arXiv subjects

Antonietta Mira

Publications and source records attributed to Antonietta Mira.

At least 19 recordsLinked to original sources

arXiv2026

Compatibility-based Bayesian inference: asymptotic limits, variational principles, and Wasserstein geometry

Approximate Bayesian Computation (ABC) replaces intractable likelihood evaluations with comparisons between observed and simulated data. We develop a measure-theoretic formulation of discrepancy-based Bayesian inference in which compatibility is encoded through nonnegative weights. For vanishing thresholds, we establish convergence of the corresponding posterior distributions in total variation. In the large-sample regime, we identify conditions under which the posterior converges to the prior conditioned on an asymptotic compatibility region, showing that concentration need not occur at a fixed positive tolerance. We also derive persistence bounds under weaker assumptions and prove stability of the associated entropy-regularized variational problems. For Wasserstein discrepancies, we obtain a geometric representation through distances from compatibility balls and an exact variational reduction to probability distributions over model laws.

math.ST↗

arXiv2026

Causal Posterior Estimation

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, where evaluating the likelihood function is intractable or computationally expensive, but generating outputs given parameter values is straightforward. CPE approximates the posterior distribution using flow matching while directly incorporating the conditional dependence structure induced by the model's graphical representation into the neural network architecture. Across extensive experiments, we demonstrate that hard-coding these conditional dependencies into the network, rather than requiring them to be learned from data, enables CPE to achieve highly accurate posterior inference that matches or outperforms state-of-the-art baselines.

cs.LG↗

arXiv2026

The Changing Geometry of Grammar: Dimensionality and Neighborhood Reorganization across Transformer Layers

Transformer representations describe trajectories through high-dimensional vector spaces, which are shaped dynamically as tokens incorporate relational context across layers. Such data tend to concentrate on lower-dimensional sub-manifolds, a form of compression quantified by the Intrinsic Dimensionality (ID), the minimum number of independent variables needed to represent them without significant information loss. In this work, we ask whether the grammatical role of tokens, as marked by their part-of-speech (PoS) tag, shapes the local geometry of this manifold. To this end: (1) We investigate the layer-wise evolution of ID, finding that closed-class items expand earlier and collapse sooner than open-class ones; (2) We show its expansion and contraction to be explained by changes in the neighborhood structure, and hence in the relations between words within a sentence; (3) We compare encoders (ModernBERT, bigbird-roberta-large) and decoders (gemma-2-2B, Llama-3.2-3B), finding that the two families evolve differently across layers, consistently with how each integrates context;(4) We show that geometric features alone recover a token's grammatical role, and use them to interpret how the semantic content of each PoS evolves across layers in a downstream classification task.

cs.CL↗

arXiv2026

Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification

The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound to the number of variables which are necessary to describe a system. However, in almost any real-world dataset the ID depends on the scale at which the data are analysed. Quite typically at a small scale, the ID is very large, as the data are affected by measurement errors. At large scale, the ID can also appear erroneously large, due to the curvature and the topology of the manifold containing the data. In this work, we introduce an automatic protocol to select the sweet spot, namely the correct range of scales in which the ID is meaningful and useful. This protocol is based on imposing that for distances smaller than the correct scale the density of the data is constant. In the presented framework, to estimate the density it is necessary to know the ID, therefore, this condition is imposed self-consistently. We illustrate the usefulness and robustness of this procedure to noise by benchmarks on artificial and real-world datasets.

stat.ML↗

arXiv2026

Likelihood distortion and Bayesian local robustness

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of quantities of interest while the prior changes within those classes. The literature has devoted much less attention to the robustness of Bayesian methods w.r.t. the likelihood function due to mathematical and computational complexity, and because it is often arguably considered a more objective choice compared to the prior. In this contribution, we propose a new approach to Bayesian local robustness, mainly focusing on robustness w.r.t. the likelihood function. Successively, we extend it to account for robustness w.r.t. the prior, as well as the prior and the likelihood jointly. This approach is based on the notion of distortion function introduced in the literature on risk theory. The novel robustness measure is a local sensitivity measure that turns out to be very tractable and easy to compute for several classes of distortion functions. Asymptotic properties are derived, and numerical experiments illustrate the theory and its applicability for modelling purposes.

