchers articulate assumptions about their data and develop models tailored for specific applications. Thanks to good methods for approximate posterior inference, researchers can now easily build, use, and revise complicated Bayesian models for large and rich data. These capabilities, however, bring into focus the problem of model criticism. Researchers need tools to diagnose the fitness of their models, to understand where they fall short, and to guide their revision. In this paper we develop a new method for Bayesian model criticism, the holdout predictive check (HPC). HPCs are built on posterior predictive checks (PPCs), a seminal method that checks a model by assessing the posterior predictive distribution on the observed data. However, PPCs use the data twice---both to calculate the posterior predictive and to evaluate it---which can lead to uncalibrated $p$-values. HPCs, in contrast, compare the posterior predictive distribution to a draw from the population distribution, a heldout dataset. This method blends Bayesian modeling with frequentist assessment. Unlike the PPC, we prove that the HPC is properly calibrated. Empirically, we study HPCs on classical regression, a hierarchical model of text data, and factor analysis.

stat.ME↗

arXiv2026

Nonlinear multi-study sparse factor analysis

High-dimensional data often exhibit variation that can be captured by lower-dimensional factors. For high-dimensional data from multiple studies, one goal is to understand which underlying factors are common to all studies, and which factors are study-specific. As a particular example, we consider platelet gene expression data from patients in different disease groups. In this data, factors correspond to clusters of genes which are co-expressed; we may expect some clusters (or biological pathways) to be active for all diseases, while some clusters are only active for a specific disease. To learn these factors, we consider a nonlinear multi-study sparse factor model, which allows for both shared and study-specific factors. To fit this model, we propose a multi-study sparse variational autoencoder. The underlying model is sparse in that each observed feature (i.e. each dimension of the data) depends on a small subset of the latent factors. In the genomics example, this means each gene is active in only a few biological processes. We prove that the latent factor distributions are identifiable (up to element-wise transformations), and that the canonical shared and study-specific support structure is identifiable. Empirically, we demonstrate our method recovers meaningful factors in the platelet gene expression data.

stat.ML↗

arXiv2026

Stochastic weather generators for high-frequency wind vector time series

Surface winds can vary substantially from one minute to the next, so there is scope for studying its variation on this fine time scale. Restricting to the month of June to minimize seasonality, this work develops a range of machine learning models for generating realistic time series of surface wind vectors at a site in Lamont, Oklahoma based on more than 30 years of high quality measurements at the minute time scale. Such a generator could be used as an input into models from a range of disciplines, notably for wind energy, but also wildfire spread and aviation, among others. The data show complex diurnal structures in both wind speed and direction that would be challenging to capture with standard time series models, so we consider a number of machine learning approaches to producing a stochastic wind generator based on time vector-quantized variational autoencoders. We consider generating a day's worth of data at a time and generating a day of wind vectors conditional on the previous day's winds. We also study methods for incorporating a discrete weather state variable in the generator. We evaluate the generators using a wide range of formal and informal methods. The best of these generators can capture many but not all of the complex features present in the observational data. In particular, the best of our approaches accurately mimic diurnal changes in wind volatility but struggle to match the observed distribution of extreme wind speeds.

stat.AP↗

arXiv2026

Beyond Interpretability: When, Why, and How Sparse Autoencoders Enable Label-Free Visual Steering

Sparse Autoencoders (SAEs) are increasingly used to interpret foundation models, but their role as an actionable intervention space remains less understood, especially in vision. We study whether sparse visual features can be used not only for post-hoc analysis, but also to steer frozen vision-language models. We introduce Visual Sparse Steering (VS2), a label-free method that trains a top-$k$ SAE on unlabeled activations from a frozen CLIP image encoder and, at test time, constructs an interpretable steering vector by amplifying the input's active sparse features and decoding the induced change. We show that this procedure admits a closed-form decomposition as centroid-deviation steering: each input is moved along its deviation from the SAE-learned centroid. The residual term is controlled exactly by the SAE's per-sample reconstruction error, measured by FVU, yielding an FVU-based residual bound and motivating a reliability gate that falls back to zero-shot CLIP when SAE reconstruction is unreliable. With target-domain SAEs trained on unlabeled CLIP image-encoder activations, VS2 improves zero-shot accuracy across nine image-classification datasets, achieving gains up to $+4.12\%$ with less than $0.1\%$ additional inference compute. Finally, a controlled upper-bound study, VS2++, shows that selective amplification of sparse features can yield gains up to $+21.44\%$, exposing a reconstruction-vs-task saliency gap: features salient for reconstruction need not align with features useful for downstream prediction.

cs.CV↗

arXiv2026

Can Cross-Layer Transcoders Replace Vision Transformer Activations? An Interpretable Perspective on Vision

