arXiv subjects

Felipe Tobar

Publications and source records attributed to Felipe Tobar.

At least 19 recordsLinked to original sources

arXiv2026

Unconditional flow-based time series generation with equivariance-regularised latent spaces

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance properties for time-series generative modelling remains underexplored. In this work, we propose a latent flow-matching framework in which equivariance is explicitly encouraged through a simple regularisation of a pre-trained autoencoder. Specifically, we introduce an equivariance loss that enforces consistency between transformed signals and their reconstructions, and use it to fine-tune latent spaces with respect to basic time-series transformations such as translation and amplitude scaling. We show that these equivariance-regularised latent spaces improve generation quality while preserving the computational advantages of latent flow models. Experiments on multiple real-world datasets demonstrate that our approach consistently outperforms existing diffusion-based baselines in standard time-series generation metrics, while achieving orders-of-magnitude faster sampling. These results highlight the practical benefits of incorporating geometric inductive biases into latent generative models for time series.

cs.LG↗

arXiv2026

Synthesizing Epileptic Seizures: Gaussian Processes for EEG Generation

Reliable seizure detection from electroencephalography (EEG) time series is a high-priority clinical goal, yet the acquisition cost and scarcity of labeled EEG data limit the performance of machine learning methods. This challenge is exacerbated by the long-range, high-dimensional, and non-stationary nature of epileptic EEG recordings, which makes realistic data generation particularly difficult. In this work, we revisit Gaussian processes as a principled and interpretable foundation for modeling EEG dynamics, and propose a novel hierarchical framework, \textit{GP-EEG}, for generating synthetic epileptic EEG recordings. At its core, our approach decomposes EEG signals into temporal segments modeled via Gaussian process regression, and integrates a domain-adaptation variational autoencoder. We validate the proposed method on two real-world, open-source epileptic EEG datasets. The synthetic EEG recordings generated by our model match real-world epileptic EEG both quantitatively and qualitatively, and can be used to augment training sets.

stat.ME↗

arXiv2026

Accelerated training of Gaussian processes using banded square exponential covariances

We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure to eliminate those entries to produce a \emph{banded}-matrix approximation to the original covariance, whose inverse and determinant can be computed at a reduced computational cost, thus contributing to an efficient approximation to the likelihood function. We provide a theoretical analysis of the proposed method to preserve the structure of the original covariance in the 1D setting with SE kernel, and validate its computational efficiency against the variational free energy approach to sparse GPs.

cs.LG↗

arXiv2026

Efficient Gaussian process learning via subspace projections

We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a closed-form expression for the information loss related to the PL and empirically show that it can be reduced with random projections on the unit sphere. We show the superiority of the PL, in terms of accuracy and computational efficiency, over the exact GP training and the variational free energy approach to sparse GPs over different optimisers, kernels and datasets of moderately large sizes.

cs.LG↗

arXiv2025

AI for a Planet Under Pressure

Artificial intelligence (AI) is already driving scientific breakthroughs in a variety of research fields, ranging from the life sciences to mathematics. This raises a critical question: can AI be applied both responsibly and effectively to address complex and interconnected sustainability challenges? This report is the result of a collaboration between the Stockholm resilience Centre (Stockholm University), the Potsdam Institute for Climate Impact Research (PIK), and Google DeepMind. Our work explores the potential and limitations of using AI as a research method to help tackle eight broad sustainability challenges. The results build on iterated expert dialogues and assessments, a systematic AI-supported literature overview including over 8,500 academic publications, and expert deep-dives into eight specific issue areas. The report also includes recommendations to sustainability scientists, research funders, the private sector, and philanthropies.

