arXiv subjects

Nicolo Colombo

Publications and source records attributed to Nicolo Colombo.

At least 19 recordsLinked to original sources

arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗

arXiv2026

Combining gravitational wave search pipelines to find subthreshold signals in GWTC-5.0

The detection of transient gravitational wave signals relies on independent search algorithms that analyse detector data and assign significance measures to candidate events. However, varying performance complicates their interpretation. We use supervised machine learning combined with conformal prediction, a framework to quantify uncertainties, to merge multi-pipeline information into well-calibrated confidence scores. We demonstrate that this approach is robust across different classifier architectures and remains stable when trained on different simulated datasets. When applied to events across the GWTC catalogue up to and including the second part of the fourth observing run, the framework identifies several subthreshold candidates with elevated confidence, including the binary neutron star candidate GW200311_103121. We examine the reliability of these up-rankings, finding evidence that high-confidence predictions correspond to signal-like events. This framework enables simplified systematic candidate assessment for gravitational wave catalogues and real-time alerts by providing a single, well-calibrated confidence measure per candidate.

gr-qc↗

arXiv2025

Residual Reweighted Conformal Prediction for Graph Neural Networks

Graph Neural Networks (GNNs) excel at modeling relational data but face significant challenges in high-stakes domains due to unquantified uncertainty. Conformal prediction (CP) offers statistical coverage guarantees, but existing methods often produce overly conservative prediction intervals that fail to account for graph heteroscedasticity and structural biases. While residual reweighting CP variants address some of these limitations, they neglect graph topology, cluster-specific uncertainties, and risk data leakage by reusing training sets. To address these issues, we propose Residual Reweighted GNN (RR-GNN), a framework designed to generate minimal prediction sets with provable marginal coverage guarantees. RR-GNN introduces three major innovations to enhance prediction performance. First, it employs Graph-Structured Mondrian CP to partition nodes or edges into communities based on topological features, ensuring cluster-conditional coverage that reflects heterogeneity. Second, it uses Residual-Adaptive Nonconformity Scores by training a secondary GNN on a held-out calibration set to estimate task-specific residuals, dynamically adjusting prediction intervals according to node or edge uncertainty. Third, it adopts a Cross-Training Protocol, which alternates the optimization of the primary GNN and the residual predictor to prevent information leakage while maintaining graph dependencies. We validate RR-GNN on 15 real-world graphs across diverse tasks, including node classification, regression, and edge weight prediction. Compared to CP baselines, RR-GNN achieves improved efficiency over state-of-the-art methods, with no loss of coverage.

cs.LG↗

arXiv2025

Enhancing gravitational-wave detection: a machine learning pipeline combination approach with robust uncertainty quantification

Gravitational-wave data from advanced-era interferometric detectors consists of background Gaussian noise, frequent transient artefacts, and rare astrophysical signals. Multiple search algorithms exist to detect the signals from compact binary coalescences, but their varying performance complicates interpretation. We present a machine learning-driven approach that combines results from individual pipelines and utilises conformal prediction to provide robust, calibrated uncertainty quantification. Using simulations, we demonstrate improved detection efficiency and apply our model to GWTC-3, enhancing confidence in multi-pipeline detections, such as the sub-threshold binary neutron star candidate GW200311_103121.

gr-qc↗

arXiv2025

Assumption-free fidelity bounds for hardware noise characterization

In the Quantum Supremacy regime, quantum computers may overcome classical machines on several tasks if we can estimate, mitigate, or correct unavoidable hardware noise. Estimating the error requires classical simulations, which become unfeasible in the Quantum Supremacy regime. We leverage Machine Learning data-driven approaches and Conformal Prediction, a Machine Learning uncertainty quantification tool known for its mild assumptions and finite-sample validity, to find theoretically valid upper bounds of the fidelity between noiseless and noisy outputs of quantum devices. Under reasonable extrapolation assumptions, the proposed scheme applies to any Quantum Computing hardware, does not require modeling the device's noise sources, and can be used when classical simulations are unavailable, e.g. in the Quantum Supremacy regime.

quant-ph↗

arXiv2025

Enhanced Route Planning with Calibrated Uncertainty Set

This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which leverages the conformal prediction technique to offer a coverage guarantee, thus improving the reliability and robustness of our predictions. By incorporating uncertainty sets derived from CQR-GAE, we substantially improve the decision-making process in route planning under a robust optimization framework. We demonstrate the effectiveness of our approach by applying the CQR-GAE model to a real-world traffic scenario. The results indicate that our model significantly outperforms baseline methods, offering a promising avenue for advancing intelligent transportation systems.

cs.LG↗

arXiv2024

Classification uncertainty for transient gravitational-wave noise artefacts with optimised conformal prediction