math.ST↗

arXiv2026

A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics

Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model parameters by comparing model simulations with observations using a few carefully chosen summary statistics and a tolerance that can be decreased over time. Here, we present a new variant of simulated-annealing ABC algorithms, drawing intuition from non-equilibrium thermodynamics. We associate each summary statistic with a state variable (energy) quantifying its distance from the observed value, as well as a temperature that controls the extent to which the statistic contributes to the posterior. We derive an optimal annealing schedule on a Riemannian manifold of state variables based on a minimal-entropy-production principle. We validate our approach on standard benchmark tasks from the simulation-based inference literature as well as on challenging real-world inference problems, and show that it is highly competitive with the state of the art.

stat.CO↗

arXiv2026

Simulation-based Inference with the Python Package sbijax

Neural simulation-based inference (SBI) describes an emerging family of methods for Bayesian inference with intractable likelihood functions that use neural networks as surrogate models. Here we introduce sbijax, a Python package that implements a wide variety of state-of-the-art methods in neural simulation-based inference using a user-friendly programming interface. sbijax offers high-level functionality to quickly construct SBI estimators, and compute and visualize posterior distributions with only a few lines of code. In addition, the package provides functionality for conventional approximate Bayesian computation, to compute model diagnostics, and to automatically estimate summary statistics. By virtue of being entirely written in JAX, sbijax is extremely computationally efficient, allowing rapid training of neural networks and executing code automatically in parallel on both CPU and GPU.

cs.LG↗

arXiv2026

A general framework for adaptive nonparametric dimensionality reduction

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based on local neighbourhood structures and require tuning the number of neighbours that define this local structure, and the dimensionality of the lower-dimensional space onto which the data are projected. Such choices critically influence the quality of the resulting embedding. In this paper, we exploit a recently proposed intrinsic dimension estimator which also returns the optimal locally adaptive neighbourhood sizes according to some desirable criteria. In principle, this adaptive framework can be employed to perform an optimal hyper-parameter tuning of any dimensionality reduction algorithm that relies on local neighbourhood structures. Numerical experiments on both real-world and simulated datasets show that the proposed method can be used to significantly improve well-known projection methods when employed for various learning tasks, with improvements measurable through both quantitative metrics and the quality of low-dimensional visualizations.

stat.ML↗

arXiv2025

Navigating through the hidden embedding space: steering LLMs to improve mental health assessment

The rapid evolution of Large Language Models (LLMs) is transforming AI, opening new opportunities in sensitive and high-impact areas such as Mental Health (MH). Yet, despite these advancements, recent evidence reveals that smaller-scale models still struggle to deliver optimal performance in domain-specific applications. In this study, we present a cost-efficient yet powerful approach to improve MH assessment capabilities of an LLM, without relying on any computationally intensive techniques. Our lightweight method consists of a linear transformation applied to a specific layer's activations, leveraging steering vectors to guide the model's output. Remarkably, this intervention enables the model to achieve improved results across two distinct tasks: (1) identifying whether a Reddit post is useful for detecting the presence or absence of depressive symptoms (relevance prediction task), and (2) completing a standardized psychological screening questionnaire for depression based on users' Reddit post history (questionnaire completion task). Results highlight the untapped potential of steering mechanisms as computationally efficient tools for LLMs' MH domain adaptation.

cs.CL↗

arXiv2025

Non-parametric Causal Discovery for EU Allowances Returns Through the Information Imbalance

We propose to use a recently introduced non-parametric tool named Differentiable Information Imbalance (DII) to identify variables that are causally related -- potentially through non-linear relationships -- to the financial returns of the European Union Allowances (EUAs) within the EU Emissions Trading System (EU ETS). We examine data from January 2013 to April 2024 and compare the DII approach with multivariate Granger causality, a well-known linear approach based on VAR models. We find significant overlap among the causal variables identified by linear and non-linear methods, such as the coal futures prices and the IBEX35 index. We also find important differences between the two causal sets identified. On two synthetic datasets, we show how these differences could originate from limitations of the linear methodology.

