Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes.

We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables.

How Much Is Enough? A Study on Diffusion Times in Score-Based Generative Models.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, a detailed understanding of the role of the diffusion time is still lacking. Current best practice advocates for a large to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of should be preferred for a better approximation of the score-matching objective and higher computational efficiency.

A Scalable Bayesian Sampling Method Based on Stochastic Gradient Descent Isotropization.

Stochastic gradient sg-based algorithms for Markov chain Monte Carlo sampling (sgmcmc) tackle large-scale Bayesian modeling problems by operating on mini-batches and injecting noise on sgsteps. The sampling properties of these algorithms are determined by user choices, such as the covariance of the injected noise and the learning rate, and by problem-specific factors, such as assumptions on the loss landscape and the covariance of sg noise. However, current sgmcmc algorithms applied to popular complex models such as Deep Nets cannot simultaneously satisfy the assumptions on loss landscapes and on the behavior of the covariance of the sg noise, while operating with the practical requirement of non-vanishing learning rates.

Statistical inference in mechanistic models: time warping for improved gradient matching.

Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation.

Probabilistic disease progression modeling to characterize diagnostic uncertainty: Application to staging and prediction in Alzheimer's disease.

Disease progression modeling (DPM) of Alzheimer's disease (AD) aims at revealing long term pathological trajectories from short term clinical data. Along with the ability of providing a data-driven description of the natural evolution of the pathology, DPM has the potential of representing a valuable clinical instrument for automatic diagnosis, by explicitly describing the biomarker transition from normal to pathological stages along the disease time axis. In this work we reformulated DPM within a probabilistic setting to quantify the diagnostic uncertainty of individual disease severity in an hypothetical clinical scenario, with respect to missing measurements, biomarkers, and follow-up information.

Decoding post-stroke motor function from structural brain imaging.

Clinical research based on neuroimaging data has benefited from machine learning methods, which have the ability to provide individualized predictions and to account for the interaction among units of information in the brain. Application of machine learning in structural imaging to investigate diseases that involve brain injury presents an additional challenge, especially in conditions like stroke, due to the high variability across patients regarding characteristics of the lesions. Extracting data from anatomical images in a way that translates brain damage information into features to be used as input to learning algorithms is still an open question.

Approximate parameter inference in systems biology using gradient matching: a comparative evaluation.

Background: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration.

Pseudo-Marginal Bayesian Inference for Gaussian Processes.

The main challenges that arise when adopting Gaussian process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior.

Automated, high accuracy classification of Parkinsonian disorders: a pattern recognition approach.

Progressive supranuclear palsy (PSP), multiple system atrophy (MSA) and idiopathic Parkinson's disease (IPD) can be clinically indistinguishable, especially in the early stages, despite distinct patterns of molecular pathology. Structural neuroimaging holds promise for providing objective biomarkers for discriminating these diseases at the single subject level but all studies to date have reported incomplete separation of disease groups. In this study, we employed multi-class pattern recognition to assess the value of anatomical patterns derived from a widely available structural neuroimaging sequence for automated classification of these disorders.