BZPEERReading, trust and collaboration for research
Menu

Discover

GraphFollow connections around a paper, topic or saved view.

Workspaces

HomePick up where your research flow left off.InboxHandle requests, replies and notifications from one place.CollectionsCurate reading lists, evidence sets and shareable dossiers.ResearchSee your private provenance graph, trail and imports.CollaborationMove from discovery into focused discussion rooms.PublishDraft, preview and publish full-text research articles.

Network

ExpertsFind specialists worth following or asking for help.CommunitiesJoin research circles organized around shared work.PartnersSee external organizations active around the same topics.

Opportunities

ListingsBrowse roles, calls and collaborations with clearer fit signals.

Account

Log inReturn to your reading and collaboration workspace.Create accountStart saving work, following people and joining teams.
Log inCreate account

Researcher profile

Daniel Hernández-Lobato

Daniel Hernández-Lobato contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningApplicationsastro-ph.HEComputationMethodologyphysics.geo-ph

Trust snapshot

Quick read

Trust 21 - EmergingVerification L1Unclaimed author
8works
0followers
6topics
4close collaborators

Actions

Decide how to stay connected

Follow researcher0

Identity and collaboration

How to connect with this researcher

Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.

Log in to claim

Direct collaboration

Open a focused conversation when the fit is right

Claim this author entity first to unlock direct invitations.

Research graph

See the researcher in context

Open full explorer

Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.

Building this graph slice

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

8 published item(s)

preprint2026arXiv

Conditional Diffusion Sampling

Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Correcting Model Bias with Sparse Implicit Processes

Model selection in machine learning (ML) is a crucial part of the Bayesian learning procedure. Model choice may impose strong biases on the resulting predictions, which can hinder the performance of methods such as Bayesian neural networks and neural samplers. On the other hand, newly proposed approaches for Bayesian ML exploit features of approximate inference in function space with implicit stochastic processes (a generalization of Gaussian processes). The approach of Sparse Implicit Processes (SIP) is particularly successful in this regard, since it is fully trainable and achieves flexible predictions. Here, we expand on the original experiments to show that SIP is capable of correcting model bias when the data generating mechanism differs strongly from the one implied by the model. We use synthetic datasets to show that SIP is capable of providing predictive distributions that reflect the data better than the exact predictions of the initial, but wrongly assumed model.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification

This work introduces the Efficient Transformed Gaussian Process (ETGP), a new way of creating C stochastic processes characterized by: 1) the C processes are non-stationary, 2) the C processes are dependent by construction without needing a mixing matrix, 3) training and making predictions is very efficient since the number of Gaussian Processes (GP) operations (e.g. inverting the inducing point's covariance matrix) do not depend on the number of processes. This makes the ETGP particularly suited for multi-class problems with a very large number of classes, which are the problems studied in this work. ETGPs exploit the recently proposed Transformed Gaussian Process (TGP), a stochastic process specified by transforming a Gaussian Process using an invertible transformation. However, unlike TGPs, ETGPs are constructed by transforming a single sample from a GP using C invertible transformations. We derive an efficient sparse variational inference algorithm for the proposed model and demonstrate its utility in 5 classification tasks which include low/medium/large datasets and a different number of classes, ranging from just a few to hundreds. Our results show that ETGPs, in general, outperform state-of-the-art methods for multi-class classification based on GPs, and have a lower computational cost (around one order of magnitude smaller).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Function-space Inference with Sparse Implicit Processes

Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in function-space. This change of formulation solves intrinsic degenerate problems of parameter-space approximate inference concerning the high number of parameters and their strong dependencies in large models. For this, previous works in the literature have attempted to employ IPs both to set up the prior and to approximate the resulting posterior. However, this has proven to be a challenging task. Existing methods that can tune the prior IP result in a Gaussian predictive distribution, which fails to capture important data patterns. By contrast, methods producing flexible predictive distributions by using another IP to approximate the posterior process cannot tune the prior IP to the observed data. We propose here the first method that can accomplish both goals. For this, we rely on an inducing-point representation of the prior IP, as often done in the context of sparse Gaussian processes. The result is a scalable method for approximate inference with IPs that can tune the prior IP parameters to the data, and that provides accurate non-Gaussian predictive distributions.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Gaussian Processes for Missing Value Imputation

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models with accurate uncertainty estimates that combined with sparse approximations and stochastic variational inference scale to large data sets. Sparse GPs can be used to compute a predictive distribution for missing data. Here, we present a hierarchical composition of sparse GPs that is used to predict missing values at each dimension using all the variables from the other dimensions. We call the approach missing GP (MGP). MGP can be trained simultaneously to impute all observed missing values. Specifically, it outputs a predictive distribution for each missing value that is then used in the imputation of other missing values. We evaluate MGP in one private clinical data set and four UCI datasets with a different percentage of missing values. We compare the performance of MGP with other state-of-the-art methods for imputing missing values, including variants based on sparse GPs and deep GPs. The results obtained show a significantly better performance of MGP.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Inference over radiative transfer models using variational and expectation maximization methods

Earth observation from satellites offers the possibility to monitor our planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the energy transfer through the atmosphere, and are used to model and understand the Earth system, as well as to estimate the parameters that describe the status of the Earth from satellite observations by inverse modeling. However, performing inference over such simulators is a challenging problem. RTMs are nonlinear, non-differentiable and computationally costly codes, which adds a high level of difficulty in inference. In this paper, we introduce two computational techniques to infer not only point estimates of biophysical parameters but also their joint distribution. One of them is based on a variational autoencoder approach and the second one is based on a Monte Carlo Expectation Maximization (MCEM) scheme. We compare and discuss benefits and drawbacks of each approach. We also provide numerical comparisons in synthetic simulations and the real PROSAIL model, a popular RTM that combines land vegetation leaf and canopy modeling. We analyze the performance of the two approaches for modeling and inferring the distribution of three key biophysical parameters for quantifying the terrestrial biosphere.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Multi-class Gaussian Process Classification with Noisy Inputs

It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly accurate. If this input noise is not taken into account, a supervised machine learning method is expected to perform sub-optimally. In this paper, we focus on multi-class classification problems and use Gaussian processes (GPs) as the underlying classifier. Motivated by a data set coming from the astrophysics domain, we hypothesize that the observed data may contain noise in the inputs. Therefore, we devise several multi-class GP classifiers that can account for input noise. Such classifiers can be efficiently trained using variational inference to approximate the posterior distribution of the latent variables of the model. Moreover, in some situations, the amount of noise can be known before-hand. If this is the case, it can be readily introduced in the proposed methods. This prior information is expected to lead to better performance results. We have evaluated the proposed methods by carrying out several experiments, involving synthetic and real data. These include several data sets from the UCI repository, the MNIST data set and a data set coming from astrophysics. The results obtained show that, although the classification error is similar across methods, the predictive distribution of the proposed methods is better, in terms of the test log-likelihood, than the predictive distribution of a classifier based on GPs that ignores input noise.

0 citations0 reviewsNo code linkedOpen access
preprint2017arXiv

Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. This function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, such as when some of the input variables take integer values, one has to introduce extra approximations. A common approach is to round the suggested variable value to the closest integer before doing the evaluation of the objective. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods on problems involving integer-valued variables.

0 citations0 reviewsNo code linkedOpen access