With the increasing use of Machine Learning (ML) algorithms in scientific research comes the need for reliable uncertainty quantification. When taking a measurement it is not enough to provide the result, we also have to declare how confident we are in the measurement. This is also true when the results are obtained from a ML algorithm, and arguably more so since the internal workings of ML algorithms are often less transparent compared to traditional statistical methods. Additionally, many ML algorithms do not provide uncertainty estimates and auxiliary algorithms must be applied. Conformal Prediction (CP) is a framework to provide such uncertainty quantifications for ML point predictors. In this paper, we explore the use and properties of CP applied in the context of glitch classification in gravitational wave astronomy. Specifically, we demonstrate the application of CP to the Gravity Spy glitch classification algorithm. CP makes use of a score function, a nonconformity measure, to convert an algorithm's heuristic notion of uncertainty to a rigorous uncertainty. We use the application on Gravity Spy to explore the performance of different nonconformity measures and optimise them for our application. Our results show that the optimal nonconformity measure depends on the specific application, as well as the metric used to quantify the performance.

gr-qc↗

arXiv2024

Learning in the Recurrent State: Gradient Descent with Linear Recurrent Networks

Linear recurrent networks (LRNNs) offer linear-time sequence modeling, but standard recurrent updates do not directly expose the supervised products needed for in-context gradient descent. We propose a sufficient constructive inductive bias for LRNNs: equip a diagonal recurrent state with multiplicative readout and a short sliding-window cross-product self-attention update. The resulting architecture, Gradient-based Recurrent In-context Learner (GRIL), can implement minibatch gradient descent on a task-specific linear predictor during a single forward pass. The same design extends to multi-step updates and cross-entropy classification, with a limited MLP-based extension to non-linear regression. Empirically, trained GRILs recover the behavior and parameters predicted by the construction on synthetic ICL tasks, and the same architectural bias yields useful performance on Long Range Arena and language modelling. These results present windowed cross-product self-attention as a practical, testable inductive bias for LRNNs that learn in context through gradient-descent-like updates.

cs.LG↗

arXiv2024

Entropy Reweighted Conformal Classification

Conformal Prediction (CP) is a powerful framework for constructing prediction sets with guaranteed coverage. However, recent studies have shown that integrating confidence calibration with CP can lead to a degradation in efficiency. In this paper, We propose an adaptive approach that considers the classifier's uncertainty and employs entropy-based reweighting to enhance the efficiency of prediction sets for conformal classification. Our experimental results demonstrate that this method significantly improves efficiency.

cs.LG↗

arXiv2024

Conformal Load Prediction with Transductive Graph Autoencoders

Predicting edge weights on graphs has various applications, from transportation systems to social networks. This paper describes a Graph Neural Network (GNN) approach for edge weight prediction with guaranteed coverage. We leverage conformal prediction to calibrate the GNN outputs and produce valid prediction intervals. We handle data heteroscedasticity through error reweighting and Conformalized Quantile Regression (CQR). We compare the performance of our method against baseline techniques on real-world transportation datasets. Our approach has better coverage and efficiency than all baselines and showcases robustness and adaptability.

cs.LG↗

arXiv2024

Normalizing Flows for Conformal Regression

Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction model by calibrating its outputs on labeled data. The same calibration scheme usually applies to any model and data without modifications. The obtained prediction intervals are valid by construction but could be inefficient, i.e. unnecessarily big, if the prediction errors are not uniformly distributed over the input space. We present a general scheme to localize the intervals by training the calibration process. The standard prediction error is replaced by an optimized distance metric that depends explicitly on the object attributes. Learning the optimal metric is equivalent to training a Normalizing Flow that acts on the joint distribution of the errors and the inputs. Unlike the Error Reweighting CP algorithm of Papadopoulos et al. (2008), the framework allows estimating the gap between nominal and empirical conditional validity. The approach is compatible with existing locally-adaptive CP strategies based on re-weighting the calibration samples and applies to any point-prediction model without retraining.

cs.LG↗

arXiv2024

Calibrating gravitational-wave search algorithms with conformal prediction

In astronomy, we frequently face the decision problem: does this data contain a signal? Typically, a statistical approach is used, which requires a threshold. The choice of threshold presents a common challenge in settings where signals and noise must be delineated, but their distributions overlap. Gravitational-wave astronomy, which has gone from the first discovery to catalogues of hundreds of events in less than a decade, presents a fascinating case study. For signals from colliding compact objects, the field has evolved from a frequentist to a Bayesian methodology. However, the issue of choosing a threshold and validating noise contamination in a catalogue persists. Confusion and debate often arise due to the misapplication of statistical concepts, the complicated nature of the detection statistics, and the inclusion of astrophysical background models. We introduce Conformal Prediction (CP), a framework developed in Machine Learning to provide distribution-free uncertainty quantification to point predictors. We show that CP can be viewed as an extension of the traditional statistical frameworks whereby thresholds are calibrated such that the uncertainty intervals are statistically rigorous and the error rate can be validated. Moreover, we discuss how CP offers a framework to optimally build a meta-pipeline combining the outputs from multiple independent searches. We introduce CP with a toy cosmic-ray detector, which captures the salient features of most astrophysical search problems and allows us to demonstrate the features of CP in a simple context. We then apply the approach to a recent gravitational-wave Mock Data Challenge using multiple search algorithms for compact binary coalescence signals in interferometric gravitational-wave data. Finally, we conclude with a discussion on the future potential of the method for gravitational-wave astronomy.

