Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching

We present three Fisher divergence (FD) minimization algorithms for learning Gaussian process (GP) based score models for lower dimensional density estimation problems. The density is formed by multiplying a base multivariate normal distribution with an exponentiated GP refinement, and so we refer to it as a GP-tilted nonparametric density. By representing the GP part of the score as a linear function using the random Fourier feature (RFF) approximation, we show that all learning problems can be solved in closed form. This includes the basic and noise conditional versions of the Fisher divergence, as well as a novel alternative to noise conditional FD models based on variational inference (VI). Here, we propose using an ELBO-like optimization of the approximate posterior with which we derive a Fisher variational predictive distribution. The RFF representation of the GP, which is functionally equivalent to a single layer neural network score model with cosine activation, provides a unique linear form for which all expectations are in closed form. The Gaussian base also helps with tractability of the VI approximation. We demonstrate our three learning algorithms, as well as a MAP baseline algorithm, on several low dimensional density estimation problems. The closed-form nature of the learning problem removes the reliance on iterative algorithms, making this technique particularly well-suited to large data sets.

FIESTA: Fisher Information-based Efficient Selective Test-time Adaptation

Robust facial expression recognition in unconstrained, "in-the-wild" environments remains challenging due to significant domain shifts between training and testing distributions. Test-time adaptation (TTA) offers a promising solution by adapting pre-trained models during inference without requiring labeled test data. However, existing TTA approaches typically rely on manually selecting which parameters to update, potentially leading to suboptimal adaptation and high computational costs. This paper introduces a novel Fisher-driven selective adaptation framework that dynamically identifies and updates only the most critical model parameters based on their importance as quantified by Fisher information. By integrating this principled parameter selection approach with temporal consistency constraints, our method enables efficient and effective adaptation specifically tailored for video-based facial expression recognition. Experiments on the challenging AffWild2 benchmark demonstrate that our approach significantly outperforms existing TTA methods, achieving a 7.7% improvement in F1 score over the base model while adapting only 22,000 parameters-more than 20 times fewer than comparable methods. Our ablation studies further reveal that parameter importance can be effectively estimated from minimal data, with sampling just 1-3 frames sufficient for substantial performance gains. The proposed approach not only enhances recognition accuracy but also dramatically reduces computational overhead, making test-time adaptation more practical for real-world affective computing applications.

Stein's unbiased risk estimate and Hyvärinen's score matching

We study two G-modeling strategies for estimating the signal distribution (the empirical Bayesian's prior) from observations corrupted with normal noise. First, we choose the signal distribution by minimizing Stein's unbiased risk estimate (SURE) of the implied Eddington/Tweedie Bayes denoiser, an approach motivated by optimal empirical Bayesian shrinkage estimation of the signals. Second, we select the signal distribution by minimizing Hyv\"arinen's score matching objective for the implied score (derivative of log-marginal density), targeting minimal Fisher divergence between estimated and true marginal densities. While these strategies appear distinct, they are known to be mathematically equivalent. We provide a unified analysis of SURE and score matching under both well-specified signal distribution classes and misspecification. In the classical well-specified setting with homoscedastic noise and compactly supported signal distribution, we establish nearly parametric rates of convergence of the empirical Bayes regret and the Fisher divergence. In a commonly studied misspecified model, we establish fast rates of convergence to the oracle denoiser and corresponding oracle inequalities. Our empirical results demonstrate competitiveness with nonparametric maximum likelihood in well-specified settings, while showing superior performance under misspecification, particularly in settings involving heteroscedasticity and side information.

Score Combining for Contrastive OOD Detection

In out-of-distribution (OOD) detection, one is asked to classify whether a test sample comes from a known inlier distribution or not. We focus on the case where the inlier distribution is defined by a training dataset and there exists no additional knowledge about the novelties that one is likely to encounter. This problem is also referred to as novelty detection, one-class classification, and unsupervised anomaly detection. The current literature suggests that contrastive learning techniques are state-of-the-art for OOD detection. We aim to improve on those techniques by combining/ensembling their scores using the framework of null hypothesis testing and, in particular, a novel generalized likelihood ratio test (GLRT). We demonstrate that our proposed GLRT-based technique outperforms the state-of-the-art CSI and SupCSI techniques from Tack et al. 2020 in dataset-vs-dataset experiments with CIFAR-10, SVHN, LSUN, ImageNet, and CIFAR-100, as well as leave-one-class-out experiments with CIFAR-10. We also demonstrate that our GLRT outperforms the score-combining methods of Fisher, Bonferroni, Simes, Benjamini-Hochwald, and Stouffer in our application.

Global dense vector representations for words or items using shared parameter alternating Tweedie model

In this article, we present a model for analyzing the cooccurrence count data derived from practical fields such as user-item or item-item data from online shopping platform, cooccurring word-word pairs in sequences of texts. Such data contain important information for developing recommender systems or studying relevance of items or words from non-numerical sources. Different from traditional regression models, there are no observations for covariates. Additionally, the cooccurrence matrix is typically of so high dimension that it does not fit into a computer's memory for modeling. We extract numerical data by defining windows of cooccurrence using weighted count on the continuous scale. Positive probability mass is allowed for zero observations. We present Shared parameter Alternating Tweedie (SA-Tweedie) model and an algorithm to estimate the parameters. We introduce a learning rate adjustment used along with the Fisher scoring method in the inner loop to help the algorithm stay on track of optimizing direction. Gradient descent with Adam update was also considered as an alternative method for the estimation. Simulation studies and an application showed that our algorithm with Fisher scoring and learning rate adjustment outperforms the other two methods. Pseudo-likelihood approach with alternating parameter update was also studied. Numerical studies showed that the pseudo-likelihood approach is not suitable in our shared parameter alternating regression models with unobserved covariates.