q-fin.CP↗

arXiv2025

Are LLMs effective psychological assessors? Leveraging adaptive RAG for interpretable mental health screening through psychometric practice

In psychological practices, standardized questionnaires serve as essential tools for assessing mental health through structured, clinically-validated questions (i.e., items). While social media platforms offer rich data for mental health screening, computational approaches often bypass these established clinical assessment tools in favor of black-box classification. We propose a novel questionnaire-guided screening framework that bridges psychological practice and computational methods through adaptive Retrieval-Augmented Generation (\textit{aRAG}). Our approach links unstructured social media content and standardized clinical assessments by retrieving relevant posts for each questionnaire item and using Large Language Models (LLMs) to complete validated psychological instruments. Our findings demonstrate two key advantages of questionnaire-guided screening: First, when completing the Beck Depression Inventory-II (BDI-II), our approach matches or outperforms state-of-the-art performance on Reddit-based benchmarks without requiring training data. Second, we show that guiding LLMs through standardized questionnaires can yield superior results compared to directly prompting them for depression screening, while also providing a more interpretable assessment by linking model outputs to clinically validated diagnostic criteria. Additionally, we show, as a proof-of-concept, how our questionnaire-based methodology can be extended to other mental conditions' screening, highlighting the promising role of LLMs as psychological assessors.

cs.CL↗

arXiv2025

Constructing Simultaneous Confidence Bands for Errors-in-variables Curves with Application to the Lorenz Curve

Errors-in-variables curves are curves where errors exist not only in the independent variable but also in the dependent variable. We address the challenge of constructing simultaneous confidence bands (SCBs) for such curves. Our method finds application in the Lorenz curve, which represents the concentration of income or wealth. Unlike ordinary regression curves, the Lorenz curve incorporates errors in its explanatory variable and requires a fundamentally different treatment. To the best of our knowledge, the development of SCBs for such curves has not been explored in previous research. Using the Lorenz curve as a case study, this paper proposes a novel approach to address this challenge.

stat.AP↗

arXiv2024

Bayesian Dynamic Generalized Additive Model for Mortality during COVID-19 Pandemic

While COVID-19 has resulted in a significant increase in global mortality rates, the impact of the pandemic on mortality from other causes remains uncertain. To gain insight into the broader effects of COVID-19 on various causes of death, we analyze an Italian dataset that includes monthly mortality counts for different causes from January 2015 to December 2020. Our approach involves a generalized additive model enhanced with correlated random effects. The generalized additive model component effectively captures non-linear relationships between various covariates and mortality rates, while the random effects are multivariate time series observations recorded in various locations, and they embody information on the dependence structure present among geographical locations and different causes of mortality. Adopting a Bayesian framework, we impose suitable priors on the model parameters. For efficient posterior computation, we employ variational inference, specifically for fixed effect coefficients and random effects, Gaussian variational approximation is assumed, which streamlines the analysis process. The optimisation is performed using a coordinate ascent variational inference algorithm and several computational strategies are implemented along the way to address the issues arising from the high dimensional nature of the data, providing accelerated and stabilised parameter estimation and statistical inference.

stat.AP↗

arXiv2024

Investigating the price determinants of the European Emission Trading System: a non-parametric approach

