arXiv subjects

Carlo Albert

Publications and source records attributed to Carlo Albert.

14 recordsLinked to original sources

arXiv2026

Archetypal Microbiome Profiles as Indicators of Nitrous Oxide Emission States in Activated Sludge

Nitrous oxide (N2O) emissions from water resource recovery facilities (WRRFs) fluctuate over time and can arise from multiple microbial pathways, making source attribution and full-scale prediction difficult. The difficulty is compounded by the high dimensionality of activated sludge microbiomes, whose complex and dynamic community structure can obscure relationships with N2O emission patterns. This study evaluated whether interpretable, low-dimensional representations of activated sludge microbiomes can be correlated with N2O emission states. Temporal 16S rRNA gene amplicon profiles and N2O emission metrics were collected from two full-scale WRRFs in Switzerland. Genus-level relative-abundance profiles were summarized using archetypal analysis (AA), which represents each sample as a convex combination of a small number of interpretable community profiles. In both WRRFs, three archetypes captured most explainable variation in community composition (63%--73%) and defined a simplex state space in which samples clustered near vertices and edges, indicating that community compositions were organized around distinct archetypal states and their mixtures. Without using emission labels while training, the archetypal state space aligned strongly with binary N2O emission states: high-emission observations in both plants concentrated around a specific archetype, and temporal trajectories showed consistent high weights of this archetype during high-emission periods. Functional summaries suggested site-specific but pathway-relevant interpretations of the high-N2O archetype. Temperature further structured the archetypal state space, indicating seasonal forcing of microbiome configurations associated with elevated N2O. Overall, AA provides an interpretable framework to track microbiome regime shifts and may support operational tracking of high-N2O emission states in full-scale WRRFs.

q-bio.QM↗

arXiv2025

A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics

Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model parameters by comparing model simulations with observations using a few carefully chosen summary statistics and a tolerance that can be decreased over time. Here, we present a new variant of simulated-annealing ABC algorithms, drawing intuition from non-equilibrium thermodynamics. We associate each summary statistic with a state variable (energy) quantifying its distance from the observed value, as well as a temperature that controls the extent to which the statistic contributes to the posterior. We derive an optimal annealing schedule on a Riemannian manifold of state variables based on a minimal-entropy-production principle. We validate our approach on standard benchmark tasks from the simulation-based inference literature as well as on challenging real-world inference problems, and show that it is highly competitive with the state of the art.

stat.CO↗

arXiv2025

When Bias Meets Trainability: Connecting Theories of Initialization

The statistical properties of deep neural networks (DNNs) at initialization play an important role to comprehend their trainability and the intrinsic architectural biases they possess before data exposure Well established mean field (MF) theories have uncovered that the distribution of parameters of randomly initialized networks strongly influences the behavior of the gradients, dictating whether they explode or vanish. Recent work has showed that untrained DNNs also manifest an initial guessing bias (IGB), in which large regions of the input space are assigned to a single class. In this work, we provide a theoretical proof that links IGB to previous MF theories for a vast class of DNNs, showing that efficient learning is tightly connected to a network prejudice towards a specific class. This connection leads to a counterintuitive conclusion: the initialization that optimizes trainability is systematically biased rather than neutral.

cs.LG↗

arXiv2024

Simulation-based Inference with the Python Package sbijax

Neural simulation-based inference (SBI) describes an emerging family of methods for Bayesian inference with intractable likelihood functions that use neural networks as surrogate models. Here we introduce sbijax, a Python package that implements a wide variety of state-of-the-art methods in neural simulation-based inference using a user-friendly programming interface. sbijax offers high-level functionality to quickly construct SBI estimators, and compute and visualize posterior distributions with only a few lines of code. In addition, the package provides functionality for conventional approximate Bayesian computation, to compute model diagnostics, and to automatically estimate summary statistics. By virtue of being entirely written in JAX, sbijax is extremely computationally efficient, allowing rapid training of neural networks and executing code automatically in parallel on both CPU and GPU.

cs.LG↗

arXiv2023

Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation

Neural likelihood estimation methods for simulation-based inference can suffer from performance degradation when the modeled data is very high-dimensional or lies along a lower-dimensional manifold, which is due to the inability of the density estimator to accurately estimate a density function. We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel member in the family of methods for simulation-based inference (SBI). SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function, which allows for computational inference via Markov chain Monte Carlo or variational Bayes methods. Among other benefits, SSNL avoids the requirement to manually craft summary statistics for inference of high-dimensional data sets, since the lower-dimensional representation is computed simultaneously with learning the likelihood and without additional computational overhead. We evaluate SSNL on a wide variety of experiments, including two challenging real-world examples from the astrophysics and neuroscience literatures, and show that it either outperforms or is on par with state-of-the-art methods, making it an excellent off-the-shelf estimator for SBI for high-dimensional data sets.

stat.ML↗

arXiv2022

Learning Summary Statistics for Bayesian Inference with Autoencoders

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

cs.LG↗

arXiv2020

Second-order Phase Transition in Phytoplankton Trait Dynamics

Key traits of unicellular species, like cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here we reveal new empirical scaling evidence associated with a transition in the population and chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This `criticality hypothesis' can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology.

q-bio.PE↗

arXiv2019

Accelerating Bayesian inference in hydrological modeling with a mechanistic emulator