cs.CY↗

arXiv2025

Diffusion Self-Weighted Guidance for Offline Reinforcement Learning

Offline reinforcement learning (RL) recovers the optimal policy $\pi$ given historical observations of an agent. In practice, $\pi$ is modeled as a weighted version of the agent's behavior policy $\mu$, using a weight function $w$ working as a critic of the agent's behavior. Though recent approaches to offline RL based on diffusion models have exhibited promising results, the computation of the required scores is challenging due to their dependence on the unknown $w$. In this work, we alleviate this issue by constructing a diffusion over both the actions and the weights. With the proposed setting, the required scores are directly obtained from the diffusion model without learning extra networks. Our main conceptual contribution is a novel guidance method, where guidance (which is a function of $w$) comes from the same diffusion model, therefore, our proposal is termed Self-Weighted Guidance (SWG). We show that SWG generates samples from the desired distribution on toy examples and performs on par with state-of-the-art methods on D4RL's challenging environments, while maintaining a streamlined training pipeline. We further validate SWG through ablation studies on weight formulations and scalability.

cs.LG↗

arXiv2025

Towards SFW sampling for diffusion models via external conditioning

Score-based generative models (SBM), also known as diffusion models, are the de facto state of the art for image synthesis. Despite their unparalleled performance, SBMs have recently been in the spotlight for being tricked into creating not-safe-for-work (NSFW) content, such as violent images and non-consensual nudity. Current approaches that prevent unsafe generation are based on the models' own knowledge, and the majority of them require fine-tuning. This article explores the use of external sources for ensuring safe outputs in SBMs. Our safe-for-work (SFW) sampler implements a Conditional Trajectory Correction step that guides the samples away from undesired regions in the ambient space using multimodal models as the source of conditioning. Furthermore, using Contrastive Language Image Pre-training (CLIP), our method admits user-defined NSFW classes, which can vary in different settings. Our experiments on the text-to-image SBM Stable Diffusion validate that the proposed SFW sampler effectively reduces the generation of explicit content while being competitive with other fine-tuning-based approaches, as assessed via independent NSFW detectors. Moreover, we evaluate the impact of the SFW sampler on image quality and show that the proposed correction scheme comes at a minor cost with negligible effect on samples not needing correction. Our study confirms the suitability of the SFW sampler towards aligned SBM models and the potential of using model-agnostic conditioning for the prevention of unwanted images.

cs.CV↗

arXiv2024

Avoiding mode collapse in diffusion models fine-tuned with reinforcement learning

Fine-tuning foundation models via reinforcement learning (RL) has proven promising for aligning to downstream objectives. In the case of diffusion models (DMs), though RL training improves alignment from early timesteps, critical issues such as training instability and mode collapse arise. We address these drawbacks by exploiting the hierarchical nature of DMs: we train them dynamically at each epoch with a tailored RL method, allowing for continual evaluation and step-by-step refinement of the model performance (or alignment). Furthermore, we find that not every denoising step needs to be fine-tuned to align DMs to downstream tasks. Consequently, in addition to clipping, we regularise model parameters at distinct learning phases via a sliding-window approach. Our approach, termed Hierarchical Reward Fine-tuning (HRF), is validated on the Denoising Diffusion Policy Optimisation method, where we show that models trained with HRF achieve better preservation of diversity in downstream tasks, thus enhancing the fine-tuning robustness and at uncompromising mean rewards.

stat.ML↗

arXiv2024

Detection of manatee vocalisations using the Audio Spectrogram Transformer

The Antillean manatee (\emph{Trichechus manatus}) is an endangered herbivorous aquatic mammal whose role as an ecological balancer and umbrella species underscores the importance of its conservation. An innovative approach to monitor manatee populations is passive acoustic monitoring (PAM), where vocalisations are extracted from submarine audio. We propose a novel end-to-end approach to detect manatee vocalisations building on the Audio Spectrogram Transformer (AST). In a transfer learning spirit, we fine-tune AST to detect manatee calls by redesigning its filterbanks and adapting a real-world dataset containing partial positive labels. Our experimental evaluation reveals the two key features of the proposed model: i) it performs on par with the state of the art without requiring hand-tuned denoising or detection stages, and ii) it can successfully identify missed vocalisations in the training dataset, thus reducing the workload of expert bioacoustic labellers. This work is a preliminary relevant step to develop novel, user-friendly tools for the conservation of the different species of manatees.