The European carbon market plays a pivotal role in the European Union's ambitious target of achieving carbon neutrality by 2050. Understanding the intricacies of factors influencing European Union Emission Trading System (EU ETS) market prices is paramount for effective policy making and strategy implementation. We propose the use of the Information Imbalance, a recently introduced non-parametric measure quantifying the degree to which a set of variables is informative with respect to another one, to study the relationships among macroeconomic, economic, uncertainty, and energy variables concerning EU ETS prices. Our analysis shows that in Phase 3 commodity related variables such as the ERIX index are the most informative to explain the behaviour of the EU ETS market price. Transitioning to Phase 4, financial fluctuations take centre stage, with the uncertainty in the EUR/CHF exchange rate emerging as a crucial determinant. These results reflect the disruptive impacts of the COVID-19 pandemic and the energy crisis in reshaping the importance of the different variables. Beyond variable analysis, we also propose to leverage the Information Imbalance to address the problem of mixed-frequency forecasting, and we identify the weekly time scale as the most informative for predicting the EU ETS price. Finally, we show how the Information Imbalance can be effectively combined with Gaussian Process regression for efficient nowcasting and forecasting using very small sets of highly informative predictors.

q-fin.ST↗

arXiv2024

Federated Learning for Non-factorizable Models using Deep Generative Prior Approximations

Federated learning (FL) allows for collaborative model training across decentralized clients while preserving privacy by avoiding data sharing. However, current FL methods assume conditional independence between client models, limiting the use of priors that capture dependence, such as Gaussian processes (GPs). We introduce the Structured Independence via deep Generative Model Approximation (SIGMA) prior which enables FL for non-factorizable models across clients, expanding the applicability of FL to fields such as spatial statistics, epidemiology, environmental science, and other domains where modeling dependencies is crucial. The SIGMA prior is a pre-trained deep generative model that approximates the desired prior and induces a specified conditional independence structure in the latent variables, creating an approximate model suitable for FL settings. We demonstrate the SIGMA prior's effectiveness on synthetic data and showcase its utility in a real-world example of FL for spatial data, using a conditional autoregressive prior to model spatial dependence across Australia. Our work enables new FL applications in domains where modeling dependent data is essential for accurate predictions and decision-making.

stat.ML↗

arXiv2024

Scalable Vertical Federated Learning via Data Augmentation and Amortized Inference

Vertical federated learning (VFL) has emerged as a paradigm for collaborative model estimation across multiple clients, each holding a distinct set of covariates. This paper introduces the first comprehensive framework for fitting Bayesian models in the VFL setting. We propose a novel approach that leverages data augmentation techniques to transform VFL problems into a form compatible with existing Bayesian federated learning algorithms. We present an innovative model formulation for specific VFL scenarios where the joint likelihood factorizes into a product of client-specific likelihoods. To mitigate the dimensionality challenge posed by data augmentation, which scales with the number of observations and clients, we develop a factorized amortized variational approximation that achieves scalability independent of the number of observations. We showcase the efficacy of our framework through extensive numerical experiments on logistic regression, multilevel regression, and a novel hierarchical Bayesian split neural net model. Our work paves the way for privacy-preserving, decentralized Bayesian inference in vertically partitioned data scenarios, opening up new avenues for research and applications in various domains.

stat.CO↗

arXiv2023

Bayesian Poisson Regression and Tensor Train Decomposition Model for Learning Mortality Pattern Changes during COVID-19 Pandemic

COVID-19 has led to excess deaths around the world, however it remains unclear how the mortality of other causes of death has changed during the pandemic. Aiming at understanding the wider impact of COVID-19 on other death causes, we study Italian data set that consists of monthly mortality counts of different causes from January 2015 to December 2020. Due to the high dimensional nature of the data, we develop a model which combines conventional Poisson regression with tensor train decomposition to explore the lower dimensional residual structure of the data. We take a Bayesian approach, impose priors on model parameters. Posterior inference is performed using an efficient Metropolis-Hastings within Gibbs algorithm. The validity of our approach is tested in simulation studies. Our method not only identifies differential effects of interventions on cause specific mortality rates through the Poisson regression component, but also offers informative interpretations of the relationship between COVID-19 and other causes of death as well as latent classes that underline demographic characteristics, temporal patterns and causes of death respectively.

stat.AP↗

arXiv2023

Multiple hypothesis screening using mixtures of non-local distributions with applications to genomic studies

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian False Discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.

stat.ME↗