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Approximately Unimodal Likelihood Models for Ordinal Regression

Yamasaki, Ryoya

arXiv.org Machine Learning

Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable. A key to successful OR models is to find a data structure `natural ordinal relation' common to many ordinal data and reflect that structure into the design of those models. A recent OR study found that many real-world ordinal data show a tendency that the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable will often be unimodal. Several previous studies thus developed unimodal likelihood models, in which a predicted CPD is guaranteed to become unimodal. However, it was also observed experimentally that many real-world ordinal data partly have values of the explanatory variable where the underlying CPD will be non-unimodal, and hence unimodal likelihood models may suffer from a bias for such a CPD. Therefore, motivated to mitigate such a bias, we propose approximately unimodal likelihood models, which can represent up to a unimodal CPD and a CPD that is close to be unimodal. We also verify experimentally that a proposed model can be effective for statistical modeling of ordinal data and OR tasks.


Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs

Neural Information Processing Systems

The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple probabilistic graphics programs that define flexible generative models and to automatically invert them to interpret real-world images. Generative probabilistic graphics programs consist of a stochastic scene generator, a renderer based on graphics software, a stochastic likelihood model linking the renderer's output and the data, and latent variables that adjust the fidelity of the renderer and the tolerance of the likelihood model. Representations and algorithms from computer graphics, originally designed to produce high-quality images, are instead used as the deterministic backbone for highly approximate and stochastic generative models.



Sampling-Based Estimation of Jaccard Containment and Similarity

Joshi, Pranav

arXiv.org Machine Learning

Estimating set similarity measures is a fundamental problem in data analysis, with applications in information retrieval, database systems, and streaming algorithms. Among such measures, the Jaccard containment of two sets A, B--defined as ϕ = | A B | |A | [0, 1] when A is treated as the reference set--is particularly important in asymmetric comparison tasks, such as detecting near-duplicates or containment-based joins. In large-scale settings, exact computation of ϕ may be infeasible, as it requires full knowledge of both sets. Sampling-based estimators that use small random subsets P A and Q B can be used as scalable alternatives when the sizes |A |, |B | are known, such as in Oracle databases. This paper presents a theoretical analysis of the likelihood models and estimation strategies for Jaccard containment based on random samples, focusing on both empirical performance and statistical guarantees.


Bayesian Inference of Training Dataset Membership

Huang, Yongchao

arXiv.org Artificial Intelligence

Machine learning models, particularly deep neural networks, are vulnerable to privacy attacks such as membership inference attacks (MIAs), which determine whether a specific data point was included in a model's training set [9, 10, 2]. These attacks exploit the tendency of models to exhibit distinct behaviors (e.g. higher confidence or lower loss) on training data compared to unseen data, potentially compromising the confidentiality of sensitive datasets, such as those containing medical or financial records. State-of-the-art MIAs typically rely on extensive knowledge of the target model. For example, shadow model-based approaches [9] train multiple models to mimic the target's behavior, while others, e.g. the likelihood ratio attack (LiRA) by Carlini et al. [2], leverage model outputs or gradients. These methods often induce significant computational costs or require access to model internals, limiting their applicability in scenarios where only model outputs are available. We propose a new MIA method that leverages Bayesian inference for post-hoc analysis of trained model and datasets. Once a ML model, e.g. a neural network, has been trained on member datasets, we pass the test data through the trained ML model, and extract resulting metrics such as accuracy, entropy, perturbation magnitude, and dataset statistics, and uses these metrics to compute posterior probabilities of membership. This approach doesn't require access to a'training' set, although known knowledge about member and non-member datasets can improve its performance. This post-hoc method is computationally efficient, interpretable, requires minimum model query and fine-tuning, making it well-suited for real-world deployment scenarios where privacy assessments are conducted after model training.


Doubly Adaptive Social Learning

Carpentiero, Marco, Bordignon, Virginia, Matta, Vincenzo, Sayed, Ali H.

arXiv.org Artificial Intelligence

In social learning, a network of agents assigns probability scores (beliefs) to some hypotheses of interest, which rule the generation of local streaming data observed by each agent. Belief formation takes place by means of an iterative two-step procedure where: i) the agents update locally their beliefs by using some likelihood model; and ii) the updated beliefs are combined with the beliefs of the neighboring agents, using a pooling rule. This procedure can fail to perform well in the presence of dynamic drifts, leading the agents to incorrect decision making. Here, we focus on the fully online setting where both the true hypothesis and the likelihood models can change over time. This goal is achieved by exploiting two adaptation stages: i) a stochastic gradient descent update to learn and track the drifts in the decision model; ii) and an adaptive belief update to track the true hypothesis changing over time. These stages are controlled by two adaptation parameters that govern the evolution of the error probability for each agent. We show that all agents learn consistently for sufficiently small adaptation parameters, in the sense that they ultimately place all their belief mass on the true hypothesis. Index T erms Social learning, belief formation, decision making, distributed optimization, online leaerning, opinion diffusion over graphs. Marco Carpentiero and Vincenzo Matta are with the Department of Information and Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, via Giovanni Paolo II, I-84084, Fisciano (SA), Italy, and Vincenzo Matta is also with the National Inter-University Consortium for Telecommunications (CNIT), Italy (e-mails: { mcarpentiero, vmatta }@unisa.it). Matta was partially supported by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Telecommunications of the Future" (PE00000001 - program "REST ART"). This work was produced while Virginia Bordignon was a post-doc with the Ecole Polytechnique F ed erale de Lausanne EPFL, School of Engineering, CH-1015 Lausanne, Switzerland (e-mail: virginia.bordignon@alumni.epfl.ch).