gr-qc↗

arXiv2023

On training locally adaptive CP

We address the problem of making Conformal Prediction (CP) intervals locally adaptive. Most existing methods focus on approximating the object-conditional validity of the intervals by partitioning or re-weighting the calibration set. Our strategy is new and conceptually different. Instead of re-weighting the calibration data, we redefine the conformity measure through a trainable change of variables, $A \to \phi_X(A)$, that depends explicitly on the object attributes, $X$. Under certain conditions and if $\phi_X$ is monotonic in $A$ for any $X$, the transformations produce prediction intervals that are guaranteed to be marginally valid and have $X$-dependent sizes. We describe how to parameterize and train $\phi_X$ to maximize the interval efficiency. Contrary to other CP-aware training methods, the objective function is smooth and can be minimized through standard gradient methods without approximations.

cs.LG↗

arXiv2021

Differentiable Architecture Pruning for Transfer Learning

We propose a new gradient-based approach for extracting sub-architectures from a given large model. Contrarily to existing pruning methods, which are unable to disentangle the network architecture and the corresponding weights, our architecture-pruning scheme produces transferable new structures that can be successfully retrained to solve different tasks. We focus on a transfer-learning setup where architectures can be trained on a large data set but very few data points are available for fine-tuning them on new tasks. We define a new gradient-based algorithm that trains architectures of arbitrarily low complexity independently from the attached weights. Given a search space defined by an existing large neural model, we reformulate the architecture search task as a complexity-penalized subset-selection problem and solve it through a two-temperature relaxation scheme. We provide theoretical convergence guarantees and validate the proposed transfer-learning strategy on real data.

cs.LG↗

arXiv2021

Adapting by Pruning: A Case Study on BERT

Adapting pre-trained neural models to downstream tasks has become the standard practice for obtaining high-quality models. In this work, we propose a novel model adaptation paradigm, adapting by pruning, which prunes neural connections in the pre-trained model to optimise the performance on the target task; all remaining connections have their weights intact. We formulate adapting-by-pruning as an optimisation problem with a differentiable loss and propose an efficient algorithm to prune the model. We prove that the algorithm is near-optimal under standard assumptions and apply the algorithm to adapt BERT to some GLUE tasks. Results suggest that our method can prune up to 50% weights in BERT while yielding similar performance compared to the fine-tuned full model. We also compare our method with other state-of-the-art pruning methods and study the topological differences of their obtained sub-networks.

cs.LG↗

arXiv2020

Disentangling Neural Architectures and Weights: A Case Study in Supervised Classification

The history of deep learning has shown that human-designed problem-specific networks can greatly improve the classification performance of general neural models. In most practical cases, however, choosing the optimal architecture for a given task remains a challenging problem. Recent architecture-search methods are able to automatically build neural models with strong performance but fail to fully appreciate the interaction between neural architecture and weights. This work investigates the problem of disentangling the role of the neural structure and its edge weights, by showing that well-trained architectures may not need any link-specific fine-tuning of the weights. We compare the performance of such weight-free networks (in our case these are binary networks with {0, 1}-valued weights) with random, weight-agnostic, pruned and standard fully connected networks. To find the optimal weight-agnostic network, we use a novel and computationally efficient method that translates the hard architecture-search problem into a feasible optimization problem.More specifically, we look at the optimal task-specific architectures as the optimal configuration of binary networks with {0, 1}-valued weights, which can be found through an approximate gradient descent strategy. Theoretical convergence guarantees of the proposed algorithm are obtained by bounding the error in the gradient approximation and its practical performance is evaluated on two real-world data sets. For measuring the structural similarities between different architectures, we use a novel spectral approach that allows us to underline the intrinsic differences between real-valued networks and weight-free architectures.

cs.LG↗

arXiv2020

Training conformal predictors

Efficiency criteria for conformal prediction, such as \emph{observed fuzziness} (i.e., the sum of p-values associated with false labels), are commonly used to \emph{evaluate} the performance of given conformal predictors. Here, we investigate whether it is possible to exploit efficiency criteria to \emph{learn} classifiers, both conformal predictors and point classifiers, by using such criteria as training objective functions. The proposed idea is implemented for the problem of binary classification of hand-written digits. By choosing a 1-dimensional model class (with one real-valued free parameter), we can solve the optimization problems through an (approximate) exhaustive search over (a discrete version of) the parameter space. Our empirical results suggest that conformal predictors trained by minimizing their observed fuzziness perform better than conformal predictors trained in the traditional way by minimizing the \emph{prediction error} of the corresponding point classifier. They also have a reasonable performance in terms of their prediction error on the test set.

cs.LG↗

arXiv2020

Multiple Metric Learning for Structured Data

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.

cs.LG↗