We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

Recently developed quasi-Bayesian (QB) methods \cite{fong2023martingale} proposed a stimulating change of paradigm in Bayesian computation by directly constructing the Bayesian predictive distribution through recursion, removing the need for expensive computations involved in sampling the Bayesian posterior distribution. This has proved to be data-efficient for univariate predictions, however, existing constructions for higher dimensional densities are only possible by relying on restrictive assumptions on the model's multivariate structure. Here, we propose a wholly different approach to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem, by decomposing the predictive distribution into one-dimensional predictive marginals and a high-dimensional copula. We use the efficient recursive QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas. Further, we tune hyperparameters using robust divergences (eg. energy score) and show that our proposed Quasi-Bayesian Vine (QB-Vine) is a fully non-parametric density estimator with \emph{an analytical form} and convergence rate independent of the dimension of the data in some situations. Our experiments illustrate that the QB-Vine is appropriate for high dimensional distributions ($\sim$64), needs very few samples to train ($\sim$200) and outperforms state-of-the-art methods with analytical forms for density estimation and supervised tasks by a considerable margin.

Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with generative neural networks, which parametrize distributions on high-dimensional spaces by transforming draws from a latent variable. Generative networks are typically trained in an adversarial framework. In contrast, we propose to train generative networks to minimize a predictive-sequential (or prequential) scoring rule on a recorded temporal sequence of the phenomenon of interest, which is appealing as it corresponds to the way forecasting systems are routinely evaluated. Adversarial-free minimization is possible for some scoring rules; hence, our framework avoids the cumbersome hyperparameter tuning and uncertainty underestimation due to unstable adversarial training, thus unlocking reliable use of generative networks in probabilistic forecasting. Further, we prove consistency of the minimizer of our objective with dependent data, while adversarial training assumes independence. We perform simulation studies on two chaotic dynamical models and a benchmark data set of global weather observations; for this last example, we define scoring rules for spatial data by drawing from the relevant literature. Our method outperforms state-of-the-art adversarial approaches, especially in probabilistic calibration, while requiring less hyperparameter tuning.

In this paper, we study the task of improving the cohesion and coherence of long-form text generated by language models.To this end, we propose RSTGen, a framework that utilises Rhetorical Structure Theory (RST), a classical language theory, to control the discourse structure, semantics and topics of generated text.Firstly, we demonstrate our model's ability to control structural discourse and semantic features of generated text in open generation evaluation.Then we experiment on the two challenging long-form text tasks of argument generation and story generation.Evaluation using automated metrics and a metric with high correlation to human evaluation, shows that our model performs competitively against existing models, while offering significantly more controls over generated text than alternative methods.

Bayesian Likelihood-Free Inference (LFI) approaches allow to obtain posterior distributions for stochastic models with intractable likelihood, by relying on model simulations. In Approximate Bayesian Computation (ABC), a popular LFI method, summary statistics are used to reduce data dimensionality. ABC algorithms adaptively tailor simulations to the observation in order to sample from an approximate posterior, whose form depends on the chosen statistics. In this work, we introduce a new way to learn ABC statistics: we first generate parameter-simulation pairs from the model independently on the observation; then, we use Score Matching to train a neural conditional exponential family to approximate the likelihood. The exponential family is the largest class of distributions with fixed-size sufficient statistics; thus, we use them in ABC, which is intuitively appealing and has state-of-the-art performance. In parallel, we insert our likelihood approximation in an MCMC for doubly intractable distributions to draw posterior samples. We can repeat that for any number of observations with no additional model simulations, with performance comparable to related approaches. We validate our methods on toy models with known likelihood and a large-dimensional time-series model.

Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present pathology tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-individual variability. Here we propose a stochastic platelet deposition model and an inferential scheme to estimate the biologically meaningful model parameters using approximate Bayesian computation with a summary statistic that maximally discriminates between different types of patients. Inferred parameters from data collected on healthy volunteers and different patient types help us to identify specific biological parameters and hence biological reasoning behind the dysfunction for each type of patients. This work opens up an unprecedented opportunity of personalized pathology test for CVD detection and medical treatment.

Abstract Climate models (CM) are used to evaluate the impact of climate change on the risk of floods and heavy precipitation events. However, these numerical simulators produce outputs with low spatial resolution that exhibit difficulties representing precipitation events accurately. This is mainly due to computational limitations on the spatial resolution used when simulating multi-scale weather dynamics in the atmosphere. To improve the prediction of high resolution precipitation we apply a Deep Learning (DL) approach using input data from a reanalysis product, that is comparable to a climate model’s output, but can be directly related to precipitation observations at a given time and location. Further, our input excludes local precipitation, but includes model fields (weather variables) that are more predictable and generalizable than local precipitation. To this end, we present TRU-NET (Temporal Recurrent U-Net), an encoder-decoder model featuring a novel 2D cross attention mechanism between contiguous convolutional-recurrent layers to effectively model multi-scale spatio-temporal weather processes. We also propose a non-stochastic variant of the conditional-continuous (CC) loss function to capture the zero-skewed patterns of rainfall. Experiments show that our models, trained with our CC loss, consistently attain lower RMSE and MAE scores than a DL model prevalent in precipitation downscaling and outperform a state-of-the-art dynamical weather model. Moreover, by evaluating the performance of our model under various data formulation strategies, for the training and test sets, we show that there is enough data for our deep learning approach to output robust, high-quality results across seasons and varying regions.

A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

MOTIVATION: Public and private repositories of experimental data are growing to sizes that require dedicated methods for finding relevant data. To improve on the state of the art of keyword searches from annotations, methods for content-based retrieval have been proposed. In the context of gene expression experiments, most methods retrieve gene expression profiles, requiring each experiment to be expressed as a single profile, typically of case versus control. A more general, recently suggested alternative is to retrieve experiments whose models are good for modelling the query dataset. However, for very noisy and high-dimensional query data, this retrieval criterion turns out to be very noisy as well. RESULTS: We propose doing retrieval using a denoised model of the query dataset, instead of the original noisy dataset itself. To this end, we introduce a general probabilistic framework, where each experiment is modelled separately and the retrieval is done by finding related models. For retrieval of gene expression experiments, we use a probabilistic model called product partition model, which induces a clustering of genes that show similar expression patterns across a number of samples. The suggested metric for retrieval using clusterings is the normalized information distance. Empirical results finally suggest that inference for the full probabilistic model can be approximated with good performance using computationally faster heuristic clustering approaches (e.g. k-means). The method is highly scalable and straightforward to apply to construct a general-purpose gene expression experiment retrieval method. AVAILABILITY AND IMPLEMENTATION: The method can be implemented using standard clustering algorithms and normalized information distance, available in many statistical software packages. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.