eess.AS↗

arXiv2023

Asynchronous Graph Generator

We introduce the asynchronous graph generator (AGG), a novel graph attention network for imputation and prediction of multi-channel time series. Free from recurrent components or assumptions about temporal/spatial regularity, AGG encodes measurements, timestamps and channel-specific features directly in the nodes via learnable embeddings. Through an attention mechanism, these embeddings allow for discovering expressive relationships among the variables of interest in the form of a homogeneous graph. Once trained, AGG performs imputation by \emph{conditional attention generation}, i.e., by creating a new node conditioned on given timestamps and channel specification. The proposed AGG is compared to related methods in the literature and its performance is analysed from a data augmentation perspective. Our experiments reveal that AGG achieved state-of-the-art results in time series imputation, classification and prediction for the benchmark datasets \emph{Beijing Air Quality}, \emph{PhysioNet ICU 2012} and \emph{UCI localisation}, outperforming other recent attention-based networks.

cs.LG↗

arXiv2023

Greedy online change point detection

Standard online change point detection (CPD) methods tend to have large false discovery rates as their detections are sensitive to outliers. To overcome this drawback, we propose Greedy Online Change Point Detection (GOCPD), a computationally appealing method which finds change points by maximizing the probability of the data coming from the (temporal) concatenation of two independent models. We show that, for time series with a single change point, this objective is unimodal and thus CPD can be accelerated via ternary search with logarithmic complexity. We demonstrate the effectiveness of GOCPD on synthetic data and validate our findings on real-world univariate and multivariate settings.

eess.SP↗

arXiv2023

Gaussian process deconvolution

Let us consider the deconvolution problem, that is, to recover a latent source $x(\cdot)$ from the observations $\mathbf{y} = [y_1,\ldots,y_N]$ of a convolution process $y = x\star h + \eta$, where $\eta$ is an additive noise, the observations in $\mathbf{y}$ might have missing parts with respect to $y$, and the filter $h$ could be unknown. We propose a novel strategy to address this task when $x$ is a continuous-time signal: we adopt a Gaussian process (GP) prior on the source $x$, which allows for closed-form Bayesian nonparametric deconvolution. We first analyse the direct model to establish the conditions under which the model is well defined. Then, we turn to the inverse problem, where we study i) some necessary conditions under which Bayesian deconvolution is feasible, and ii) to which extent the filter $h$ can be learnt from data or approximated for the blind deconvolution case. The proposed approach, termed Gaussian process deconvolution (GPDC) is compared to other deconvolution methods conceptually, via illustrative examples, and using real-world datasets.

stat.ML↗

arXiv2022

Computationally-efficient initialisation of GPs: The generalised variogram method

We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for maximum-likelihood (ML) training, or as a standalone method to compute hyperparameters values to be plugged in directly into the GP model. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide hyperparameter values that are close to those found via ML. In practice, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal and frequency domains. Our contribution extends the variogram method developed by the geostatistics literature and, accordingly, it is referred to as the generalised variogram method (GVM). In addition to the theoretical presentation of GVM, we provide experimental validation in terms of accuracy, consistency with ML and computational complexity for different kernels using synthetic and real-world data.

cs.LG↗

arXiv2022

Detecting the periodicity of highly irregularly sampled light-curves with Gaussian processes: the case of SDSSJ025214.67-002813.7

Based on a 20-year-long multiband observation of its light-curve, it was conjectured that the quasar SDSSJ025214.67-002813.7 has a periodicity of ~4.4 years. These observations were acquired at a highly irregular sampling rate and feature long intervals of missing data. In this setting, the inference over the light-curve's spectral content requires, in addition to classic Fourier methods, a proper model of the probability distribution of the missing observations. In this article, we address the detection of the periodicity of a light-curve from partial and irregularly-sampled observations using Gaussian processes, a Bayesian nonparametric model for time series. This methodology allows us to evaluate the veracity of the claimed periodicity of the abovementioned quasar and also to estimate its power spectral density. Our main contribution is the confirmation that considering periodic component definitely improves the modeling of the data, although being the source originally selected by a large sample of objects, the possibility that this is a chance result cannot be ruled out.