Matrix factorization and prediction for high dimensional co-occurrence count data via shared parameter alternating zero inflated Gamma model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word-word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item-item or user-item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize this data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item-item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to fi nd the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

Biological and Radiological Dictionary of Radiomics Features: Addressing Understandable AI Issues in Personalized Prostate Cancer; Dictionary version PM1.0

This study investigates the connection between visual semantic features in PI-RADS and associated risk factors, moving beyond abnormal imaging findings by creating a standardized dictionary of biological/radiological radiomics features (RFs). Using multiparametric prostate MRI sequences (T2-weighted imaging [T2WI], diffusion-weighted imaging [DWI], and apparent diffusion coefficient [ADC]), six interpretable and seven complex classifiers, combined with nine feature selection algorithms (FSAs), were applied to segmented lesions to predict UCLA scores. Combining T2WI, DWI, and ADC with FSAs such as ANOVA F-test, Correlation Coefficient, and Fisher Score, and utilizing logistic regression, identified key features: the 90th percentile from T2WI (hypo-intensity linked to cancer risk), variance from T2WI (lesion heterogeneity), shape metrics like Least Axis Length and Surface Area to Volume ratio from ADC (lesion compactness), and Run Entropy from ADC (texture consistency). This approach achieved an average accuracy of 0.78, outperforming single-sequence methods (p < 0.05). The developed dictionary provides a common language, fostering collaboration between clinical professionals and AI developers to enable trustworthy, interpretable AI for reliable clinical decisions.

AdaptiveMDL-GenClust: A Robust Clustering Framework Integrating Normalized Mutual Information and Evolutionary Algorithms

Clustering algorithms are pivotal in data analysis, enabling the organization of data into meaningful groups. However, individual clustering methods often exhibit inherent limitations and biases, preventing the development of a universal solution applicable to diverse datasets. To address these challenges, we introduce a robust clustering framework that integrates the Minimum Description Length (MDL) principle with a genetic optimization algorithm. The framework begins with an ensemble clustering approach to generate an initial clustering solution, which is then refined using MDL-guided evaluation functions and optimized through a genetic algorithm. This integration allows the method to adapt to the dataset's intrinsic properties, minimizing dependency on the initial clustering input and ensuring a data-driven, robust clustering process. We evaluated the proposed method on thirteen benchmark datasets using four established validation metrics: accuracy, normalized mutual information (NMI), Fisher score, and adjusted Rand index (ARI). Experimental results demonstrate that our approach consistently outperforms traditional clustering methods, yielding higher accuracy, improved stability, and reduced bias. The methods adaptability makes it effective across datasets with diverse characteristics, highlighting its potential as a versatile and reliable tool for complex clustering tasks. By combining the MDL principle with genetic optimization, this study offers a significant advancement in clustering methodology, addressing key limitations and delivering superior performance in varied applications.

Efficient Model Compression Techniques with FishLeg

In many domains, the most successful AI models tend to be the largest, indeed often too large to be handled by AI players with limited computational resources. To mitigate this, a number of compression methods have been developed, including methods that prune the network down to high sparsity whilst retaining performance. The best-performing pruning techniques are often those that use second-order curvature information (such as an estimate of the Fisher information matrix) to score the importance of each weight and to predict the optimal compensation for weight deletion. However, these methods are difficult to scale to high-dimensional parameter spaces without making heavy approximations. Here, we propose the FishLeg surgeon (FLS), a new second-order pruning method based on the Fisher-Legendre (FishLeg) optimizer. At the heart of FishLeg is a meta-learning approach to amortising the action of the inverse FIM, which brings a number of advantages. Firstly, the parameterisation enables the use of flexible tensor factorisation techniques to improve computational and memory efficiency without sacrificing much accuracy, alleviating challenges associated with scalability of most second-order pruning methods. Secondly, directly estimating the inverse FIM leads to less sensitivity to the amplification of stochasticity during inversion, thereby resulting in more precise estimates. Thirdly, our approach also allows for progressive assimilation of the curvature into the parameterisation. In the gradual pruning regime, this results in a more efficient estimate refinement as opposed to re-estimation. We find that FishLeg achieves higher or comparable performance against two common baselines in the area, most notably in the high sparsity regime when considering a ResNet18 model on CIFAR-10 (84% accuracy at 95% sparsity vs 60% for OBS) and TinyIM (53% accuracy at 80% sparsity vs 48% for OBS).

A Hybrid Framework for Statistical Feature Selection and Image-Based Noise-Defect Detection

In industrial imaging, accurately detecting and distinguishing surface defects from noise is critical and challenging, particularly in complex environments with noisy data. This paper presents a hybrid framework that integrates both statistical feature selection and classification techniques to improve defect detection accuracy while minimizing false positives. The motivation of the system is based on the generation of scalar scores that represent the likelihood that a region of interest (ROI) is classified as a defect or noise. We present around 55 distinguished features that are extracted from industrial images, which are then analyzed using statistical methods such as Fisher separation, chi-squared test, and variance analysis. These techniques identify the most discriminative features, focusing on maximizing the separation between true defects and noise. Fisher's criterion ensures robust, real-time performance for automated systems. This statistical framework opens up multiple avenues for application, functioning as a standalone assessment module or as an a posteriori enhancement to machine learning classifiers. The framework can be implemented as a black-box module that applies to existing classifiers, providing an adaptable layer of quality control and optimizing predictions by leveraging intuitive feature extraction strategies, emphasizing the rationale behind feature significance and the statistical rigor of feature selection. By integrating these methods with flexible machine learning applications, the proposed framework improves detection accuracy and reduces false positives and misclassifications, especially in complex, noisy environments.