Understanding the internal activations of Vision Transformers (ViTs) is critical for building interpretable and trustworthy models. While Sparse Autoencoders (SAEs) have been used to extract human-interpretable features, they operate on individual layers and fail to capture the cross-layer computational structure of Transformers, as well as the relative significance of each layer in forming the last-layer representation. Alternatively, we introduce the adoption of Cross-Layer Transcoders (CLTs) as reliable, sparse, and depth-aware proxy models for MLP blocks in ViTs. CLTs use an encoder-decoder scheme to reconstruct each post-MLP activation from learned sparse embeddings of preceding layers, yielding a linear decomposition that transforms the final representation of ViTs from an opaque embedding into an additive, layer-resolved construction that enables faithful attribution and process-level interpretability. We train CLTs on CLIP ViT-B/32 and ViT-B/16 across CIFAR-100, COCO, and ImageNet-100. We show that CLTs achieve high reconstruction fidelity with post-MLP activations while preserving and even improving, in some cases, CLIP zero-shot classification accuracy. In terms of interpretability, we show that the cross-layer contribution scores provide faithful attribution, revealing that the final representation is concentrated in a smaller set of dominant layer-wise terms whose removal degrades performance and whose retention largely preserves it. These results showcase the significance of adopting CLTs as an alternative interpretable proxy of ViTs in the vision domain.

cs.CV↗

arXiv2026

Towards Interpretable Deep Generative Models via Causal Representation Learning

Recent developments in generative artificial intelligence (AI) rely on machine learning techniques such as deep learning and generative modeling to achieve state-of-the-art performance across wide-ranging domains. These methods' surprising performance is due in part to their ability to learn implicit "representations" of complex, multi-modal data. Unfortunately, deep neural networks are notoriously black boxes that obscure these representations, making them difficult to interpret or analyze. To resolve these difficulties, one approach is to build new interpretable neural network models from the ground up. This is the goal of the emerging field of causal representation learning (CRL) that uses causality as a vector for building flexible, interpretable, and transferable generative AI. CRL can be seen as a synthesis of three intrinsically statistical ideas: (i) latent variable models such as factor analysis; (ii) causal graphical models with latent variables; and (iii) nonparametric statistics and deep learning. This paper introduces CRL from a statistical perspective, focusing on connections to classical models as well as statistical and causal identifiability results. We also highlights key application areas, implementation strategies, and open statistical questions.

stat.ML↗

arXiv2022

The Posterior Predictive Null

Bayesian model criticism is an important part of the practice of Bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to Bayesian modeling and an effective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of Bayesian model criticism. Code to replicate the results in this paper is available at \url{https://github.com/gemoran/ppn-code}.

stat.ME↗

arXiv2022

Identifiable Deep Generative Models via Sparse Decoding

We develop the sparse VAE for unsupervised representation learning on high-dimensional data. The sparse VAE learns a set of latent factors (representations) which summarize the associations in the observed data features. The underlying model is sparse in that each observed feature (i.e. each dimension of the data) depends on a small subset of the latent factors. As examples, in ratings data each movie is only described by a few genres; in text data each word is only applicable to a few topics; in genomics, each gene is active in only a few biological processes. We prove such sparse deep generative models are identifiable: with infinite data, the true model parameters can be learned. (In contrast, most deep generative models are not identifiable.) We empirically study the sparse VAE with both simulated and real data. We find that it recovers meaningful latent factors and has smaller heldout reconstruction error than related methods.

stat.ML↗

arXiv2020

Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and automatic self-adaptivity to different levels of sparsity. We develop theory to uniquely characterize the global posterior mode under the SSGL and introduce a highly efficient block coordinate ascent algorithm for maximum a posteriori (MAP) estimation. We further employ de-biasing methods to provide uncertainty quantification of our estimates. Thus, implementation of our model avoids the computational intensiveness of Markov chain Monte Carlo (MCMC) in high dimensions. We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through extensive simulations and data analysis.

stat.ME↗

arXiv2018

Variance prior forms for high-dimensional Bayesian variable selection

Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection can have detrimental consequences for such variance estimation. Such priors are often motivated by the invariance argument of Jeffreys (1961). Revisiting this work, however, we highlight a caveat that Jeffreys himself noticed; namely that biased estimators can result from inducing dependence between parameters a priori. In a similar way, we show that conjugate priors for linear regression, which induce prior dependence, can lead to such underestimation in the Bayesian high-dimensional regression setting. Following Jeffreys, we recommend as a remedy to treat regression coefficients and the error variance as independent a priori. Using such an independence prior framework, we extend the Spike-and-Slab Lasso of Rockova and George (2018) to the unknown variance case. This extended procedure outperforms both the fixed variance approach and alternative penalized likelihood methods on simulated data. On the protein activity dataset of Clyde and Parmigiani (1998), the Spike-and-Slab Lasso with unknown variance achieves lower cross-validation error than alternative penalized likelihood methods, demonstrating the gains in predictive accuracy afforded by simultaneous error variance estimation.

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