astro-ph.IM↗

arXiv2022

Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures

Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently. In particular, the Multi-Output Spectral Mixture kernel (MOSM) arXiv:1709.01298 approach has been praised as a general model in the sense that it extends other approaches such as Linear Model of Corregionalization, Intrinsic Corregionalization Model and Cross-Spectral Mixture. MOSM relies on Cram\'er's theorem to parametrise the power spectral densities (PSD) as a Gaussian mixture, thus, having a structural restriction: by assuming the existence of a PSD, the method is only suited for multi-output stationary applications. We develop a nonstationary extension of MOSM by proposing the family of harmonizable kernels for MOGPs, a class of kernels that contains both stationary and a vast majority of non-stationary processes. A main contribution of the proposed harmonizable kernels is that they automatically identify a possible nonstationary behaviour meaning that practitioners do not need to choose between stationary or non-stationary kernels. The proposed method is first validated on synthetic data with the purpose of illustrating the key properties of our approach, and then compared to existing MOGP methods on two real-world settings from finance and electroencephalography.

stat.ML↗

arXiv2022

Stochastic Gradient Descent for Barycenters in Wasserstein Space

We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure in the 2-Wasserstein space, as well as a manifestation of a Law of Large Numbers therein. The algorithm aims at finding a Karcher mean or critical point in this setting, and can be implemented ``online", sequentially using i.i.d. random measures sampled from the population law. We provide natural sufficient conditions for this algorithm to a.s. converge in the Wasserstein space towards the population barycenter, and we introduce a novel, general condition which ensures uniqueness of Karcher means and moreover allows us to obtain explicit, parametric convergence rates for the expected optimality gap. We furthermore study the mini-batch version of this algorithm, and discuss examples of families of population laws to which our method and results can be applied. This work expands and deepens ideas and results introduced in an early version of \cite{backhoff2018bayesian}, in which a statistical application (and numerical implementation) of this method is developed in the context of Bayesian learning.

math.OC↗

arXiv2021

Studying the Interplay between Information Loss and Operation Loss in Representations for Classification

Information-theoretic measures have been widely adopted in the design of features for learning and decision problems. Inspired by this, we look at the relationship between i) a weak form of information loss in the Shannon sense and ii) the operation loss in the minimum probability of error (MPE) sense when considering a family of lossy continuous representations (features) of a continuous observation. We present several results that shed light on this interplay. Our first result offers a lower bound on a weak form of information loss as a function of its respective operation loss when adopting a discrete lossy representation (quantization) instead of the original raw observation. From this, our main result shows that a specific form of vanishing information loss (a weak notion of asymptotic informational sufficiency) implies a vanishing MPE loss (or asymptotic operational sufficiency) when considering a general family of lossy continuous representations. Our theoretical findings support the observation that the selection of feature representations that attempt to capture informational sufficiency is appropriate for learning, but this selection is a rather conservative design principle if the intended goal is achieving MPE in classification. Supporting this last point, and under some structural conditions, we show that it is possible to adopt an alternative notion of informational sufficiency (strictly weaker than pure sufficiency in the mutual information sense) to achieve operational sufficiency in learning.

cs.LG↗

arXiv2021

Late reverberation suppression using U-nets

In real-world settings, speech signals are almost always affected by reverberation produced by the working environment; these corrupted signals need to be \emph{dereverberated} prior to performing, e.g., speech recognition, speech-to-text conversion, compression, or general audio enhancement. In this paper, we propose a supervised dereverberation technique using \emph{U-nets with skip connections}, which are fully-convolutional encoder-decoder networks with layers arranged in the form of an "U" and connections that "skip" some layers. Building on this architecture, we address speech dereverberation through the lens of Late Reverberation Suppression (LS). Via experiments on synthetic and real-world data with different noise levels and reverberation settings, we show that our proposed method termed "LS U-net" improves quality, intelligibility and other performance metrics compared to the original U-net method and it is on par with the state-of-the-art GAN-based approaches.

eess.AS↗