As in many fields of dynamic modeling, the long runtime of hydrological models hinders Bayesian inference of model parameters from data. By replacing a model with an approximation of its output as a function of input and/or parameters, emulation allows us to complete this task by trading-off accuracy for speed. We combine (i) the use of a mechanistic emulator, (ii) low-discrepancy sampling of the parameter space, and (iii) iterative refinement of the design data set, to perform Bayesian inference with a very small design data set constructed with 128 model runs in a parameter space of up to eight dimensions. In our didactic example we use a model implemented with the hydrological simulator SWMM that allows us to compare our inference results against those derived with the full model. This comparison demonstrates that iterative improvements lead to reasonable results with a very small design data set.

stat.ME↗

arXiv2017

Appraisal of data-driven and mechanistic emulators of nonlinear hydrodynamic urban drainage simulators

Many model based scientific and engineering methodologies, such as system identification, sensitivity analysis, optimization and control, require a large number of model evaluations. In particular, model based real-time control of urban water infrastructures and online flood alarm systems require fast prediction of the network response at different actuation and/or parameter values. General purpose urban drainage simulators are too slow for this application. Fast surrogate models, so-called emulators, provide a solution to this efficiency demand. Emulators are attractive, because they sacrifice unneeded accuracy in favor of speed. However, they have to be fine-tuned to predict the system behavior satisfactorily. Also, some emulators fail to extrapolate the system behavior beyond the training set. Although, there are many strategies for developing emulators, up until now the selection of the emulation strategy remains subjective. In this paper, we therefore compare the performance of two families of emulators for open channel flows in the context of urban drainage simulators. We compare emulators that explicitly use knowledge of the simulator's equations, i.e. mechanistic emulators based on Gaussian Processes, with purely data-driven emulators using matrix factorization. Our results suggest that in many urban applications, naive data-driven emulation outperforms mechanistic emulation. Nevertheless, we discuss scenarios in which we think that mechanistic emulation might be favorable for i) extrapolation in time and ii) dealing with sparse and unevenly sampled data. We also provide many references to advances in the field of Machine Learning that have not yet permeated into the Bayesian environmental science community.

stat.ME↗

arXiv2016

Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model, for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact and very efficient approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

cs.DS↗

arXiv2015

A Simulated Annealing Approach to Bayesian Inference

A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each particle update consists of a random jump in parameter space followed by a simulation of a model output and a Metropolis acceptance/rejection step based on a comparison of the simulated output to the data. The distance of a particle to the data is interpreted as an energy and the algorithm is reducing the associated temperature of the ensemble such that entropy production is minimized. If this simulated annealing is not too fast compared to the mixing speed in parameter space, the parameter marginal of the ensemble approaches the Bayesian posterior distribution. Annealing is adaptive and depends on certain extensive thermodynamic quantities that can easily be measured throughout run-time. In the general case, we propose annealing with a constant entropy production rate, which is optimal as long as annealing is not too fast. For the practically relevant special case of no prior knowledge, we derive an optimal fast annealing schedule with a non-constant entropy production rate. The algorithm does not require the calculation of the density of the model likelihood, which makes it interesting for Bayesian parameter inference with stochastic models, whose likelihood functions are typically very high dimensional integrals.

stat.CO↗

arXiv2014

A Simulated Annealing Approach to Approximate Bayes Computations

Approximate Bayes Computations (ABC) are used for parameter inference when the likelihood function of the model is expensive to evaluate but relatively cheap to sample from. In particle ABC, an ensemble of particles in the product space of model outputs and parameters is propagated in such a way that its output marginal approaches a delta function at the data and its parameter marginal approaches the posterior distribution. Inspired by Simulated Annealing, we present a new class of particle algorithms for ABC, based on a sequence of Metropolis kernels, associated with a decreasing sequence of tolerances w.r.t. the data. Unlike other algorithms, our class of algorithms is not based on importance sampling. Hence, it does not suffer from a loss of effective sample size due to re-sampling. We prove convergence under a condition on the speed at which the tolerance is decreased. Furthermore, we present a scheme that adapts the tolerance and the jump distribution in parameter space according to some mean-fields of the ensemble, which preserves the statistical independence of the particles, in the limit of infinite sample size. This adaptive scheme aims at converging as close as possible to the correct result with as few system updates as possible via minimizing the entropy production in the system. The performance of this new class of algorithms is compared against two other recent algorithms on two toy examples.

stat.CO↗

arXiv2012

A Mechanistic Dynamic Emulator

In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of ordinary non-linear differential equations, is developed. The non-linear differential equations are linearized and Gaussian white noise is added to account for the non-linearities. The resulting linear stochastic system is conditioned on a set of solutions of the non-linear equations that have been calculated prior to the emulation. A path-integral approach is used to derive the Gaussian distribution of the emulated solution. The solution reveals that most of the computational burden can be shifted to the conditioning phase of the emulator and the complexity of the actual emulation step only scales like $\mathcal O(Nn)$ in multiplications of matrices of the dimension of the state space. Here, $N$ is the number of time-points at which the solution is to be emulated and $n$ the number of solutions the emulator is conditioned on. The applicability of the algorithm is demonstrated with the hydrological model logSPM.

stat.ME↗

arXiv2008

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.

math-ph↗